**AHRQ Quality Indicators**

**Risk Adjustment and Hierarchical Modeling Approaches**

# Introduction

The Inpatient Quality Indicators (IQIs) are a set of measures that
provide a perspective on hospital quality of care using hospital
administrative data. These indicators reflect quality of care inside
hospitals and include inpatient mortality for certain procedures and
medical conditions; utilization of procedures for which there are
questions of overuse, underuse, and misuse; and volume of procedures for
which there is some evidence that a higher volume of procedures is
associated with lower mortality.

The IQIs are a software tool distributed free by the Agency for
Healthcare Research and Quality (AHRQ). The software can be used to help
hospitals identify potential problem areas that might need further study
and which can provide an indirect measure of inhospital quality of care.
The IQI software programs can be applied to any hospital inpatient
administrative data. These data are readily available and relatively
inexpensive to use.

Inpatient Quality Indicators:

-   Can be used to help hospitals identify potential problem areas that
    might need further study.

-   Provide the opportunity to assess quality of care inside the
    hospital using administrative data found in the typical discharge
    record.

-   Include 15 mortality indicators for conditions or procedures for
    which mortality can vary from hospital to hospital.

-   Include 11 utilization indicators for procedures for which
    utilization varies across hospitals or geographic areas.

-   Include 6 volume indicators for procedures for which outcomes may be
    related to the volume of those procedures performed.

-   Are publicly available without cost , and are available for download

The IQIs include the following 32 measures:

1.  Mortality Rates for Medical Conditions (7 Indicators)

    -   Acute myocardial infarction (AMI) (IQI 15)

    -   AMI, Without Transfer Cases (IQI 32)

    -   Congestive heart failure (IQI 16)

    -   Stroke (IQI 17)

    -   Gastrointestinal hemorrhage (IQI 18)

    -   Hip fracture (IQI 19)

    -   Pneumonia (IQI 20)

2.  Mortality Rates for Surgical Procedures (8 Indicators)

    -   Esophageal resection (IQI 8)

    -   Pancreatic resection (IQI 9)

    -   Abdominal aortic aneurysm repair (IQI 11)

    -   Coronary artery bypass graft (IQI 12)

    -   Percutaneous transluminal coronary angioplasty (IQI 30)

    -   Carotid endarterectomy (IQI 31)

    -   Craniotomy (IQI 13)

    -   Hip replacement (IQI 14)

3.  Hospital-level Procedure Utilization Rates (7 Indicators)

    -   Cesarean section delivery (IQI 21)

    -   Primary Cesarean delivery (IQI 33)

    -   Vaginal Birth After Cesarean (VBAC), Uncomplicated (IQI 22)

    -   VBAC, All (IQI 34)

    -   Laparoscopic cholecystectomy (IQI 23)

    -   Incidental appendectomy in the elderly (IQI 24)

    -   Bi-lateral cardiac catheterization (IQI 25)

4.  Area-level Utilization Rates (4 Indicators)

    -   Coronary artery bypass graft (IQI 26)

    -   Percutaneous transluminal coronary angioplasty (IQI 27)

    -   Hysterectomy (IQI 28)

    -   Laminectomy or spinal fusion (IQI 29)

5.  Volume of Procedures (6 Indicators)

    -   Esophageal resection (IQI 1)

    -   Pancreatic resection (IQI 2)

    -   Abdominal aortic aneurysm repair (IQI 4)

    -   Coronary artery bypass graft (IQI 5)

    -   Percutaneous transluminal coronary angioplasty (IQI 6)

    -   Carotid endarterectomy (IQI 7)

# Statistical Methods

This section provides a brief overview of the structure of the
administrative data from the Nationwide Inpatient Sample, and the
statistical models and tools currently being used within the AHRQ
Quality Indicators Project. We then propose several alternative
statistical models and methods for consideration, including (1) models
that account for trends in the response variable over time; and (2)
statistical approaches that adjust for the potential positive
correlation on patient outcomes from the same provider. We provide an
overview of how these proposed alternative statistical approaches will
impact the fitting of risk-adjusted models to the reference population,
and on the tools that are provided to users of the QI methodology.

This is followed by an overview of the statistical modeling
investigation, including (1) the selection of five IQIs to investigate
in this report, (2) fitting current and alternative statistical models
to data from the Nationwide Inpatient Sample, (3) statistical methods to
compare parameter estimates between current and alternative modeling
approaches using a Wald test-statistic, and (4) statistical methods to
compare differences between current and alternative modeling approaches
on provider-level model predictions (expected and risk-adjusted rates).

## Structure of the Administrative Data

Hospital administrative data are collected as a routine step in the
delivery of hospital services throughout the U.S., and provide
information on diagnoses, procedures, age, gender, admission source, and
discharge status on all admitted patients. These data can be used to
describe the quality of medical care within individual providers
(hospitals), within groups of providers (e.g., states, regions), and
across the nation as a whole. Although in certain circumstances quality
assessments based on administrative data are potentially prone to bias
compared to possibly more clinically detailed data sources such as
medical chart records, the fact that administrative data are universally
available among the 37 States participating in the Healthcare Cost and
Utilization Project (HCUP) allowed AHRQ to develop analytical
methodologies to identify potential quality problems and success stories
that merit further investigation and study.

The investigation in this report focuses on five select inpatient
quality indicators, as applied to the Nationwide Inpatient Sample (NIS)
from 2001-2003. The Nationwide Inpatient Sample represents a sample of
administrative records from a sample of approximately 20 percent of the
providers participating in the HCUP. There is significant overlap in the
HCUP hospitals selected in the NIS, with several of the hospitals being
repeatedly sampled in more than one year.

The NIS data is collected at the patient admission level. For each
hospital admission, data is collected on patient age, gender, admission
source, diagnoses, procedures, and discharge status. There is no unique
patient identifier, so the same patient may be represented more than
once in the NIS data (with some patients potentially being represented
more than once within the same hospital, and other patients potentially
being represented more than once within multiple hospitals).

The purpose of the QI statistical models is to provide parameter
estimates for each quality indicator that are adjusted for age, gender,
and all patient refined diagnosis related group (APR-DRG). The APR-DRG
classification methodology was developed by 3M, and provides a basis to
adjust the QIs for the severity of illness or risk of mortality, and is
explained elsewhere.

For each selected quality indicator, the administrative data is coded to
indicate whether they contain the outcome of interest as follows:

> Let Y~ijk~ represent the outcome for the j^th^ patient admission
> within the i^th^ hospital, for the k^th^ Quality Indicator. Y~ijk~ is
> equal to one for patients who experience the adverse event, zero for
> patients captured within the appropriate reference population but do
> not experience the adverse event, and is missing for all patients that
> are excluded from the reference population for the k^th^ Quality
> Indicator.

For each Quality Indicator, patients with a missing value for Y~ijk~ are
excluded from the analysis dataset. For all patients with Y~ijk~ = 0 or
1, appropriate age-by-gender and APR-DRG explanatory variables are
constructed for use in the statistical models.

## Current Statistical Models and Tools

The following two subsections provide a brief overview of the
statistical models that are currently fit to the HCUP reference
population, and the manner in which these models are utilized in
software tools provided by the AHRQ Quality Indicators Project.

### Models for the Reference Population

Currently, a simple logistic regression model is applied to three years
of administrative data from the HCUP for each Quality Indicator, as
follows:

$\text{log}\text{it}(\text{Pr}(Y_{\text{ijk}} = 1)) = \beta_{k0} + \sum_{p = 1}^{P_{k}}{\alpha_{\text{kp}} \cdot (\frac{\text{Age}}{\text{Gender}_{p}})_{\text{ij}} +}\sum_{q = 1}^{Q_{k}}{\theta_{\text{kq}}(\text{APR} - \text{DRG}_{q})_{\text{ijk}}}$,
(1)

where Y~ijk~ represents the response variable for the j^th^ patient in
the i^th^ hospital for the k^th^ quality indicator;
*(Age/Gender~p~)~ij~* represents the p^th^ age-by-gender zero/one
indicator variable associated with the j^th^ patient in the i^th^
hospital; and *(APR-DRG~q~)~ijk~* represents the q^th^ APR-DRG zero/one
indicator variable associated with the j^th^ patient in the i^th^
hospital for the k^th^ quality indicator.

For the k^th^ quality indicator, we assume that there are *P~k~*
age-by-gender categories and *Q~k~* APR-DRG categories that will enter
the model for risk-adjustment purposes.

The *α~kp~* parameters capture the effects of each of the *P~k~*
age-by-gender categories on the QI response variable; and similarly, the
*θ~kq~* parameters capture the effects of each of the *Q~k~* APR-DRG
categories on the QI response variable. The *α~kp~* and *θ~kq~*
parameters each have ln(odds-ratio) interpretation, when compared to the
reference population. The logit-risk of an adverse outcome for the
reference population is captured by the *β~k0~* intercept term in the
model associated with the k^th^ Quality Indicator.

Model (1) can be fit using several procedures in SAS. For simplicity and
consistency with other modeling approaches investigated in this report,
we used SAS Proc Genmod to fit Model (1) to data from the Nationwide
Inpatient Sample.

### Software Tools Provided to Users

The AHRQ Quality Indicators Project provides access to software that can
be downloaded by users to calculate expected and risk-adjusted QIs for
their own sample of administrative data. The expected rate represents
the rate that the provider would have experienced if it's quality of
performance was identical to the reference (National) population, given
the provider's actual case mix (e.g. age, gender, DRG and comorbidity
categories). Expected rates are calculated based on combining the
regression coefficients from the reference model (based on fitting Model
(1) above to the reference HCUP population) with the patient
characteristics from a specific provider.

Risk-adjusted rates are the estimated performance if the provider had an
\"average\" patient mix, given their actual performance.  It is the most
appropriate rate upon which to compare *across hospitals*, and is
calculated by adjusting the observed National Average Rate for the ratio
of observed vs. expected rates at the provider-level:

*Risk-adjusted rate = (Observed Rate / Expected Rate) x National Average
Rate* (2)

The AHRQ Inpatient Quality Indicator software appropriately applies the
National Model Regression Coefficients to the provider specific
administrative records being analyzed to calculate both expected and
risk-adjusted rates.

## Alternative Statistical Methods

In the following sections, we propose several alternative statistical
models and methods for consideration, including (1) models that account
for trends in the response variable over time; and (2) statistical
approaches that adjust for the potential positive correlation on patient
outcomes from the same provider.

### Adjusting for Trends over Time

The following alternative model formulation is proposed as a simple
method for adjusting for the effects of quality improvement over time
with the addition of a single covariate to Model (1):

$\begin{matrix}
\text{log}\text{it}(\text{Pr}(Y_{\text{ijk}} = 1)) = & \beta_{k0} + \sum_{p = 1}^{P_{k}}{\alpha_{\text{kp}} \cdot (\frac{\text{Age}}{\text{Gender}_{p}})_{\text{ij}} +}\sum_{q = 1}^{Q_{k}}{\theta_{\text{kq}}(\text{APR} - \text{DRG}_{q})_{\text{ijk}}} \\
 & + \lambda_{k}(\text{Year}_{\text{ijk}} - \text{2002})
\end{matrix}$ (3)

The parameter λ~k~ adjusts the model for a simple linear trend over time
(on the logit-scale for risk of an adverse event), with the covariate
(Year~ijk~-2002) being a continuous variable that captures the calendar
year that the j^th^ patient was admitted to the i^th^ hospital. This
time-trend covariate is centered on calendar year 2002 in our analyses,
to preserve a similar interpretation of the *β~k0~* intercept term in
Model (1), as our national reference dataset represents administrative
records reported in calendar years 2001 through 2003.

Additional complexities can be introduced into the above simple
time-trend model to investigate (1) non-linear time-trends on the logit
scale, and (2) any changes over time in the age-by-gender or APR-DRG
variable effects on risk of adverse outcomes. Such investigations were
not explored within this report -- but could be the subject of later
data analyses. The authors of this report also suggest combining data
over a longer period of time (e.g., five years or more) to better
capture long-term trends in hospital quality of care.

The introduction of a time-trend into the model serves three purposes.
First, it provides AHRQ (and users) with an understanding of how
hospital quality is changing over time through the interpretation of the
λ~k~ parameter (or similar time-trend parameters in any expanded
time-trend model). Secondly, if the λ~k~ parameter is found to be
statistically significant, the time-trend model will likely offer more
precise expected and risk-adjusted rates. Thirdly, it may allow more
accurate model predictions (expected and risk-adjusted rates for
providers) when users apply a model based on older data to more recent
data (often, a user might utilize software that is based on a 2001-2003
reference population to calculate rates for provider-specific data from
calendar year 2005).

### Adjusting for Within-Provider Correlation

The current simple logistic regression modeling approach being used by
AHRQ in the risk-adjusted model fitting assumes that all patient
responses are independent and identically distributed. However, it is
likely that responses of patients from within the same hospital may be
correlated, even after adjusting for the effects of age, gender,
severity of illness and risk of mortality. This anticipated positive
correlation results from the fact that each hospital has a unique
mixture of staff, policies and medical culture that combine to influence
patient results. It is often the case that fitting simple models to
correlated data results in similar parameter estimates, but biased
standard errors of those parameter estimates -- however, this does not
always hold true. In the following two subsections, we provide an
overview of generalized estimating equations (GEE) and generalized
linear mixed modeling (GLMMIX) approaches for adjusting the QI
statistical models for the anticipated effects of within-provider
correlation. These approaches will be investigated on a sample of five
selected Quality Indicators to determine whether (or not) the parameter
estimates from a simple logistic regression model result in different
parameter estimates or provider-level model predictions (expected and
risk adjusted rates), in comparison to GEE or GLMMIX approaches that
account for the within-provider correlation.

#### Generalized Estimating Equations

In many studies, we are faced with a problem where the responses Y~i~
are not independent of each other ( Cov\[Y~i~,Y~j~\] ≠ 0 when i≠j ). The
responses from studies with correlated data can often be organized into
clusters, where observations from within a cluster are dependent, and
observations from two different clusters are independent:

Y~ij~ is the j^th^ response from the i^th^ cluster:
Cov\[Y~ij~,Y~i\'j\'~\]= 0 when i≠i\'

Cov\[Y~ij~,Y~ij\'~\] ≠ 0 when j≠j\'

In the context of the AHRQ Quality Indicators project, the providers
(hospitals) serve as clusters. There are usually two objectives for the
analysis of clustered data:

1\) Describing the response variable Y~ij~ as a function of explanatory
variables (X~ij~),and

2\) Measuring the within-cluster dependence.

When Y~ij~ is continuous and follows a normal distribution, there is a
well developed set of statistical methodology for meeting the above two
objectives. This methodology usually assumes that the residuals from
within each cluster are jointly normal, so that each cluster is
distributed MVN(X~i~β, Σ~i~). Thus, when faced with normally distributed
dependent responses, the assumption of a multivariate normal
distribution allows us to model clustered data with our usual maximum
likelihood solutions.

When the response variable does not follow a normal distribution, we are
often left without a multivariate generalization which allows us to meet
the two objectives for the analysis of clustered data through use of a
maximum likelihood solution. For example, there are no multivariate
extensions of the binomial distribution that provides a likelihood
function for clustered data.

The theory of Generalized Estimating Equations (GEE) provides a
statistical methodology for analyzing clustered data under the
conceptual framework of Generalized Linear Models. GEE was developed in
1986 by Kung-Yee Liang and Scott Zeger, and is an estimating procedure
which makes use of Quasi-Likelihood theory under a marginal model.

When the regression analysis for the mean is of primary interest, the β
coefficients can be estimated by solving the following estimating
equation:

where μ~i~(β) = E\[Y~i~\], the marginal expectation of Y~i~

Note that U~1~ (the GEE) has exactly the same form as the score equation
from a simple logistic regression model, with the exception that:

1\) Y~i~ is now an n~i~1 vector which comprises the n~i~ observations
from the i^th^ cluster

2\) The covariance matrix, cov(Y~i~), for Y~i~ depends not only on β,
but on α which characterizes the within cluster dependence.

The additional complication of the parameter α can be alleviated by
iterating until convergence between solving U~1~( β, α(β) ) = 0 and
updating α(β), an estimate of α.

Thus, the GEE approach is simply to choose parameter values β so that
the expected μ~i~(β) is as close to the observed Y~i~ as possible,
weighting each cluster of data inversely to its variance matrix
cov(Y~i~;β,α) which is a function of the within-cluster dependence.

The marginal GEE approach has some theoretical and practical advantages:

1\) No joint distribution assumption for Y~i~ = (Y~i1~,\...,Y~ini~) is
required to use the method. The GEE approach utilizes a method of
moments estimator for α, the within-cluster dependence parameter.

2\) β, the solution of U~1~( β, α(β) ) = 0, has high efficiency compared
to the maximum likelihood estimate of β in many cases studied.

3\) Liang and Zeger have proposed the use of both a model-based and a
robust variance of β. The model-based variance of β is more efficient --
but is sensitive to misspecification of the model for within-cluster
dependence. The robust variance is less efficient, but provides valid
inferences for β even when the model for dependence is misspecified.

Specifically, suppose the investigators mistakenly assume that the
observations from the same cluster are independent from each other. The
95% confidence interval for each regression coefficient β~j~, j=1,..,p,
based upon β~j~ ± 1.96 (V~β~ )^2^ remains valid in large sample
situations. Thus, investigators are protected against misspecification
of the within-cluster dependence structure. This is especially appealing
when the data set is comprised of a large number of small clusters.

When the within-cluster dependence is of primary interest, this marginal
GEE approach has an important limitation -- in that β and α are
estimated as if they are independent of each other. Consequently, very
little information from β is used when estimating α.

The marginal model for correlated binary outcomes (such as those from
the AHRQ QI Project) can be thought of as a simple extension to a simple
logistic regression model that directly incorporates the within-cluster
correlation among patient responses from within the same hospital. To
estimate the regression parameters in a marginal model, we make
assumptions about the marginal distribution of the response variable
(e.g. assumptions about the mean, its dependence on the explanatory
variables, the variance of each Y~ij~, and the covariance among
responses from within the same hospital). The cross-sectional model
(Model (1)) and time-trend model (Model (3)) can be fit using the
generalized estimating equations approach using SAS Proc Genmod, through
the introduction of a repeated statement that accounts for the
within-provider clustering.

#### Generalized Linear Mixed Models

In the previous section, we described marginal models for
correlated/clustered data using a generalized estimating equations
approach. An alternative approach for accounting for the within-hospital
correlation is through the introduction of random effects into Model(1)
as follows:

$\text{log}\text{it}(\text{Pr}(Y_{\text{ijk}} = 1)) = \beta_{k0} + \sum_{p = 1}^{P_{k}}{\alpha_{\text{kp}} \cdot (\frac{\text{Age}}{\text{Gender}_{p}})_{\text{ij}} +}\sum_{q = 1}^{Q_{k}}{\theta_{\text{kq}}(\text{APR} - \text{DRG}_{q})_{\text{ijk}}} + \gamma_{\text{ki}}$,
(4)

where γ~ki~ is a random effect associated with each provider, and is
assumed to follow a normal distribution with mean zero, and variance
$\sigma_{\text{Hosp}}^{2}$. The time-trend model can be similarly
expanded using a random effects model, as follows:

$\begin{matrix}
\text{log}\text{it}(\text{Pr}(Y_{\text{ijk}} = 1)) = & \beta_{k0} + \sum_{p = 1}^{P_{k}}{\alpha_{\text{kp}} \cdot (\frac{\text{Age}}{\text{Gender}_{p}})_{\text{ij}} +}\sum_{q = 1}^{Q_{k}}{\theta_{\text{kq}}(\text{APR} - \text{DRG}_{q})_{\text{ijk}}} \\
 & + \lambda_{k}(\text{Year}_{\text{ijk}} - \text{2002}) + \gamma_{0\text{ki}} + \gamma_{1\text{ki}}(\text{Year}_{\text{ijk}} - \text{2002})
\end{matrix}$, (5)

where γ~0ki~ and γ~1ki~ are random intercept and slope terms associated
with each provider (thus allowing each provider to depart from the fixed
effects portion of the model with a provider-specific trend over time).
In Model (5), we assume that γ~0ki~ and γ~1ki~ jointly follow a
multivariate normal distribution with mean zero and covariance matrix
$\Sigma = \begin{bmatrix}
\sigma_{\text{Hosp}}^{2} & \sigma_{\frac{\text{Hosp}}{\text{Year}}}^{2} \\
\sigma_{\frac{\text{Hosp}}{\text{Year}}}^{2} & \sigma_{\text{Year}}^{2}
\end{bmatrix}$.

Models (4) and (5) can be fit using SAS Proc GLIMMIX, and can also be
expanded to allow for different probability distributions for the random
effects (i.e. we can relax the assumption of normality for the random
effects, if necessary).

### Impact of Adopting Alternative Methods on Model Fitting and Tools

Currently, the risk-adjusted models for each quality indicator are fit
to three calendar years of administrative data from the HCUP using
various different data manipulations and model fitting procedures
available from within the SAS software system. The addition of a
time-trend covariate (or series of covariates) will not introduce any
significant additional complexity to fitting these models to the
reference (national) data. Adjusting the models for the anticipated
positive correlation among patient responses from within the same
hospital will require the use of Generalized Estimating Equations (GEE)
approaches available through Proc GENMOD in SAS, or the use of
Generalized Linear Mixed Modeling (GLMMIX) approaches available through
Proc GLIMMIX in SAS. Both of these methods are more computationally
intense compared to fitting a simple logistic regression model, and may
be subject to convergence problems and model mis-specification that is
typical of such iterative modeling approaches.

Once the models are fit to the reference (national) population,
integration of the modeling results into the software tools provided to
users should be relatively straightforward. The introduction of a
time-trend model would require the user to keep track of the calendar
year associated with each patient response, for inclusion as a predictor
variable in the model. If additional time-trend variables (either
non-linear, or interactions with the other predictor variables) are
introduced, the software can be quickly updated to accommodate these
model changes.

Use of the GLMMIX approach may yield additional information, in which
the vector of random effects from the National Model can be exploited to
determine the distribution of expected risk of adverse events (after
adjusting for age, gender, severity of illness, and risk of mortality)
across participating hospitals. This distribution can be used to
identify (approximately) where within the national distribution of
providers a particular hospital lies (currently, the AHRQ methodology
only provides information related to whether an individual user is above
or below the national mean). This use of the estimated vector of random
effects would require additional software development at AHRQ, as well
as additional work to ensure that the GLMMIX random effects model is
adequately fitting the data from the reference population.

## Overview of Statistical Modeling Investigation

The purpose of this report is to investigate the use of alternative
modeling approaches to potentially adjust the risk-adjusted Quality
Indicator Models for the effects of trends over time and the effects of
positive correlation among responses from within the same hospital. In
the following sections, we provide:

-   an overview of the five Inpatient Quality Indicators that were
    selected for this investigation;

-   a description of the various models fit to the Nationwide Inpatient
    Sample;

-   statistical methodology used to assess whether or not the
    alternative modeling approaches yield parameter estimates that are
    significantly different from each other; and

-   statistical methodology used to assess whether or not the
    alternative modeling approaches yield provider-level estimates
    (expected and risk-adjusted rates of adverse events) that are
    significantly different from each other.

### Selection of IQIs to Investigate

The following five Inpatient Quality Indicators were selected for
exploration in this report (*with the descriptions for each QI copied
directly from the AHRQ Guide to Prevention Quality Indicators*):

**IQI 11: Abdominal Aortic Aneurism Repair Mortality Rate**

*Abdominal aortic aneurysm (AAA) repair is a relatively rare procedure
that requires proficiency with the use of complex equipment; and
technical errors may lead to clinically significant complications, such
as arrhythmias, acute myocardial infarction, colonic ischemia, and
death. The adverse event for this Quality Indicator is recorded as
positive for any patient who dies with a code of AAA repair in any
procedure field, and a diagnosis of AAA in any field. The reference
population for this Quality Indicator includes any patient discharge
with ICD-9-CM codes of 3834, 3844, and 3864 in any procedure field and a
diagnosis code of AAA in any field. The reference population excludes
patients with missing discharge disposition, who transfer to another
short-term hospital, MDC 14 (pregnancy, childbirth, and puerperium), and
MDC 15 (newborns and other neonates).*

**IQI 14: Hip Replacement Mortality Rate**

*Total hip arthroplasty (without hip fracture) is an elective procedure
preformed to improve function and relieve pain among patients with
chronic osteoarthritis, rheumatoid arthritis, or other degenerative
processes involving the hip joint. The adverse event for this Quality
Indicator is recorded as positive for any patient who dies with a code
of paritial or full hip replacement in any procedure field. The
reference population for this Quality Indicator includes any patient
with procedure code of partial or full hip replacement in any field, and
includes only discharges with uncomplicated cases: diagnosis codes for
osteoarthritis of hip in any field. The reference population excludes
patients with missing discharge disposition, who transfer to another
short-term hospital, MDC 14 (pregnancy, childbirth, and puerperium), and
MDC 15 (newborns and other neonates).*

**IQI 17: Acute Stroke Mortality Rate**

*Quality treatment for acute stroke must be timely and efficient to
prevent potentially fatal brain tissue death, and patients may not
present until after the fragile window of time has passed. The adverse
event for this Quality Indicator is recorded as positive for any patient
who dies with a principal diagnosis code of stroke. The reference
population for this Quality Indicator includes any patient aged 18 or
older with a principal diagnosis code of stroke. The reference
population excludes patients with missing discharge disposition, who
transfer to another short-term hospital, MDC 14 (pregnancy, childbirth,
and puerperium), and MDC 15 (newborns and other neonates).*

**IQI 19: Hip Fracture Mortality Rate**

*Hip fractures, which are a common cause of morbidity and functional
decline among elderly patients are associated with a significant
increase in the subsequent risk of mortality. The adverse event for this
Quality Indicator is recorded as positive for any patient who dies with
a principal diagnosis code of hip fracture. The reference population for
this Quality Indicator includes any patient aged 18 or older with a
principal diagnosis code of hip fracture. The reference population
excludes patients with missing discharge disposition, who transfer to
another short-term hospital, MDC 14 (pregnancy, childbirth, and
puerperium), and MDC 15 (newborns and other neonates).*

**IQI 25: Bilateral Cardiac Catherization Rate**

*Righ- side coronary catheterization incidental to left side
catheterization has little additional benefit for patient without
clinical indications for right-side catheterization. The adverse event
for this Quality Indicator is recorded as positive for any patient with
coronary artery disease who has simultaneous right and left heart
catheterizations in any procedure field (excluding valid indications for
right-sided catherization in any diagnosis field, MDC 14 (pregnancy,
childbirth, and puerperium), and MDC 15 (newborns and other neonates)).
The reference population for this Quality Indicator includes any patient
with coronary artery disease discharged with heart catheterization in
any procedure field. The reference population excludes patients with MDC
14 (pregnancy, childbirth, and puerperium), and MDC 15 (newborns and
other neonates).*

### Fitting Current and Alternative Models to NIS Data

For each selected IQI, we fit risk-adjusted cross-sectional and
time-trend adjusted models using a simple logistic regression,
generalized estimating equations and generalized linear mixed modeling
approach (for a combined six models for each IQI). The models were fit
to three-years of combined data from the Nationwide Inpatient Sample,
which represents an approximate 20 percent sample of hospitals from
within the HCUP (with administrative records included for all patients
treated within each selected hospital).

The data were processed to eliminate any patient records that are
excluded from the reference population prior to modeling (thus, only
patients with a zero or one response were included in the analysis for
each IQI). The form of the model followed what was included in the
models currently fit to the HCUP data -- with minor modifications to
remove covariates that represented very sparse cells.

For the GEE and GLMMIX approaches, we retained both the robust and
model-based variance/covariance matrices for the vector of parameter
estimates, to allow for appropriate statistical comparisons using both
methods. We also retained the vector of random effects from the GLMMIX
approach, to assess for distributional assumptions.

### Methods to Compare Parameter Estimates

Given that the parameter estimates from each of the logistic regression
models follow an approximate normal distribution (as shown in McCulloch
& Nelder, 1989 within the Generalized Linear Model conceptual
framework), a Wald Statistic can be used to assess whether there are
statistically significant differences between a specific pair of
modeling approaches. For example, when comparing the simple linear
regression model results to the results of the GEE approach, we have the
following three potential Wald Statistics:

$$\begin{matrix}
W_{1} = \left( {\hat{\beta}}_{\text{SLR}} - {\hat{\beta}}_{\text{GEE}} \right)^{T}V_{\beta_{\text{SLR}}}^{- 1}\left( {\hat{\beta}}_{\text{SLR}} - {\hat{\beta}}_{\text{GEE}} \right) \\
W_{2} = \left( {\hat{\beta}}_{\text{SLR}} - {\hat{\beta}}_{\text{GEE}} \right)^{T}V_{\beta_{\text{GEE} - \text{Model}}}^{- 1}\left( {\hat{\beta}}_{\text{SLR}} - {\hat{\beta}}_{\text{GEE}} \right) \\
W_{3} = \left( {\hat{\beta}}_{\text{SLR}} - {\hat{\beta}}_{\text{GEE}} \right)^{T}V_{\beta_{\text{GEE} - \text{Robust}}}^{- 1}\left( {\hat{\beta}}_{\text{SLR}} - {\hat{\beta}}_{\text{GEE}} \right)
\end{matrix}$$

In the above formulas, ${\hat{\beta}}_{\text{SLR}}$
and${\hat{\beta}}_{\text{GEE}}$ represent the parameter estimates from
the simple logistic and GEE models.
$V_{\beta_{\text{SLR}}}^{- 1}$represents the inverse of the
variance-covariance matrix of the regression parameters from the simple
logistic regression model. Similarly,
$V_{\beta_{\text{GEE} - \text{Model}}}^{- 1}$and
$V_{\beta_{\text{GEE} - \text{Robust}}}^{- 1}$represent the inverse of
the model-based and robust variance-covariance matrix of the regression
parameters from the GEE regression model.

Under the null hypothesis, that there are no statistically significant
differences between the simple logistic regression model and GEE
parameter estimates, the above three Wald test statistics are expected
to follow a $Χ_{(p)}^{2}$distribution (a Chi-squared distribution with p
degrees of freedom, where p represents the number of explanatory
variables that were used within the statistical model).

### Methods to Compare Provider-Level Model Predictions

For each select IQI, we identified a simple random sample of 50
providers to use for assessing differences between provider-level model
predictions (both expected and risk-adjusted rates). Simple descriptive
statistics (mean and standard deviation) were generated for the
distribution differences in provider-level model predictions to assess
whether (or not) changes in the model might result in any potential bias
or increased variability in provider-level estimates.

The distributional summaries were conducted separately for the
cross-sectional and time-trend models (so that the statistics isolate
any differences attributable to adjusting the models for the potential
correlation among responses within the same provider).

Subsequent analyses will be conducted at a later date to provide
comparisons between the cross-sectional and time-trend models within
each model type (and potentially across model types).

# Results

All models were successfully fit to the NIS data source. The GLMMIX
approach initially suffered from convergence problems while using the
default optimization techniques, but converged for all five IQIs (both
cross sectional and time-trend adjusted models) when using
Newton-Raphson optimization with ridging. Due to the large sample size
of the dataset, the personal computer used to fit the model ran out of
memory when calculating the robust variance-covariance matrix associated
with the parameter estimates for IQI-25 with the GLMMIX approach (the
computer had 2GB of RAM).

Section 3.1 below provides summary statistics for the quality indicator
response variables that were modeled from within the National Inpatient
Sample. Sections 3.2 through 3.6 provide model results for each of the
five select IQIs explored in this report.

## Summary Statistics for NIS Data

Table 3.1 below provides summary statistics for the five selected
quality indicators. The summary statistics include:

-   The number of adverse events observed

-   The number of patients in the reference population

-   The number of hospitals that had patients within the reference
    population

-   The mean response (proportion of patients who experienced the
    adverse event)

-   The standard error associated with the mean response

-   Select percentiles from the distribution (5^th^, 25^th^, 50^th^,
    75^th^, and 95^th^)

Separate summary statistics were generated for each year of data (2001,
2002, and 2003) and then for all years combined. Prior to calculating
the mean, standard error, and percentiles, the responses were averaged
at the hospital level. These statistics therefore represent the
distribution of hospital mean responses, and are presented in two ways
(weighted and unweighted). The weighted results weigh each provider
according to the number of patients observed within the reference
population, whereas the unweighted results treat each hospital equally.

The weighted analysis mean was used as the National Average Rate when
constructing the provider-specific risk-adjusted rates. Conceptually,
the standard-error of the mean from the unweighted analysis should be
proportional to the standard-error of the mean from the vector of random
effects intercepts generated using the GLMMIX approach from the
cross-sectional model (although we anticipate that the variability of
the random effects would be smaller due to the fact that other factors
(age, gender, severity of illness and risk of mortality) are explaining
variability in the Quality Indicator response variable.

**Table 3.1 Summary Statistics (at the Provider Level) for the Five
Selected Quality Indicators**

<table style="width:100%;">
<colgroup>
<col style="width: 4%" />
<col style="width: 7%" />
<col style="width: 12%" />
<col style="width: 7%" />
<col style="width: 8%" />
<col style="width: 6%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>IQI</strong></td>
<td rowspan="2"><strong>Year</strong></td>
<td rowspan="2"><strong>Analysis Type</strong></td>
<td colspan="10"><strong>Summary Statistics</strong></td>
</tr>
<tr class="even">
<td><strong>n<sub>cases</sub></strong></td>
<td><strong>n<sub>Pop</sub></strong></td>
<td><strong>n<sub>Hosp</sub></strong></td>
<td><strong>Mean</strong></td>
<td><strong>Std Error</strong></td>
<td><strong>5<sup>th</sup> %ile</strong></td>
<td><strong>25<sup>th</sup> %ile</strong></td>
<td><strong>50<sup>th</sup> %ile</strong></td>
<td><strong>75<sup>th</sup> %ile</strong></td>
<td><strong>95<sup>th</sup> %ile</strong></td>
</tr>
<tr class="odd">
<td rowspan="8">11</td>
<td rowspan="2">2001</td>
<td>Unweighted</td>
<td rowspan="2">726</td>
<td rowspan="2">8833.0</td>
<td rowspan="2">470</td>
<td>0.141</td>
<td>0.010</td>
<td>0.000</td>
<td>0.000</td>
<td>0.067</td>
<td>0.161</td>
<td>0.500</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.082</td>
<td>0.004</td>
<td>0.000</td>
<td>0.032</td>
<td>0.063</td>
<td>0.107</td>
<td>0.222</td>
</tr>
<tr class="odd">
<td rowspan="2">2002</td>
<td>Unweighted</td>
<td rowspan="2">655</td>
<td rowspan="2">8099.0</td>
<td rowspan="2">449</td>
<td>0.152</td>
<td>0.011</td>
<td>0.000</td>
<td>0.000</td>
<td>0.070</td>
<td>0.188</td>
<td>0.750</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.081</td>
<td>0.005</td>
<td>0.000</td>
<td>0.028</td>
<td>0.063</td>
<td>0.098</td>
<td>0.231</td>
</tr>
<tr class="odd">
<td rowspan="2">2003</td>
<td>Unweighted</td>
<td rowspan="2">558</td>
<td rowspan="2">8144.0</td>
<td rowspan="2">447</td>
<td>0.132</td>
<td>0.011</td>
<td>0.000</td>
<td>0.000</td>
<td>0.050</td>
<td>0.143</td>
<td>0.500</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.069</td>
<td>0.004</td>
<td>0.000</td>
<td>0.027</td>
<td>0.048</td>
<td>0.078</td>
<td>0.200</td>
</tr>
<tr class="odd">
<td rowspan="2"><p>All</p>
<p>Years</p></td>
<td>Unweighted</td>
<td rowspan="2">1939</td>
<td rowspan="2">25076</td>
<td rowspan="2">1050</td>
<td>0.149</td>
<td>0.007</td>
<td>0.000</td>
<td>0.000</td>
<td>0.071</td>
<td>0.176</td>
<td>0.667</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.077</td>
<td>0.003</td>
<td>0.000</td>
<td>0.034</td>
<td>0.057</td>
<td>0.094</td>
<td>0.208</td>
</tr>
<tr class="odd">
<td rowspan="8">14</td>
<td rowspan="2">2001</td>
<td>Unweighted</td>
<td rowspan="2">104</td>
<td rowspan="2">34628</td>
<td rowspan="2">687</td>
<td>0.004</td>
<td>0.001</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.022</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.003</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.001</td>
<td>0.015</td>
</tr>
<tr class="odd">
<td rowspan="2">2002</td>
<td>Unweighted</td>
<td rowspan="2">112</td>
<td rowspan="2">39677</td>
<td rowspan="2">682</td>
<td>0.004</td>
<td>0.001</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.020</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.003</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.002</td>
<td>0.014</td>
</tr>
<tr class="odd">
<td rowspan="2">2003</td>
<td>Unweighted</td>
<td rowspan="2">86</td>
<td rowspan="2">39068</td>
<td rowspan="2">689</td>
<td>0.004</td>
<td>0.001</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.016</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.002</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.012</td>
</tr>
<tr class="odd">
<td rowspan="2"><p>All</p>
<p>Years</p></td>
<td>Unweighted</td>
<td rowspan="2">302</td>
<td rowspan="2">113373</td>
<td rowspan="2">1544</td>
<td>0.004</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.020</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.003</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.000</td>
<td>0.003</td>
<td>0.013</td>
</tr>
<tr class="odd">
<td rowspan="8">17</td>
<td rowspan="2">2001</td>
<td>Unweighted</td>
<td rowspan="2">12616</td>
<td rowspan="2">108886</td>
<td rowspan="2">957</td>
<td>0.115</td>
<td>0.003</td>
<td>0.000</td>
<td>0.065</td>
<td>0.105</td>
<td>0.143</td>
<td>0.250</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.116</td>
<td>0.002</td>
<td>0.045</td>
<td>0.086</td>
<td>0.115</td>
<td>0.140</td>
<td>0.186</td>
</tr>
<tr class="odd">
<td rowspan="2">2002</td>
<td>Unweighted</td>
<td rowspan="2">12298</td>
<td rowspan="2">109670</td>
<td rowspan="2">959</td>
<td>0.113</td>
<td>0.003</td>
<td>0.000</td>
<td>0.067</td>
<td>0.103</td>
<td>0.143</td>
<td>0.250</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.112</td>
<td>0.001</td>
<td>0.050</td>
<td>0.084</td>
<td>0.112</td>
<td>0.134</td>
<td>0.183</td>
</tr>
<tr class="odd">
<td rowspan="2">2003</td>
<td>Unweighted</td>
<td rowspan="2">12385</td>
<td rowspan="2">108720</td>
<td rowspan="2">951</td>
<td>0.108</td>
<td>0.003</td>
<td>0.000</td>
<td>0.060</td>
<td>0.100</td>
<td>0.139</td>
<td>0.238</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.114</td>
<td>0.001</td>
<td>0.046</td>
<td>0.087</td>
<td>0.112</td>
<td>0.137</td>
<td>0.194</td>
</tr>
<tr class="odd">
<td rowspan="2"><p>All</p>
<p>Years</p></td>
<td>Unweighted</td>
<td rowspan="2">37299</td>
<td rowspan="2">327276</td>
<td rowspan="2">2095</td>
<td>0.111</td>
<td>0.002</td>
<td>0.000</td>
<td>0.069</td>
<td>0.102</td>
<td>0.141</td>
<td>0.238</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.114</td>
<td>0.001</td>
<td>0.053</td>
<td>0.089</td>
<td>0.112</td>
<td>0.136</td>
<td>0.184</td>
</tr>
<tr class="odd">
<td rowspan="8">19</td>
<td rowspan="2">2001</td>
<td>Unweighted</td>
<td rowspan="2">1916</td>
<td rowspan="2">60318</td>
<td rowspan="2">809</td>
<td>0.036</td>
<td>0.003</td>
<td>0.000</td>
<td>0.000</td>
<td>0.026</td>
<td>0.044</td>
<td>0.095</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.032</td>
<td>0.001</td>
<td>0.000</td>
<td>0.017</td>
<td>0.031</td>
<td>0.043</td>
<td>0.066</td>
</tr>
<tr class="odd">
<td rowspan="2">2002</td>
<td>Unweighted</td>
<td rowspan="2">2008</td>
<td rowspan="2">60597</td>
<td rowspan="2">800</td>
<td>0.039</td>
<td>0.003</td>
<td>0.000</td>
<td>0.000</td>
<td>0.026</td>
<td>0.047</td>
<td>0.092</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.033</td>
<td>0.001</td>
<td>0.000</td>
<td>0.019</td>
<td>0.031</td>
<td>0.044</td>
<td>0.069</td>
</tr>
<tr class="odd">
<td rowspan="2">2003</td>
<td>Unweighted</td>
<td rowspan="2">1919</td>
<td rowspan="2">60559</td>
<td rowspan="2">804</td>
<td>0.037</td>
<td>0.003</td>
<td>0.000</td>
<td>0.000</td>
<td>0.024</td>
<td>0.043</td>
<td>0.100</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.032</td>
<td>0.001</td>
<td>0.000</td>
<td>0.019</td>
<td>0.029</td>
<td>0.040</td>
<td>0.070</td>
</tr>
<tr class="odd">
<td rowspan="2"><p>All</p>
<p>Years</p></td>
<td>Unweighted</td>
<td rowspan="2">5843</td>
<td rowspan="2">181474</td>
<td rowspan="2">1806</td>
<td>0.038</td>
<td>0.002</td>
<td>0.000</td>
<td>0.000</td>
<td>0.027</td>
<td>0.044</td>
<td>0.091</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.032</td>
<td>0.000</td>
<td>0.005</td>
<td>0.020</td>
<td>0.031</td>
<td>0.041</td>
<td>0.065</td>
</tr>
<tr class="odd">
<td rowspan="8">25</td>
<td rowspan="2">2001</td>
<td>Unweighted</td>
<td rowspan="2">22858</td>
<td rowspan="2">283099</td>
<td rowspan="2">437</td>
<td>0.098</td>
<td>0.006</td>
<td>0.000</td>
<td>0.032</td>
<td>0.065</td>
<td>0.121</td>
<td>0.293</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.081</td>
<td>0.003</td>
<td>0.018</td>
<td>0.037</td>
<td>0.061</td>
<td>0.103</td>
<td>0.208</td>
</tr>
<tr class="odd">
<td rowspan="2">2002</td>
<td>Unweighted</td>
<td rowspan="2">21455</td>
<td rowspan="2">286259</td>
<td rowspan="2">444</td>
<td>0.085</td>
<td>0.005</td>
<td>0.000</td>
<td>0.030</td>
<td>0.057</td>
<td>0.111</td>
<td>0.255</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.075</td>
<td>0.003</td>
<td>0.014</td>
<td>0.038</td>
<td>0.059</td>
<td>0.097</td>
<td>0.196</td>
</tr>
<tr class="odd">
<td rowspan="2">2003</td>
<td>Unweighted</td>
<td rowspan="2">21697</td>
<td rowspan="2">298744</td>
<td rowspan="2">455</td>
<td>0.086</td>
<td>0.005</td>
<td>0.000</td>
<td>0.026</td>
<td>0.056</td>
<td>0.103</td>
<td>0.267</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.073</td>
<td>0.003</td>
<td>0.015</td>
<td>0.031</td>
<td>0.056</td>
<td>0.087</td>
<td>0.201</td>
</tr>
<tr class="odd">
<td rowspan="2"><p>All</p>
<p>Years</p></td>
<td>Unweighted</td>
<td rowspan="2">66010</td>
<td rowspan="2">868102</td>
<td rowspan="2">997</td>
<td>0.090</td>
<td>0.004</td>
<td>0.000</td>
<td>0.029</td>
<td>0.057</td>
<td>0.107</td>
<td>0.261</td>
</tr>
<tr class="even">
<td>Weighted</td>
<td>0.076</td>
<td>0.002</td>
<td>0.017</td>
<td>0.037</td>
<td>0.057</td>
<td>0.095</td>
<td>0.208</td>
</tr>
</tbody>
</table>

## IQI 11 -- Abdominal Aortic Aneurysm Repair Mortality Rate

### Model Parameter Estimates

Below we provide the model parameter estimates from fitting the simple
logistic regression, generalized estimating equations, and generalized
linear mixed model to the 2001-2003 Nationwide Inpatient Sample for IQI
11 (Abdominal Aortic Aneurysm Repair Mortality Rate). Table 3.2.1a
provides the parameter estimates associated with the cross-sectional
model, and Table 3.2.1b provides the parameter estimates associate with
the model that adjusts for a simple linear trend over time. Across these
two tables, we see that the parameter estimates and associated standard
errors are quite comparable among the three modeling approaches. In
fact, the estimated correlation coefficient from the GEE modeling
approach is nearly zero in both the cross-sectional (ρ=0.0073) and
time-trend adjusted (ρ=0.0073) models. The estimated variance components
associated with provider-specific random effects from the GLIMMIX model
were subtle, yet statistically significant in both models
(σ^2^~Btw\ Hosp~ = 0.191 for the cross sectional model, and 0.185 for
the time-trend model). The variance component that captures
provider-specific variation in the time-trend slope was estimated as
zero.

Table 3.2.1c provides the Wald Statistics to determine whether there are
statistically significant differences between the vector of parameter
estimates generated by each modeling approach. The Wald Statistics
consider pair-wise comparisons, and suggest that there were no
significant differences between the different modeling approaches for
IQI 11.

**Table 3.2.1a Parameter Estimates from Cross Sectional Models fit to
IQI-11 (Abdominal Aortic Artery Repair Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 0%" />
<col style="width: 8%" />
<col style="width: 0%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="5"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td colspan="2"><strong>Estimate</strong></td>
<td colspan="2"><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.218</td>
<td>0.258</td>
<td>0.000</td>
<td>-1.198</td>
<td>0.255</td>
<td>0.000</td>
<td>-1.177</td>
<td colspan="2">0.262</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>0.074</td>
<td>0.184</td>
<td>0.689</td>
<td>0.062</td>
<td>0.181</td>
<td>0.734</td>
<td>0.038</td>
<td colspan="2">0.188</td>
<td colspan="2">0.839</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-0.905</td>
<td>0.111</td>
<td>0.000</td>
<td>-0.898</td>
<td>0.109</td>
<td>0.000</td>
<td>-0.938</td>
<td colspan="2">0.113</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE13</td>
<td>-0.410</td>
<td>0.128</td>
<td>0.001</td>
<td>-0.408</td>
<td>0.125</td>
<td>0.001</td>
<td>-0.431</td>
<td colspan="2">0.130</td>
<td colspan="2">0.001</td>
</tr>
<tr class="odd">
<td>AGE15</td>
<td>0.354</td>
<td>0.199</td>
<td>0.076</td>
<td>0.354</td>
<td>0.196</td>
<td>0.071</td>
<td>0.393</td>
<td colspan="2">0.203</td>
<td colspan="2">0.052</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>0.261</td>
<td>0.231</td>
<td>0.259</td>
<td>0.253</td>
<td>0.227</td>
<td>0.265</td>
<td>0.281</td>
<td colspan="2">0.235</td>
<td colspan="2">0.233</td>
</tr>
<tr class="odd">
<td>C2</td>
<td>0.626</td>
<td>1.147</td>
<td>0.585</td>
<td>0.684</td>
<td>1.118</td>
<td>0.541</td>
<td>0.750</td>
<td colspan="2">1.164</td>
<td colspan="2">0.519</td>
</tr>
<tr class="even">
<td>C3</td>
<td>-0.697</td>
<td>1.063</td>
<td>0.512</td>
<td>-0.645</td>
<td>1.028</td>
<td>0.530</td>
<td>-0.555</td>
<td colspan="2">1.069</td>
<td colspan="2">0.604</td>
</tr>
<tr class="odd">
<td>C4</td>
<td>-0.507</td>
<td>1.075</td>
<td>0.637</td>
<td>-0.403</td>
<td>1.023</td>
<td>0.693</td>
<td>-0.354</td>
<td colspan="2">1.089</td>
<td colspan="2">0.745</td>
</tr>
<tr class="even">
<td>C5</td>
<td>-3.141</td>
<td>0.299</td>
<td>0.000</td>
<td>-2.979</td>
<td>0.291</td>
<td>0.000</td>
<td>-3.099</td>
<td colspan="2">0.302</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C6</td>
<td>-2.619</td>
<td>0.272</td>
<td>0.000</td>
<td>-2.487</td>
<td>0.267</td>
<td>0.000</td>
<td>-2.565</td>
<td colspan="2">0.275</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C7</td>
<td>-0.938</td>
<td>0.254</td>
<td>0.000</td>
<td>-0.893</td>
<td>0.251</td>
<td>0.000</td>
<td>-0.880</td>
<td colspan="2">0.257</td>
<td colspan="2">0.001</td>
</tr>
<tr class="odd">
<td>C8</td>
<td>1.451</td>
<td>0.239</td>
<td>0.000</td>
<td>1.451</td>
<td>0.237</td>
<td>0.000</td>
<td>1.496</td>
<td colspan="2">0.242</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C9</td>
<td>-1.465</td>
<td>0.243</td>
<td>0.000</td>
<td>-1.366</td>
<td>0.241</td>
<td>0.000</td>
<td>-1.387</td>
<td colspan="2">0.247</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>ρ</td>
<td colspan="3" rowspan="2"></td>
<td>0.0073</td>
<td>.</td>
<td>.</td>
<td colspan="5"></td>
</tr>
<tr class="even">
<td>σ<sup>2</sup><sub>Btw Hosp</sub></td>
<td colspan="3"></td>
<td>0.191</td>
<td colspan="2">0.043</td>
<td colspan="2">.</td>
</tr>
</tbody>
</table>

The effect of the *YEAR* parameter (which captures the trend over time)
was highly significant for all three modeling approaches, as seen in
Table 3.2.1b below.

**Table 3.2.1b Parameter Estimates from Time Trend Models fit to IQI-11
(Abdominal Aortic Artery Repair Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="3"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.224</td>
<td>0.258</td>
<td>0.000</td>
<td>-1.203</td>
<td>0.255</td>
<td>0.000</td>
<td>-1.182</td>
<td>0.262</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>0.076</td>
<td>0.184</td>
<td>0.681</td>
<td>0.064</td>
<td>0.181</td>
<td>0.725</td>
<td>0.041</td>
<td>0.187</td>
<td>0.828</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-0.907</td>
<td>0.111</td>
<td>0.000</td>
<td>-0.900</td>
<td>0.109</td>
<td>0.000</td>
<td>-0.939</td>
<td>0.113</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE13</td>
<td>-0.409</td>
<td>0.128</td>
<td>0.001</td>
<td>-0.407</td>
<td>0.125</td>
<td>0.001</td>
<td>-0.429</td>
<td>0.130</td>
<td>0.001</td>
</tr>
<tr class="odd">
<td>AGE15</td>
<td>0.355</td>
<td>0.199</td>
<td>0.075</td>
<td>0.355</td>
<td>0.196</td>
<td>0.069</td>
<td>0.394</td>
<td>0.203</td>
<td>0.052</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>0.261</td>
<td>0.232</td>
<td>0.260</td>
<td>0.252</td>
<td>0.227</td>
<td>0.267</td>
<td>0.279</td>
<td>0.235</td>
<td>0.235</td>
</tr>
<tr class="odd">
<td>C2</td>
<td>0.678</td>
<td>1.146</td>
<td>0.554</td>
<td>0.723</td>
<td>1.121</td>
<td>0.519</td>
<td>0.769</td>
<td>1.165</td>
<td>0.509</td>
</tr>
<tr class="even">
<td>C3</td>
<td>-0.677</td>
<td>1.062</td>
<td>0.524</td>
<td>-0.629</td>
<td>1.029</td>
<td>0.541</td>
<td>-0.546</td>
<td>1.069</td>
<td>0.609</td>
</tr>
<tr class="odd">
<td>C4</td>
<td>-0.485</td>
<td>1.075</td>
<td>0.652</td>
<td>-0.381</td>
<td>1.022</td>
<td>0.710</td>
<td>-0.325</td>
<td>1.087</td>
<td>0.765</td>
</tr>
<tr class="even">
<td>C5</td>
<td>-3.152</td>
<td>0.299</td>
<td>0.000</td>
<td>-2.990</td>
<td>0.291</td>
<td>0.000</td>
<td>-3.110</td>
<td>0.302</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C6</td>
<td>-2.626</td>
<td>0.272</td>
<td>0.000</td>
<td>-2.496</td>
<td>0.267</td>
<td>0.000</td>
<td>-2.573</td>
<td>0.275</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C7</td>
<td>-0.943</td>
<td>0.254</td>
<td>0.000</td>
<td>-0.897</td>
<td>0.252</td>
<td>0.000</td>
<td>-0.885</td>
<td>0.258</td>
<td>0.001</td>
</tr>
<tr class="odd">
<td>C8</td>
<td>1.450</td>
<td>0.239</td>
<td>0.000</td>
<td>1.449</td>
<td>0.237</td>
<td>0.000</td>
<td>1.493</td>
<td>0.242</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C9</td>
<td>-1.453</td>
<td>0.243</td>
<td>0.000</td>
<td>-1.357</td>
<td>0.241</td>
<td>0.000</td>
<td>-1.379</td>
<td>0.247</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>YEAR</td>
<td>-0.108</td>
<td>0.034</td>
<td>0.001</td>
<td>-0.105</td>
<td>0.035</td>
<td>0.002</td>
<td>-0.101</td>
<td>0.037</td>
<td>0.007</td>
</tr>
<tr class="even">
<td>ρ</td>
<td colspan="3" rowspan="3"></td>
<td>0.0071</td>
<td>.</td>
<td>.</td>
<td colspan="3"></td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3" rowspan="2"></td>
<td>0.185</td>
<td>0.043</td>
<td>.</td>
</tr>
<tr class="even">
<td>σ<sup>2</sup><sub>Year</sub></td>
<td>0.000</td>
<td>.</td>
<td>.</td>
</tr>
</tbody>
</table>

**Table 3.2.1c Wald Test Statistics and (P-Value) Comparing Models fit
to IQI-11 (Abdominal Aortic Artery Repair Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | 7.880   | 6.21    |         | 7.624   | 6.05    |
|         |         |         |         |         |         |         |
|         |         | (       | (0.961) |         | (0.938) | (0.979) |
|         |         | 0.895)  |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 6.070   |         | 2.452   | 5.907   |         | 2.400   |
|         |         |         |         |         |         |         |
|         | (0.965) |         | (1.000) | (0.981) |         | (1.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 4.117   | 2.311   |         | 4.047   | 2.260   |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.995) | (1.000) |         | (0.998) | (1.000) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** Wald Test uses the estimated covariance matrix from the model
listed in each row

### Provider-Level Model Predictions

Table 3.2.2 below provides the mean and standard deviation of
differences between model predictions (expected rates above the
diagonal, and risk-adjusted rates below the diagonal) from a random
sample of 50 providers within the NIS reference population for IQI 11.
For example, the mean difference in expected rates between the simple
logistic regression and GEE approaches for the cross sectional model was
0.004 (relative to a national mean response rate of 0.077 from Table
3.1). Mean differences (and standard deviations) attributable to model
specification (simple logistic vs GEE vs GLMMIX) for the risk-adjusted
rates appear to be higher than the expected rates.

**Table 3.2.2 Estimated Differences (and Standard Deviation) in
Provider-Level Model Predictions of Expected and Risk Adjusted Rates for
IQI-11**

> **(Abdominal Aortic Artery Repair Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | -0.004  | -0.002  |         | -0.004  | -0.002  |
|         |         |         |         |         |         |         |
|         |         | (0.001) | (0.002) |         | (0.001) | (0.002) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 0.061   |         | 0.001   | 0.061   |         | 0.001   |
|         |         |         |         |         |         |         |
|         | (0.065) |         | (0.002) | (0.068) |         | (0.002) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 0.033   | -0.028  |         | 0.034   | -0.027  |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.032) | (0.037) |         | (0.034) | (0.038) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** In each 3x3 table above, Expected Rate Differences (and Standard
Deviations) are above the diagonal, and Adjusted Rate Differences (and
Standard Deviations) are below the diagonal.

## IQI 14 -- Hip Replacement Mortality Rate

### Model Parameter Estimates

Below we provide the model parameter estimates from fitting the simple
logistic regression, generalized estimating equations, and generalized
linear mixed model to the 2001-2003 Nationwide Inpatient Sample for IQI
14 (Hip Replacement Mortality Rate). Table 3.3.1a provides the parameter
estimates associated with the cross-sectional model, and Table 3.3.1b
provides the parameter estimates associate with the model that adjusts
for a simple linear trend over time. Across these two tables, we see
that the parameter estimates and associated standard errors are
identical among the three modeling approaches, with the estimated
correlation coefficient from the GEE modeling approach being estimated
as zero in both the cross-sectional and time-trend adjusted models. The
estimated variance components associated with provider-specific random
effects from the GLIMMIX model was also zero in both models, as well as
the variance component that captures provider-specific variation in the
time-trend slope was estimated as zero.

Table 3.3.1c provides the Wald Statistics to determine whether there are
statistically significant differences between the vector of parameter
estimates generated by each modeling approach. The Wald Statistics
consider pair-wise comparisons, and suggest that there were no
significant differences between the different modeling approaches for
IQI 14.

**Table 3.3.1a Parameter Estimates from Cross Sectional Models fit to
IQI-14 (Hip Replacement Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="3"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-2.377</td>
<td>0.394</td>
<td>0.000</td>
<td>-2.376</td>
<td>0.394</td>
<td>0.000</td>
<td>-2.377</td>
<td>0.394</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>-0.363</td>
<td>0.215</td>
<td>0.091</td>
<td>-0.363</td>
<td>0.215</td>
<td>0.091</td>
<td>-0.363</td>
<td>0.215</td>
<td>0.091</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-1.573</td>
<td>0.343</td>
<td>0.000</td>
<td>-1.573</td>
<td>0.343</td>
<td>0.000</td>
<td>-1.573</td>
<td>0.343</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-1.539</td>
<td>0.404</td>
<td>0.000</td>
<td>-1.539</td>
<td>0.405</td>
<td>0.000</td>
<td>-1.539</td>
<td>0.404</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-1.586</td>
<td>0.333</td>
<td>0.000</td>
<td>-1.587</td>
<td>0.333</td>
<td>0.000</td>
<td>-1.586</td>
<td>0.333</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-1.017</td>
<td>0.274</td>
<td>0.000</td>
<td>-1.017</td>
<td>0.274</td>
<td>0.000</td>
<td>-1.017</td>
<td>0.274</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>-0.608</td>
<td>0.252</td>
<td>0.016</td>
<td>-0.608</td>
<td>0.252</td>
<td>0.016</td>
<td>-0.608</td>
<td>0.252</td>
<td>0.016</td>
</tr>
<tr class="even">
<td>AGE15</td>
<td>0.549</td>
<td>0.441</td>
<td>0.213</td>
<td>0.549</td>
<td>0.441</td>
<td>0.213</td>
<td>0.549</td>
<td>0.441</td>
<td>0.213</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>0.347</td>
<td>0.543</td>
<td>0.523</td>
<td>0.347</td>
<td>0.543</td>
<td>0.524</td>
<td>0.347</td>
<td>0.543</td>
<td>0.523</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>0.079</td>
<td>0.461</td>
<td>0.865</td>
<td>0.079</td>
<td>0.462</td>
<td>0.864</td>
<td>0.079</td>
<td>0.461</td>
<td>0.865</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>0.142</td>
<td>0.355</td>
<td>0.690</td>
<td>0.141</td>
<td>0.355</td>
<td>0.691</td>
<td>0.142</td>
<td>0.355</td>
<td>0.690</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.092</td>
<td>0.335</td>
<td>0.783</td>
<td>-0.092</td>
<td>0.335</td>
<td>0.783</td>
<td>-0.092</td>
<td>0.335</td>
<td>0.783</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-4.016</td>
<td>0.399</td>
<td>0.000</td>
<td>-4.020</td>
<td>0.399</td>
<td>0.000</td>
<td>-4.016</td>
<td>0.399</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-2.260</td>
<td>0.383</td>
<td>0.000</td>
<td>-2.262</td>
<td>0.383</td>
<td>0.000</td>
<td>-2.260</td>
<td>0.383</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>0.088</td>
<td>0.378</td>
<td>0.815</td>
<td>0.088</td>
<td>0.378</td>
<td>0.816</td>
<td>0.088</td>
<td>0.378</td>
<td>0.815</td>
</tr>
<tr class="even">
<td>C4</td>
<td>2.061</td>
<td>0.384</td>
<td>0.000</td>
<td>2.061</td>
<td>0.384</td>
<td>0.000</td>
<td>2.061</td>
<td>0.384</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>0.384</td>
<td>0.559</td>
<td>0.492</td>
<td>0.384</td>
<td>0.559</td>
<td>0.492</td>
<td>0.384</td>
<td>0.559</td>
<td>0.492</td>
</tr>
<tr class="even">
<td>ρ</td>
<td colspan="3" rowspan="2"></td>
<td>0.0000</td>
<td>.</td>
<td>.</td>
<td colspan="3"></td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Btw Hosp</sub></td>
<td colspan="3"></td>
<td>0.000</td>
<td>.</td>
<td>.</td>
</tr>
</tbody>
</table>

The effect of the *YEAR* parameter (which captures the trend over time)
was highly significant for all three modeling approaches, as seen in
Table 3.3.1b below.

**Table 3.3.1b Parameter Estimates from Time Trend Models fit to IQI-14
(Hip Replacement Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="3"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-2.385</td>
<td>0.394</td>
<td>0.000</td>
<td>-2.385</td>
<td>0.394</td>
<td>0.000</td>
<td>-2.385</td>
<td>0.394</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>-0.372</td>
<td>0.215</td>
<td>0.083</td>
<td>-0.372</td>
<td>0.215</td>
<td>0.083</td>
<td>-0.372</td>
<td>0.215</td>
<td>0.083</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-1.570</td>
<td>0.343</td>
<td>0.000</td>
<td>-1.571</td>
<td>0.343</td>
<td>0.000</td>
<td>-1.570</td>
<td>0.343</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-1.547</td>
<td>0.404</td>
<td>0.000</td>
<td>-1.547</td>
<td>0.405</td>
<td>0.000</td>
<td>-1.547</td>
<td>0.404</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-1.595</td>
<td>0.333</td>
<td>0.000</td>
<td>-1.596</td>
<td>0.334</td>
<td>0.000</td>
<td>-1.595</td>
<td>0.333</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-1.027</td>
<td>0.275</td>
<td>0.000</td>
<td>-1.027</td>
<td>0.275</td>
<td>0.000</td>
<td>-1.027</td>
<td>0.275</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>-0.622</td>
<td>0.252</td>
<td>0.014</td>
<td>-0.622</td>
<td>0.253</td>
<td>0.014</td>
<td>-0.622</td>
<td>0.252</td>
<td>0.014</td>
</tr>
<tr class="even">
<td>AGE15</td>
<td>0.564</td>
<td>0.441</td>
<td>0.201</td>
<td>0.564</td>
<td>0.442</td>
<td>0.202</td>
<td>0.564</td>
<td>0.441</td>
<td>0.201</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>0.369</td>
<td>0.543</td>
<td>0.497</td>
<td>0.368</td>
<td>0.544</td>
<td>0.498</td>
<td>0.369</td>
<td>0.543</td>
<td>0.497</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>0.089</td>
<td>0.461</td>
<td>0.846</td>
<td>0.090</td>
<td>0.462</td>
<td>0.845</td>
<td>0.089</td>
<td>0.461</td>
<td>0.846</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>0.156</td>
<td>0.355</td>
<td>0.661</td>
<td>0.155</td>
<td>0.355</td>
<td>0.662</td>
<td>0.156</td>
<td>0.355</td>
<td>0.661</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.070</td>
<td>0.335</td>
<td>0.835</td>
<td>-0.070</td>
<td>0.335</td>
<td>0.834</td>
<td>-0.070</td>
<td>0.335</td>
<td>0.835</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-4.013</td>
<td>0.399</td>
<td>0.000</td>
<td>-4.019</td>
<td>0.399</td>
<td>0.000</td>
<td>-4.013</td>
<td>0.399</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-2.250</td>
<td>0.384</td>
<td>0.000</td>
<td>-2.252</td>
<td>0.384</td>
<td>0.000</td>
<td>-2.250</td>
<td>0.384</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>0.102</td>
<td>0.378</td>
<td>0.788</td>
<td>0.101</td>
<td>0.378</td>
<td>0.789</td>
<td>0.102</td>
<td>0.378</td>
<td>0.788</td>
</tr>
<tr class="even">
<td>C4</td>
<td>2.085</td>
<td>0.384</td>
<td>0.000</td>
<td>2.085</td>
<td>0.384</td>
<td>0.000</td>
<td>2.085</td>
<td>0.384</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>0.401</td>
<td>0.560</td>
<td>0.474</td>
<td>0.400</td>
<td>0.560</td>
<td>0.475</td>
<td>0.401</td>
<td>0.560</td>
<td>0.474</td>
</tr>
<tr class="even">
<td>YEAR</td>
<td>-0.200</td>
<td>0.076</td>
<td>0.009</td>
<td>-0.201</td>
<td>0.076</td>
<td>0.008</td>
<td>-0.200</td>
<td>0.076</td>
<td>0.009</td>
</tr>
<tr class="odd">
<td>ρ</td>
<td colspan="3" rowspan="3"></td>
<td>-0.0001</td>
<td>.</td>
<td>.</td>
<td colspan="3"></td>
</tr>
<tr class="even">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3" rowspan="2"></td>
<td>0.000</td>
<td>.</td>
<td></td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Year</sub></td>
<td>0.000</td>
<td>.</td>
<td></td>
</tr>
</tbody>
</table>

**Table 3.3.1c Wald Test Statistics and (P-Value) Comparing Models fit
to IQI-14 (Hip Replacement Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | 0.001   | 0.000   |         | 0.002   | 0.000   |
|         |         |         |         |         |         |         |
|         |         | (1.000) | (1.000) |         | (1.000) | (1.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 0.001   |         | 0.001   | 0.002   |         | 0.002   |
|         |         |         |         |         |         |         |
|         | (1.000) |         | (1.000) | (1.000) |         | (1.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 0.000   | 0.001   |         | 0.000   | 0.002   |         |
| LMMIX** |         |         |         |         |         |         |
|         | (1.000) | (1.000) |         | (1.000) | (1.000) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** Wald Test uses the estimated covariance matrix from the model
listed in each row

### Provider-Level Model Predictions

Table 3.3.2 below provides the mean and standard deviation of
differences between model predictions (expected rates above the
diagonal, and risk-adjusted rates below the diagonal) from a random
sample of 50 providers within the NIS reference population for IQI 14.
Due to the fact that the three modeling approaches yielded identical
parameter estimates (the within-provider correlation was estimated as
zero), there were no differences in expected or risk-adjusted rates
attributable to the modeling approach.

**Table 3.3.2 Estimated Differences (and Standard Deviation) in
Provider-Level Model Predictions of Expected and Risk Adjusted Rates for
IQI-14**

**(Hip Replacement Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | 0.000   | 0.000   |         | 0.000   | 0.000   |
|         |         |         |         |         |         |         |
|         |         | (0.000) | (0.000) |         | (0.000) | (0.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | -0.000  |         | 0.000   | -0.000  |         | 0.000   |
|         |         |         |         |         |         |         |
|         | (0.000) |         | (0.000) | (0.000) |         | (0.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | -0.000  | -0.000  |         | -0.000  | -0.000  |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.000) | (0.000) |         | (0.000) | (0.000) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** In each 3x3 table above, Expected Rate Differences (and Standard
Deviations) are above the diagonal, and Adjusted Rate Differences (and
Standard Deviations) are below the diagonal.

## IQI 17 -- Acute Stroke Mortality Rate

### Model Parameter Estimates

Below we provide the model parameter estimates from fitting the simple
logistic regression, generalized estimating equations, and generalized
linear mixed model to the 2001-2003 Nationwide Inpatient Sample for IQI
17 (Acute Stroke Mortality Rate). Table 3.4.1a provides the parameter
estimates associated with the cross-sectional model, and Table 3.4.1b
provides the parameter estimates associate with the model that adjusts
for a simple linear trend over time. Across these two tables, we see
that the parameter estimates and associated standard errors are
comparable among the three modeling approaches (but with noticeable
differences). In this model, the estimated correlation coefficient from
the GEE modeling approach is nearly zero in both the cross-sectional
(ρ=0.0082) and time-trend adjusted (ρ=0.0079) models. The estimated
variance components associated with provider-specific random effects
from the GLIMMIX model were small, yet statistically significant in both
models (σ^2^~Btw\ Hosp~ = 0.173 for the cross sectional model, and 0.161
for the time-trend model). The variance component that captures
provider-specific variation in the time-trend slope was estimated as
statistically significant (σ^2^~Year~ = 0.019).

The effect of the *YEAR* parameter (which captures the trend over time)
was highly significant for all three modeling approaches, as seen in
Table 3.4.1b below.

Table 3.4.1c provides the Wald Statistics to determine whether there are
statistically significant differences between the vector of parameter
estimates generated by each modeling approach. The Wald Statistics
consider pair-wise comparisons, and suggest that there were significant
differences between the different modeling approaches for IQI 17. In
fact, the first row of Table 3.2.1c suggests that there are highly
significant differences between the parameter estimates from the simple
logistic regression model compared to both approaches (GEE and GLMMIX)
that adjust for the potential within-hospital correlation among
responses. This first row corresponds to a Wald Test that uses the
estimated variance/covariance matrix from the simple logistic regression
model. The corresponding Wald-Statistic Results that utilize the
variance-covariance matrices from the GEE or GLMMIX approaches are
contained in the SLR columns (on each side of the table) -- and
interestingly enough do not meet the threshold of being significantly
different. These variance/covariance matrices are model-based and may be
subject to model misspecification. A subsequent iteration of this report
will integrate similar Wald Test statistics using the robust
variance/covariance estimates for the GEE and GLMMIX approaches.

Another interesting phenomenon is that there are statistically
significant differences between the GEE and GLMMIX approaches (for both
the cross-sectional and time-trend models). Again, this result
necessitates further diagnoses of the fit of these models.

**Table 3.4.1a Parameter Estimates from Cross Sectional Models fit to
IQI-17 (Acute Stroke Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 0%" />
<col style="width: 8%" />
<col style="width: 0%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="5"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td colspan="2"><strong>Estimate</strong></td>
<td colspan="2"><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.727</td>
<td>0.068</td>
<td>0.000</td>
<td>-1.655</td>
<td>0.066</td>
<td>0.000</td>
<td>-1.660</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>0.067</td>
<td>0.028</td>
<td>0.018</td>
<td>0.063</td>
<td>0.028</td>
<td>0.024</td>
<td>0.063</td>
<td colspan="2">0.028</td>
<td colspan="2">0.028</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-0.951</td>
<td>0.177</td>
<td>0.000</td>
<td>-0.910</td>
<td>0.173</td>
<td>0.000</td>
<td>-0.945</td>
<td colspan="2">0.180</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE2</td>
<td>-0.994</td>
<td>0.168</td>
<td>0.000</td>
<td>-0.935</td>
<td>0.163</td>
<td>0.000</td>
<td>-0.952</td>
<td colspan="2">0.170</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE3</td>
<td>-0.682</td>
<td>0.110</td>
<td>0.000</td>
<td>-0.640</td>
<td>0.107</td>
<td>0.000</td>
<td>-0.663</td>
<td colspan="2">0.112</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE4</td>
<td>-0.663</td>
<td>0.090</td>
<td>0.000</td>
<td>-0.619</td>
<td>0.088</td>
<td>0.000</td>
<td>-0.636</td>
<td colspan="2">0.091</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE5</td>
<td>-0.669</td>
<td>0.068</td>
<td>0.000</td>
<td>-0.636</td>
<td>0.067</td>
<td>0.000</td>
<td>-0.662</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE6</td>
<td>-0.472</td>
<td>0.055</td>
<td>0.000</td>
<td>-0.439</td>
<td>0.054</td>
<td>0.000</td>
<td>-0.454</td>
<td colspan="2">0.056</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE7</td>
<td>-0.483</td>
<td>0.049</td>
<td>0.000</td>
<td>-0.454</td>
<td>0.048</td>
<td>0.000</td>
<td>-0.473</td>
<td colspan="2">0.049</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE8</td>
<td>-0.453</td>
<td>0.047</td>
<td>0.000</td>
<td>-0.421</td>
<td>0.046</td>
<td>0.000</td>
<td>-0.437</td>
<td colspan="2">0.048</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE9</td>
<td>-0.442</td>
<td>0.044</td>
<td>0.000</td>
<td>-0.411</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.422</td>
<td colspan="2">0.045</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-0.375</td>
<td>0.040</td>
<td>0.000</td>
<td>-0.352</td>
<td>0.039</td>
<td>0.000</td>
<td>-0.362</td>
<td colspan="2">0.041</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-0.419</td>
<td>0.037</td>
<td>0.000</td>
<td>-0.393</td>
<td>0.036</td>
<td>0.000</td>
<td>-0.405</td>
<td colspan="2">0.037</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-0.329</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.311</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.320</td>
<td colspan="2">0.035</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>-0.208</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.197</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.205</td>
<td colspan="2">0.034</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE15</td>
<td>-0.366</td>
<td>0.279</td>
<td>0.190</td>
<td>-0.336</td>
<td>0.271</td>
<td>0.215</td>
<td>-0.336</td>
<td colspan="2">0.284</td>
<td colspan="2">0.236</td>
</tr>
<tr class="odd">
<td>AGE16</td>
<td>-0.211</td>
<td>0.252</td>
<td>0.403</td>
<td>-0.203</td>
<td>0.244</td>
<td>0.405</td>
<td>-0.235</td>
<td colspan="2">0.255</td>
<td colspan="2">0.356</td>
</tr>
<tr class="even">
<td>AGE17</td>
<td>-0.304</td>
<td>0.162</td>
<td>0.060</td>
<td>-0.287</td>
<td>0.157</td>
<td>0.068</td>
<td>-0.292</td>
<td colspan="2">0.163</td>
<td colspan="2">0.075</td>
</tr>
<tr class="odd">
<td>AGE18</td>
<td>-0.252</td>
<td>0.129</td>
<td>0.051</td>
<td>-0.243</td>
<td>0.126</td>
<td>0.053</td>
<td>-0.258</td>
<td colspan="2">0.131</td>
<td colspan="2">0.048</td>
</tr>
<tr class="even">
<td>AGE19</td>
<td>0.126</td>
<td>0.093</td>
<td>0.177</td>
<td>0.127</td>
<td>0.091</td>
<td>0.163</td>
<td>0.134</td>
<td colspan="2">0.094</td>
<td colspan="2">0.155</td>
</tr>
<tr class="odd">
<td>AGE20</td>
<td>-0.114</td>
<td>0.077</td>
<td>0.140</td>
<td>-0.107</td>
<td>0.075</td>
<td>0.155</td>
<td>-0.110</td>
<td colspan="2">0.078</td>
<td colspan="2">0.160</td>
</tr>
<tr class="even">
<td>AGE21</td>
<td>-0.149</td>
<td>0.069</td>
<td>0.030</td>
<td>-0.131</td>
<td>0.067</td>
<td>0.049</td>
<td>-0.125</td>
<td colspan="2">0.069</td>
<td colspan="2">0.073</td>
</tr>
<tr class="odd">
<td>AGE22</td>
<td>-0.150</td>
<td>0.066</td>
<td>0.023</td>
<td>-0.149</td>
<td>0.064</td>
<td>0.021</td>
<td>-0.152</td>
<td colspan="2">0.067</td>
<td colspan="2">0.022</td>
</tr>
<tr class="even">
<td>AGE23</td>
<td>-0.049</td>
<td>0.062</td>
<td>0.425</td>
<td>-0.050</td>
<td>0.060</td>
<td>0.408</td>
<td>-0.051</td>
<td colspan="2">0.062</td>
<td colspan="2">0.411</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>-0.138</td>
<td>0.055</td>
<td>0.013</td>
<td>-0.134</td>
<td>0.054</td>
<td>0.013</td>
<td>-0.139</td>
<td colspan="2">0.056</td>
<td colspan="2">0.013</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>-0.014</td>
<td>0.048</td>
<td>0.764</td>
<td>-0.018</td>
<td>0.047</td>
<td>0.700</td>
<td>-0.018</td>
<td colspan="2">0.049</td>
<td colspan="2">0.716</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>-0.045</td>
<td>0.044</td>
<td>0.301</td>
<td>-0.041</td>
<td>0.043</td>
<td>0.342</td>
<td>-0.039</td>
<td colspan="2">0.044</td>
<td colspan="2">0.380</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.087</td>
<td>0.042</td>
<td>0.039</td>
<td>-0.083</td>
<td>0.041</td>
<td>0.044</td>
<td>-0.083</td>
<td colspan="2">0.042</td>
<td colspan="2">0.050</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-1.548</td>
<td>0.140</td>
<td>0.000</td>
<td>-1.465</td>
<td>0.130</td>
<td>0.000</td>
<td>-1.558</td>
<td colspan="2">0.141</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-0.111</td>
<td>0.082</td>
<td>0.175</td>
<td>-0.113</td>
<td>0.079</td>
<td>0.154</td>
<td>-0.114</td>
<td colspan="2">0.083</td>
<td colspan="2">0.169</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>1.019</td>
<td>0.070</td>
<td>0.000</td>
<td>0.986</td>
<td>0.068</td>
<td>0.000</td>
<td>1.022</td>
<td colspan="2">0.071</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C4</td>
<td>2.289</td>
<td>0.074</td>
<td>0.000</td>
<td>2.260</td>
<td>0.072</td>
<td>0.000</td>
<td>2.341</td>
<td colspan="2">0.075</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>-0.211</td>
<td>0.085</td>
<td>0.013</td>
<td>-0.222</td>
<td>0.082</td>
<td>0.007</td>
<td>-0.236</td>
<td colspan="2">0.086</td>
<td colspan="2">0.006</td>
</tr>
<tr class="even">
<td>C6</td>
<td>0.411</td>
<td>0.066</td>
<td>0.000</td>
<td>0.377</td>
<td>0.064</td>
<td>0.000</td>
<td>0.383</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C7</td>
<td>1.578</td>
<td>0.068</td>
<td>0.000</td>
<td>1.535</td>
<td>0.066</td>
<td>0.000</td>
<td>1.580</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C8</td>
<td>3.312</td>
<td>0.068</td>
<td>0.000</td>
<td>3.290</td>
<td>0.066</td>
<td>0.000</td>
<td>3.375</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C9</td>
<td>-2.565</td>
<td>0.077</td>
<td>0.000</td>
<td>-2.425</td>
<td>0.074</td>
<td>0.000</td>
<td>-2.610</td>
<td colspan="2">0.077</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C10</td>
<td>-1.224</td>
<td>0.066</td>
<td>0.000</td>
<td>-1.204</td>
<td>0.064</td>
<td>0.000</td>
<td>-1.264</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C11</td>
<td>0.295</td>
<td>0.067</td>
<td>0.000</td>
<td>0.277</td>
<td>0.064</td>
<td>0.000</td>
<td>0.284</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C12</td>
<td>2.126</td>
<td>0.067</td>
<td>0.000</td>
<td>2.089</td>
<td>0.065</td>
<td>0.000</td>
<td>2.152</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C13</td>
<td>-2.451</td>
<td>0.094</td>
<td>0.000</td>
<td>-2.387</td>
<td>0.090</td>
<td>0.000</td>
<td>-2.525</td>
<td colspan="2">0.095</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C14</td>
<td>-0.958</td>
<td>0.068</td>
<td>0.000</td>
<td>-0.984</td>
<td>0.066</td>
<td>0.000</td>
<td>-1.030</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C15</td>
<td>0.359</td>
<td>0.072</td>
<td>0.000</td>
<td>0.315</td>
<td>0.070</td>
<td>0.000</td>
<td>0.315</td>
<td colspan="2">0.073</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C16</td>
<td>2.031</td>
<td>0.078</td>
<td>0.000</td>
<td>1.987</td>
<td>0.076</td>
<td>0.000</td>
<td>2.047</td>
<td colspan="2">0.079</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C17</td>
<td>-0.014</td>
<td>0.072</td>
<td>0.843</td>
<td>-0.010</td>
<td>0.069</td>
<td>0.880</td>
<td>-0.007</td>
<td colspan="2">0.073</td>
<td colspan="2">0.922</td>
</tr>
<tr class="even">
<td>ρ</td>
<td colspan="3" rowspan="2"></td>
<td>0.0082</td>
<td>.</td>
<td>.</td>
<td colspan="5"></td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3"></td>
<td>0.173</td>
<td colspan="2">0.011</td>
<td colspan="2">.</td>
</tr>
</tbody>
</table>

**Table 3.4.1b Parameter Estimates from Time Trend Models fit to IQI-17
(Acute Stroke Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 0%" />
<col style="width: 8%" />
<col style="width: 0%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="5"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td colspan="2"><strong>Estimate</strong></td>
<td colspan="2"><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.725</td>
<td>0.068</td>
<td>0.000</td>
<td>-1.656</td>
<td>0.066</td>
<td>0.000</td>
<td>-1.662</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>0.066</td>
<td>0.028</td>
<td>0.020</td>
<td>0.062</td>
<td>0.028</td>
<td>0.025</td>
<td>0.062</td>
<td colspan="2">0.028</td>
<td colspan="2">0.029</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-0.951</td>
<td>0.177</td>
<td>0.000</td>
<td>-0.913</td>
<td>0.173</td>
<td>0.000</td>
<td>-0.944</td>
<td colspan="2">0.180</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE2</td>
<td>-0.990</td>
<td>0.168</td>
<td>0.000</td>
<td>-0.936</td>
<td>0.163</td>
<td>0.000</td>
<td>-0.951</td>
<td colspan="2">0.170</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE3</td>
<td>-0.681</td>
<td>0.110</td>
<td>0.000</td>
<td>-0.640</td>
<td>0.107</td>
<td>0.000</td>
<td>-0.664</td>
<td colspan="2">0.112</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE4</td>
<td>-0.661</td>
<td>0.090</td>
<td>0.000</td>
<td>-0.620</td>
<td>0.088</td>
<td>0.000</td>
<td>-0.638</td>
<td colspan="2">0.091</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE5</td>
<td>-0.669</td>
<td>0.068</td>
<td>0.000</td>
<td>-0.637</td>
<td>0.067</td>
<td>0.000</td>
<td>-0.663</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE6</td>
<td>-0.468</td>
<td>0.055</td>
<td>0.000</td>
<td>-0.438</td>
<td>0.054</td>
<td>0.000</td>
<td>-0.454</td>
<td colspan="2">0.056</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE7</td>
<td>-0.480</td>
<td>0.049</td>
<td>0.000</td>
<td>-0.453</td>
<td>0.048</td>
<td>0.000</td>
<td>-0.474</td>
<td colspan="2">0.049</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE8</td>
<td>-0.451</td>
<td>0.047</td>
<td>0.000</td>
<td>-0.421</td>
<td>0.046</td>
<td>0.000</td>
<td>-0.438</td>
<td colspan="2">0.048</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE9</td>
<td>-0.441</td>
<td>0.045</td>
<td>0.000</td>
<td>-0.412</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.423</td>
<td colspan="2">0.045</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-0.375</td>
<td>0.040</td>
<td>0.000</td>
<td>-0.353</td>
<td>0.039</td>
<td>0.000</td>
<td>-0.363</td>
<td colspan="2">0.041</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-0.420</td>
<td>0.037</td>
<td>0.000</td>
<td>-0.395</td>
<td>0.036</td>
<td>0.000</td>
<td>-0.405</td>
<td colspan="2">0.037</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-0.331</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.313</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.322</td>
<td colspan="2">0.035</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>-0.209</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.198</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.205</td>
<td colspan="2">0.034</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE15</td>
<td>-0.352</td>
<td>0.279</td>
<td>0.207</td>
<td>-0.326</td>
<td>0.271</td>
<td>0.229</td>
<td>-0.334</td>
<td colspan="2">0.284</td>
<td colspan="2">0.240</td>
</tr>
<tr class="odd">
<td>AGE16</td>
<td>-0.207</td>
<td>0.252</td>
<td>0.411</td>
<td>-0.201</td>
<td>0.244</td>
<td>0.410</td>
<td>-0.232</td>
<td colspan="2">0.255</td>
<td colspan="2">0.363</td>
</tr>
<tr class="even">
<td>AGE17</td>
<td>-0.307</td>
<td>0.162</td>
<td>0.058</td>
<td>-0.290</td>
<td>0.158</td>
<td>0.066</td>
<td>-0.291</td>
<td colspan="2">0.164</td>
<td colspan="2">0.075</td>
</tr>
<tr class="odd">
<td>AGE18</td>
<td>-0.257</td>
<td>0.129</td>
<td>0.046</td>
<td>-0.246</td>
<td>0.126</td>
<td>0.050</td>
<td>-0.258</td>
<td colspan="2">0.131</td>
<td colspan="2">0.048</td>
</tr>
<tr class="even">
<td>AGE19</td>
<td>0.129</td>
<td>0.093</td>
<td>0.167</td>
<td>0.129</td>
<td>0.091</td>
<td>0.157</td>
<td>0.135</td>
<td colspan="2">0.094</td>
<td colspan="2">0.154</td>
</tr>
<tr class="odd">
<td>AGE20</td>
<td>-0.113</td>
<td>0.077</td>
<td>0.142</td>
<td>-0.107</td>
<td>0.075</td>
<td>0.156</td>
<td>-0.110</td>
<td colspan="2">0.078</td>
<td colspan="2">0.160</td>
</tr>
<tr class="even">
<td>AGE21</td>
<td>-0.150</td>
<td>0.069</td>
<td>0.029</td>
<td>-0.132</td>
<td>0.067</td>
<td>0.049</td>
<td>-0.123</td>
<td colspan="2">0.069</td>
<td colspan="2">0.076</td>
</tr>
<tr class="odd">
<td>AGE22</td>
<td>-0.150</td>
<td>0.066</td>
<td>0.023</td>
<td>-0.149</td>
<td>0.064</td>
<td>0.021</td>
<td>-0.152</td>
<td colspan="2">0.067</td>
<td colspan="2">0.023</td>
</tr>
<tr class="even">
<td>AGE23</td>
<td>-0.048</td>
<td>0.062</td>
<td>0.433</td>
<td>-0.049</td>
<td>0.060</td>
<td>0.415</td>
<td>-0.050</td>
<td colspan="2">0.062</td>
<td colspan="2">0.424</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>-0.137</td>
<td>0.055</td>
<td>0.013</td>
<td>-0.133</td>
<td>0.054</td>
<td>0.014</td>
<td>-0.139</td>
<td colspan="2">0.056</td>
<td colspan="2">0.013</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>-0.014</td>
<td>0.048</td>
<td>0.770</td>
<td>-0.018</td>
<td>0.047</td>
<td>0.705</td>
<td>-0.018</td>
<td colspan="2">0.049</td>
<td colspan="2">0.708</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>-0.044</td>
<td>0.044</td>
<td>0.317</td>
<td>-0.040</td>
<td>0.043</td>
<td>0.354</td>
<td>-0.038</td>
<td colspan="2">0.044</td>
<td colspan="2">0.386</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.086</td>
<td>0.042</td>
<td>0.039</td>
<td>-0.083</td>
<td>0.041</td>
<td>0.044</td>
<td>-0.083</td>
<td colspan="2">0.042</td>
<td colspan="2">0.049</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-1.550</td>
<td>0.140</td>
<td>0.000</td>
<td>-1.468</td>
<td>0.130</td>
<td>0.000</td>
<td>-1.558</td>
<td colspan="2">0.141</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-0.112</td>
<td>0.082</td>
<td>0.173</td>
<td>-0.113</td>
<td>0.079</td>
<td>0.155</td>
<td>-0.113</td>
<td colspan="2">0.083</td>
<td colspan="2">0.174</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>1.016</td>
<td>0.070</td>
<td>0.000</td>
<td>0.986</td>
<td>0.068</td>
<td>0.000</td>
<td>1.021</td>
<td colspan="2">0.071</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C4</td>
<td>2.291</td>
<td>0.074</td>
<td>0.000</td>
<td>2.264</td>
<td>0.072</td>
<td>0.000</td>
<td>2.344</td>
<td colspan="2">0.075</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>-0.210</td>
<td>0.085</td>
<td>0.014</td>
<td>-0.221</td>
<td>0.082</td>
<td>0.007</td>
<td>-0.234</td>
<td colspan="2">0.086</td>
<td colspan="2">0.006</td>
</tr>
<tr class="even">
<td>C6</td>
<td>0.409</td>
<td>0.066</td>
<td>0.000</td>
<td>0.378</td>
<td>0.064</td>
<td>0.000</td>
<td>0.383</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C7</td>
<td>1.579</td>
<td>0.068</td>
<td>0.000</td>
<td>1.538</td>
<td>0.066</td>
<td>0.000</td>
<td>1.582</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C8</td>
<td>3.314</td>
<td>0.068</td>
<td>0.000</td>
<td>3.293</td>
<td>0.066</td>
<td>0.000</td>
<td>3.378</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C9</td>
<td>-2.568</td>
<td>0.077</td>
<td>0.000</td>
<td>-2.429</td>
<td>0.074</td>
<td>0.000</td>
<td>-2.609</td>
<td colspan="2">0.077</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C10</td>
<td>-1.225</td>
<td>0.066</td>
<td>0.000</td>
<td>-1.204</td>
<td>0.064</td>
<td>0.000</td>
<td>-1.263</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C11</td>
<td>0.297</td>
<td>0.067</td>
<td>0.000</td>
<td>0.280</td>
<td>0.065</td>
<td>0.000</td>
<td>0.286</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C12</td>
<td>2.128</td>
<td>0.067</td>
<td>0.000</td>
<td>2.093</td>
<td>0.065</td>
<td>0.000</td>
<td>2.155</td>
<td colspan="2">0.067</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C13</td>
<td>-2.458</td>
<td>0.094</td>
<td>0.000</td>
<td>-2.391</td>
<td>0.090</td>
<td>0.000</td>
<td>-2.526</td>
<td colspan="2">0.095</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C14</td>
<td>-0.965</td>
<td>0.068</td>
<td>0.000</td>
<td>-0.987</td>
<td>0.066</td>
<td>0.000</td>
<td>-1.030</td>
<td colspan="2">0.069</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C15</td>
<td>0.353</td>
<td>0.072</td>
<td>0.000</td>
<td>0.313</td>
<td>0.070</td>
<td>0.000</td>
<td>0.314</td>
<td colspan="2">0.073</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C16</td>
<td>2.026</td>
<td>0.078</td>
<td>0.000</td>
<td>1.986</td>
<td>0.076</td>
<td>0.000</td>
<td>2.047</td>
<td colspan="2">0.079</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C17</td>
<td>-0.011</td>
<td>0.072</td>
<td>0.874</td>
<td>-0.009</td>
<td>0.070</td>
<td>0.901</td>
<td>-0.005</td>
<td colspan="2">0.073</td>
<td colspan="2">0.945</td>
</tr>
<tr class="even">
<td>YEAR</td>
<td>-0.065</td>
<td>0.008</td>
<td>0.000</td>
<td>-0.053</td>
<td>0.010</td>
<td>0.000</td>
<td>-0.059</td>
<td colspan="2">0.013</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>ρ</td>
<td colspan="3" rowspan="3"></td>
<td>0.0079</td>
<td>.</td>
<td>.</td>
<td colspan="5"></td>
</tr>
<tr class="even">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3" rowspan="2"></td>
<td>0.161</td>
<td colspan="2">0.011</td>
<td colspan="2">.</td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Year</sub></td>
<td>0.019</td>
<td colspan="2">0.007</td>
<td colspan="2">.</td>
</tr>
</tbody>
</table>

**Table 3.4.1c Wald Test Statistics and (P-Value) Comparing Models fit
to IQI-17 (Acute Stroke Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | 154.85  | 127.77  |         | 149.27  | 120.62  |
|         |         |         |         |         |         |         |
|         |         | (0.000) | (0.000) |         | (0.000) | (0.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 57.362  |         | 64.972  | 56.246  |         | 62.365  |
|         |         |         |         |         |         |         |
|         | (0.102) |         | (0.027) | (0.143) |         | (0.054) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 49.287  | 70.869  |         | 46.309  | 68.044  |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.306) | (0.008) |         | (0.460) | (0.019) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** Wald Test uses the estimated covariance matrix from the model
listed in each row

### Provider-Level Model Predictions

Table 3.4.2 below provides the mean and standard deviation of
differences between model predictions (expected rates above the
diagonal, and risk-adjusted rates below the diagonal) from a random
sample of 50 providers within the NIS reference population for IQI 17.
For example, the mean difference in expected rates between the simple
logistic regression and GEE approaches for the cross sectional model was
-0.006 (relative to a national mean response rate of 0.114 from Table
3.1). Mean differences (and standard deviations) attributable to model
specification (simple logistic vs GEE vs GLMMIX) for the risk-adjusted
rates appear to be higher than the expected rates.

**Table 3.4.2 Estimated Differences (and Standard Deviation) in
Provider-Level Model Predictions of Expected and Risk Adjusted Rates for
IQI-17**

> **(Acute Stroke Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | -0.006  | -0.002  |         | -0.005  | -0.002  |
|         |         |         |         |         |         |         |
|         |         | (0.001) | (0.001) |         | (0.001) | (0.001) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 0.021   |         | 0.004   | 0.021   |         | 0.004   |
|         |         |         |         |         |         |         |
|         | (0.015) |         | (0.000) | (0.015) |         | (0.001) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 0.007   | -0.014  |         | 0.007   | -0.014  |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.004) | (0.011) |         | (0.005) | (0.011) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** In each 3x3 table above, Expected Rate Differences (and Standard
Deviations) are above the diagonal, and Adjusted Rate Differences (and
Standard Deviations) are below the diagonal.

## IQI 19 -- Hip Fracture Mortality Rate

### Model Parameter Estimates

Below we provide the model parameter estimates from fitting the simple
logistic regression, generalized estimating equations, and generalized
linear mixed model to the 2001-2003 Nationwide Inpatient Sample for IQI
19 (Hip Fracture Mortality Rate). Table 3.5.1a provides the parameter
estimates associated with the cross-sectional model, and Table 3.5.1b
provides the parameter estimates associate with the model that adjusts
for a simple linear trend over time. Across these two tables, we see
that the parameter estimates and associated standard errors are quite
comparable among the three modeling approaches. In fact, the estimated
correlation coefficient from the GEE modeling approach is nearly zero
(ρ=0.0017) in both the cross-sectional and time-trend adjusted models.
The estimated variance components associated with provider-specific
random effects from the GLIMMIX model were subtle, yet statistically
significant in both models (σ^2^~Btw\ Hosp~ = 0.126 for the cross
sectional model, and 0.109 for the time-trend model). The variance
component that captures provider-specific variation in the time-trend
slope was statistically significant (σ^2^~Year~ = 0.043).

Table 3.5.1c provides the Wald Statistics to determine whether there are
statistically significant differences between the vector of parameter
estimates generated by each modeling approach. The Wald Statistics
consider pair-wise comparisons, and suggest that there were no
significant differences between the different modeling approaches for
IQI 19.

**Table 3.5.1a Parameter Estimates from Cross Sectional Models fit to
IQI-19 (Hip Fracture Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="3"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.569</td>
<td>0.139</td>
<td>0.000</td>
<td>-1.565</td>
<td>0.139</td>
<td>0.000</td>
<td>-1.560</td>
<td>0.141</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>-0.310</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.310</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.317</td>
<td>0.044</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE3</td>
<td>-2.610</td>
<td>1.007</td>
<td>0.010</td>
<td>-2.569</td>
<td>0.979</td>
<td>0.009</td>
<td>-2.609</td>
<td>1.008</td>
<td>0.010</td>
</tr>
<tr class="even">
<td>AGE4</td>
<td>-1.244</td>
<td>0.459</td>
<td>0.007</td>
<td>-1.224</td>
<td>0.452</td>
<td>0.007</td>
<td>-1.233</td>
<td>0.461</td>
<td>0.007</td>
</tr>
<tr class="odd">
<td>AGE5</td>
<td>-2.137</td>
<td>0.587</td>
<td>0.000</td>
<td>-2.131</td>
<td>0.580</td>
<td>0.000</td>
<td>-2.167</td>
<td>0.588</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE6</td>
<td>-0.905</td>
<td>0.271</td>
<td>0.001</td>
<td>-0.912</td>
<td>0.269</td>
<td>0.001</td>
<td>-0.955</td>
<td>0.273</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE7</td>
<td>-0.729</td>
<td>0.224</td>
<td>0.001</td>
<td>-0.728</td>
<td>0.222</td>
<td>0.001</td>
<td>-0.732</td>
<td>0.225</td>
<td>0.001</td>
</tr>
<tr class="even">
<td>AGE8</td>
<td>-0.860</td>
<td>0.225</td>
<td>0.000</td>
<td>-0.853</td>
<td>0.223</td>
<td>0.000</td>
<td>-0.866</td>
<td>0.226</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE9</td>
<td>-0.525</td>
<td>0.170</td>
<td>0.002</td>
<td>-0.524</td>
<td>0.169</td>
<td>0.002</td>
<td>-0.546</td>
<td>0.172</td>
<td>0.001</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-0.453</td>
<td>0.122</td>
<td>0.000</td>
<td>-0.454</td>
<td>0.122</td>
<td>0.000</td>
<td>-0.462</td>
<td>0.123</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-0.713</td>
<td>0.096</td>
<td>0.000</td>
<td>-0.711</td>
<td>0.096</td>
<td>0.000</td>
<td>-0.721</td>
<td>0.097</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-0.449</td>
<td>0.071</td>
<td>0.000</td>
<td>-0.448</td>
<td>0.071</td>
<td>0.000</td>
<td>-0.453</td>
<td>0.072</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>-0.296</td>
<td>0.061</td>
<td>0.000</td>
<td>-0.293</td>
<td>0.061</td>
<td>0.000</td>
<td>-0.293</td>
<td>0.062</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>AGE17</td>
<td>1.740</td>
<td>1.245</td>
<td>0.162</td>
<td>1.703</td>
<td>1.219</td>
<td>0.162</td>
<td>1.744</td>
<td>1.248</td>
<td>0.162</td>
</tr>
<tr class="odd">
<td>AGE18</td>
<td>-0.155</td>
<td>1.109</td>
<td>0.889</td>
<td>-0.167</td>
<td>1.094</td>
<td>0.879</td>
<td>-0.173</td>
<td>1.110</td>
<td>0.876</td>
</tr>
<tr class="even">
<td>AGE19</td>
<td>0.950</td>
<td>0.835</td>
<td>0.256</td>
<td>0.951</td>
<td>0.826</td>
<td>0.249</td>
<td>0.965</td>
<td>0.837</td>
<td>0.249</td>
</tr>
<tr class="odd">
<td>AGE20</td>
<td>0.687</td>
<td>0.420</td>
<td>0.102</td>
<td>0.690</td>
<td>0.418</td>
<td>0.099</td>
<td>0.746</td>
<td>0.422</td>
<td>0.077</td>
</tr>
<tr class="even">
<td>AGE21</td>
<td>-0.103</td>
<td>0.376</td>
<td>0.785</td>
<td>-0.098</td>
<td>0.373</td>
<td>0.793</td>
<td>-0.099</td>
<td>0.378</td>
<td>0.794</td>
</tr>
<tr class="odd">
<td>AGE22</td>
<td>0.437</td>
<td>0.310</td>
<td>0.159</td>
<td>0.430</td>
<td>0.307</td>
<td>0.161</td>
<td>0.446</td>
<td>0.311</td>
<td>0.152</td>
</tr>
<tr class="even">
<td>AGE23</td>
<td>0.345</td>
<td>0.232</td>
<td>0.137</td>
<td>0.348</td>
<td>0.230</td>
<td>0.131</td>
<td>0.376</td>
<td>0.234</td>
<td>0.108</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>-0.053</td>
<td>0.171</td>
<td>0.755</td>
<td>-0.048</td>
<td>0.170</td>
<td>0.776</td>
<td>-0.046</td>
<td>0.172</td>
<td>0.788</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>0.141</td>
<td>0.124</td>
<td>0.256</td>
<td>0.140</td>
<td>0.123</td>
<td>0.255</td>
<td>0.135</td>
<td>0.125</td>
<td>0.279</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>-0.078</td>
<td>0.093</td>
<td>0.401</td>
<td>-0.074</td>
<td>0.092</td>
<td>0.420</td>
<td>-0.078</td>
<td>0.093</td>
<td>0.405</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.074</td>
<td>0.077</td>
<td>0.339</td>
<td>-0.073</td>
<td>0.077</td>
<td>0.340</td>
<td>-0.078</td>
<td>0.078</td>
<td>0.313</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-3.211</td>
<td>0.166</td>
<td>0.000</td>
<td>-3.191</td>
<td>0.166</td>
<td>0.000</td>
<td>-3.223</td>
<td>0.167</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-2.221</td>
<td>0.145</td>
<td>0.000</td>
<td>-2.204</td>
<td>0.145</td>
<td>0.000</td>
<td>-2.224</td>
<td>0.146</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>-0.330</td>
<td>0.142</td>
<td>0.020</td>
<td>-0.325</td>
<td>0.142</td>
<td>0.022</td>
<td>-0.325</td>
<td>0.143</td>
<td>0.023</td>
</tr>
<tr class="even">
<td>C4</td>
<td>1.293</td>
<td>0.145</td>
<td>0.000</td>
<td>1.298</td>
<td>0.145</td>
<td>0.000</td>
<td>1.328</td>
<td>0.146</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>-3.925</td>
<td>0.169</td>
<td>0.000</td>
<td>-3.886</td>
<td>0.169</td>
<td>0.000</td>
<td>-3.930</td>
<td>0.170</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C6</td>
<td>-2.462</td>
<td>0.143</td>
<td>0.000</td>
<td>-2.440</td>
<td>0.143</td>
<td>0.000</td>
<td>-2.461</td>
<td>0.144</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C7</td>
<td>-0.377</td>
<td>0.140</td>
<td>0.007</td>
<td>-0.369</td>
<td>0.140</td>
<td>0.008</td>
<td>-0.365</td>
<td>0.141</td>
<td>0.010</td>
</tr>
<tr class="even">
<td>C8</td>
<td>1.427</td>
<td>0.143</td>
<td>0.000</td>
<td>1.431</td>
<td>0.143</td>
<td>0.000</td>
<td>1.458</td>
<td>0.145</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C9</td>
<td>-1.960</td>
<td>0.177</td>
<td>0.000</td>
<td>-1.928</td>
<td>0.175</td>
<td>0.000</td>
<td>-1.920</td>
<td>0.178</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C10</td>
<td>-0.639</td>
<td>0.146</td>
<td>0.000</td>
<td>-0.623</td>
<td>0.145</td>
<td>0.000</td>
<td>-0.597</td>
<td>0.147</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C11</td>
<td>1.058</td>
<td>0.145</td>
<td>0.000</td>
<td>1.063</td>
<td>0.145</td>
<td>0.000</td>
<td>1.097</td>
<td>0.147</td>
<td>0.000</td>
</tr>
<tr class="even">
<td>C12</td>
<td>2.582</td>
<td>0.161</td>
<td>0.000</td>
<td>2.584</td>
<td>0.161</td>
<td>0.000</td>
<td>2.620</td>
<td>0.163</td>
<td>0.000</td>
</tr>
<tr class="odd">
<td>C13</td>
<td>-0.502</td>
<td>0.152</td>
<td>0.001</td>
<td>-0.492</td>
<td>0.152</td>
<td>0.001</td>
<td>-0.483</td>
<td>0.153</td>
<td>0.002</td>
</tr>
<tr class="even">
<td>ρ</td>
<td colspan="3" rowspan="2"></td>
<td>0.0017</td>
<td>.</td>
<td>.</td>
<td colspan="3"></td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3"></td>
<td>0.126</td>
<td>0.017</td>
<td>.</td>
</tr>
</tbody>
</table>

The effect of the *YEAR* parameter (which captures the trend over time)
was highly significant for all three modeling approaches, as seen in
Table 3.5.1b below.

**Table 3.5.1b Parameter Estimates from Time Trend Models fit to IQI-19
(Hip Fracture Mortality Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 0%" />
<col style="width: 8%" />
<col style="width: 0%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="5"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td colspan="2"><strong>Estimate</strong></td>
<td colspan="2"><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.570</td>
<td>0.139</td>
<td>0.000</td>
<td>-1.567</td>
<td>0.139</td>
<td>0.000</td>
<td>-1.566</td>
<td colspan="2">0.141</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>-0.311</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.311</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.318</td>
<td colspan="2">0.044</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE3</td>
<td>-2.609</td>
<td>1.007</td>
<td>0.010</td>
<td>-2.570</td>
<td>0.980</td>
<td>0.009</td>
<td>-2.618</td>
<td colspan="2">1.008</td>
<td colspan="2">0.009</td>
</tr>
<tr class="even">
<td>AGE4</td>
<td>-1.242</td>
<td>0.460</td>
<td>0.007</td>
<td>-1.222</td>
<td>0.452</td>
<td>0.007</td>
<td>-1.230</td>
<td colspan="2">0.461</td>
<td colspan="2">0.008</td>
</tr>
<tr class="odd">
<td>AGE5</td>
<td>-2.141</td>
<td>0.587</td>
<td>0.000</td>
<td>-2.135</td>
<td>0.581</td>
<td>0.000</td>
<td>-2.177</td>
<td colspan="2">0.588</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE6</td>
<td>-0.897</td>
<td>0.270</td>
<td>0.001</td>
<td>-0.903</td>
<td>0.269</td>
<td>0.001</td>
<td>-0.949</td>
<td colspan="2">0.273</td>
<td colspan="2">0.001</td>
</tr>
<tr class="odd">
<td>AGE7</td>
<td>-0.727</td>
<td>0.224</td>
<td>0.001</td>
<td>-0.725</td>
<td>0.222</td>
<td>0.001</td>
<td>-0.731</td>
<td colspan="2">0.225</td>
<td colspan="2">0.001</td>
</tr>
<tr class="even">
<td>AGE8</td>
<td>-0.858</td>
<td>0.225</td>
<td>0.000</td>
<td>-0.851</td>
<td>0.223</td>
<td>0.000</td>
<td>-0.866</td>
<td colspan="2">0.226</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE9</td>
<td>-0.521</td>
<td>0.170</td>
<td>0.002</td>
<td>-0.520</td>
<td>0.169</td>
<td>0.002</td>
<td>-0.546</td>
<td colspan="2">0.172</td>
<td colspan="2">0.001</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-0.448</td>
<td>0.122</td>
<td>0.000</td>
<td>-0.449</td>
<td>0.122</td>
<td>0.000</td>
<td>-0.458</td>
<td colspan="2">0.123</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-0.714</td>
<td>0.096</td>
<td>0.000</td>
<td>-0.713</td>
<td>0.096</td>
<td>0.000</td>
<td>-0.722</td>
<td colspan="2">0.097</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-0.447</td>
<td>0.071</td>
<td>0.000</td>
<td>-0.446</td>
<td>0.071</td>
<td>0.000</td>
<td>-0.454</td>
<td colspan="2">0.072</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>-0.296</td>
<td>0.061</td>
<td>0.000</td>
<td>-0.293</td>
<td>0.061</td>
<td>0.000</td>
<td>-0.293</td>
<td colspan="2">0.062</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE17</td>
<td>1.751</td>
<td>1.246</td>
<td>0.160</td>
<td>1.715</td>
<td>1.220</td>
<td>0.160</td>
<td>1.770</td>
<td colspan="2">1.248</td>
<td colspan="2">0.156</td>
</tr>
<tr class="odd">
<td>AGE18</td>
<td>-0.159</td>
<td>1.109</td>
<td>0.886</td>
<td>-0.170</td>
<td>1.093</td>
<td>0.876</td>
<td>-0.170</td>
<td colspan="2">1.110</td>
<td colspan="2">0.879</td>
</tr>
<tr class="even">
<td>AGE19</td>
<td>0.952</td>
<td>0.836</td>
<td>0.254</td>
<td>0.954</td>
<td>0.826</td>
<td>0.248</td>
<td>0.975</td>
<td colspan="2">0.837</td>
<td colspan="2">0.244</td>
</tr>
<tr class="odd">
<td>AGE20</td>
<td>0.682</td>
<td>0.420</td>
<td>0.105</td>
<td>0.685</td>
<td>0.418</td>
<td>0.101</td>
<td>0.747</td>
<td colspan="2">0.422</td>
<td colspan="2">0.077</td>
</tr>
<tr class="even">
<td>AGE21</td>
<td>-0.107</td>
<td>0.376</td>
<td>0.777</td>
<td>-0.102</td>
<td>0.373</td>
<td>0.785</td>
<td>-0.099</td>
<td colspan="2">0.378</td>
<td colspan="2">0.794</td>
</tr>
<tr class="odd">
<td>AGE22</td>
<td>0.443</td>
<td>0.310</td>
<td>0.152</td>
<td>0.437</td>
<td>0.307</td>
<td>0.154</td>
<td>0.452</td>
<td colspan="2">0.311</td>
<td colspan="2">0.146</td>
</tr>
<tr class="even">
<td>AGE23</td>
<td>0.347</td>
<td>0.232</td>
<td>0.135</td>
<td>0.350</td>
<td>0.230</td>
<td>0.129</td>
<td>0.380</td>
<td colspan="2">0.234</td>
<td colspan="2">0.105</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>-0.059</td>
<td>0.171</td>
<td>0.729</td>
<td>-0.054</td>
<td>0.170</td>
<td>0.750</td>
<td>-0.049</td>
<td colspan="2">0.172</td>
<td colspan="2">0.778</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>0.143</td>
<td>0.124</td>
<td>0.249</td>
<td>0.142</td>
<td>0.123</td>
<td>0.249</td>
<td>0.137</td>
<td colspan="2">0.125</td>
<td colspan="2">0.272</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>-0.079</td>
<td>0.093</td>
<td>0.393</td>
<td>-0.075</td>
<td>0.092</td>
<td>0.413</td>
<td>-0.077</td>
<td colspan="2">0.093</td>
<td colspan="2">0.408</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.074</td>
<td>0.077</td>
<td>0.339</td>
<td>-0.073</td>
<td>0.077</td>
<td>0.340</td>
<td>-0.077</td>
<td colspan="2">0.078</td>
<td colspan="2">0.320</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-3.213</td>
<td>0.166</td>
<td>0.000</td>
<td>-3.192</td>
<td>0.166</td>
<td>0.000</td>
<td>-3.221</td>
<td colspan="2">0.168</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-2.220</td>
<td>0.145</td>
<td>0.000</td>
<td>-2.204</td>
<td>0.145</td>
<td>0.000</td>
<td>-2.219</td>
<td colspan="2">0.146</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>-0.326</td>
<td>0.142</td>
<td>0.022</td>
<td>-0.321</td>
<td>0.142</td>
<td>0.024</td>
<td>-0.317</td>
<td colspan="2">0.143</td>
<td colspan="2">0.027</td>
</tr>
<tr class="even">
<td>C4</td>
<td>1.299</td>
<td>0.145</td>
<td>0.000</td>
<td>1.304</td>
<td>0.145</td>
<td>0.000</td>
<td>1.338</td>
<td colspan="2">0.146</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>-3.927</td>
<td>0.169</td>
<td>0.000</td>
<td>-3.887</td>
<td>0.169</td>
<td>0.000</td>
<td>-3.928</td>
<td colspan="2">0.170</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C6</td>
<td>-2.461</td>
<td>0.143</td>
<td>0.000</td>
<td>-2.439</td>
<td>0.143</td>
<td>0.000</td>
<td>-2.456</td>
<td colspan="2">0.144</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C7</td>
<td>-0.374</td>
<td>0.140</td>
<td>0.008</td>
<td>-0.366</td>
<td>0.140</td>
<td>0.009</td>
<td>-0.358</td>
<td colspan="2">0.142</td>
<td colspan="2">0.012</td>
</tr>
<tr class="even">
<td>C8</td>
<td>1.433</td>
<td>0.143</td>
<td>0.000</td>
<td>1.437</td>
<td>0.143</td>
<td>0.000</td>
<td>1.468</td>
<td colspan="2">0.145</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C9</td>
<td>-1.966</td>
<td>0.177</td>
<td>0.000</td>
<td>-1.933</td>
<td>0.175</td>
<td>0.000</td>
<td>-1.919</td>
<td colspan="2">0.178</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C10</td>
<td>-0.641</td>
<td>0.146</td>
<td>0.000</td>
<td>-0.625</td>
<td>0.145</td>
<td>0.000</td>
<td>-0.592</td>
<td colspan="2">0.147</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C11</td>
<td>1.057</td>
<td>0.145</td>
<td>0.000</td>
<td>1.062</td>
<td>0.145</td>
<td>0.000</td>
<td>1.102</td>
<td colspan="2">0.147</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C12</td>
<td>2.589</td>
<td>0.161</td>
<td>0.000</td>
<td>2.592</td>
<td>0.161</td>
<td>0.000</td>
<td>2.634</td>
<td colspan="2">0.163</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C13</td>
<td>-0.501</td>
<td>0.152</td>
<td>0.001</td>
<td>-0.490</td>
<td>0.152</td>
<td>0.001</td>
<td>-0.478</td>
<td colspan="2">0.154</td>
<td colspan="2">0.002</td>
</tr>
<tr class="even">
<td>YEAR</td>
<td>-0.063</td>
<td>0.018</td>
<td>0.001</td>
<td>-0.066</td>
<td>0.019</td>
<td>0.000</td>
<td>-0.066</td>
<td colspan="2">0.021</td>
<td colspan="2">0.002</td>
</tr>
<tr class="odd">
<td>ρ</td>
<td colspan="3" rowspan="3"></td>
<td>0.0017</td>
<td>.</td>
<td>.</td>
<td colspan="5"></td>
</tr>
<tr class="even">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3" rowspan="2"></td>
<td>0.109</td>
<td colspan="2">0.018</td>
<td colspan="2">.</td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Year</sub></td>
<td>0.043</td>
<td colspan="2">0.019</td>
<td colspan="2">.</td>
</tr>
</tbody>
</table>

**Table 3.5.1c Wald Test Statistics and (P-Value) Comparing Models fit
to IQI-19 (Hip Fracture Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | 1.473   | 3.396   |         | 1.557   | 3.440   |
|         |         |         |         |         |         |         |
|         |         | (1.000) | (1.000) |         | (1.000) | (1.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 1.178   |         | 2.391   | 1.252   |         | 2.509   |
|         |         |         |         |         |         |         |
|         | (1.000) |         | (1.000) | (1.000) |         | (1.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 2.614   | 2.332   |         | 2.696   | 2.470   |         |
| LMMIX** |         |         |         |         |         |         |
|         | (1.000) | (1.000) |         | (1.000) | (1.000) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** Wald Test uses the estimated covariance matrix from the model
listed in each row

### Provider-Level Model Predictions

Table 3.4.2 below provides the mean and standard deviation of
differences between model predictions (expected rates above the
diagonal, and risk-adjusted rates below the diagonal) from a random
sample of 50 providers within the NIS reference population for IQI 17.
The mean difference in expected rates and risk-adjusted rates was nearly
zero for all modeling approach pairwise comparisons -- despite the fact
that the GLMMIX modeling approaches identified statistically significant
variance components associated with the random effects.

**Table 3.5.2 Estimated Differences (and Standard Deviation) in
Provider-Level Model Predictions of Expected and Risk Adjusted Rates for
IQI-19**

**(Hip Fracture Mortality Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | -0.000  | -0.000  |         | -0.000  | -0.000  |
|         |         |         |         |         |         |         |
|         |         | (0.000) | (0.001) |         | (0.000) | (0.001) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 0.004   |         | 0.000   | 0.004   |         | 0.000   |
|         |         |         |         |         |         |         |
|         | (0.006) |         | (0.000) | (0.006) |         | (0.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 0.001   | -0.003  |         | 0.001   | -0.003  |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.005) | (0.005) |         | (0.005) | (0.006) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** In each 3x3 table above, Expected Rate Differences (and Standard
Deviations) are above the diagonal, and Adjusted Rate Differences (and
Standard Deviations) are below the diagonal.

## IQI 25 -- Bilateral Cardiac Catheterization Rate

### Model Parameter Estimates

Below we provide the model parameter estimates from fitting the simple
logistic regression, generalized estimating equations, and generalized
linear mixed model to the 2001-2003 Nationwide Inpatient Sample for IQI
25 (Bilateral Cardiac Catheterization Rate). Table 3.6.1a provides the
parameter estimates associated with the cross-sectional model, and Table
3.6.1b provides the parameter estimates associate with the model that
adjusts for a simple linear trend over time. Across these two tables, we
see that the parameter estimates and associated standard errors are
comparable, but with noticeable differences among the three modeling
approaches. The estimated correlation coefficient from the GEE modeling
approach was largest for this Quality Indicator (compared to the other
four QIs investigated), with ρ=0.0412 in the cross-sectional and
ρ=0.0405 in the time-trend adjusted model. The estimated variance
components associated with provider-specific random effects from the
GLIMMIX model were also comparatively larger, and statistically
significant in both models (σ^2^~Btw\ Hosp~ = 0.779 for the cross
sectional model, and 0.766 for the time-trend model). The variance
component that captures provider-specific variation in the time-trend
slope was statistically significant (σ^2^~Year~ = 0.031).

The effect of the *YEAR* parameter (which captures the trend over time)
was highly significant for all three modeling approaches, as seen in
Table 3.6.1b below.

Table 3.6.1c provides the Wald Statistics to determine whether there are
statistically significant differences between the vector of parameter
estimates generated by each modeling approach. The Wald Statistics
consider pair-wise comparisons, and suggest that there were highly
significant differences between the different modeling approaches for
IQI 25.

**Table 3.6.1a Parameter Estimates from Cross Sectional Models fit to
IQI-25 (Bilateral Cardiac Catheterization Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 0%" />
<col style="width: 8%" />
<col style="width: 0%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="5"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td colspan="2"><strong>Estimate</strong></td>
<td colspan="2"><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.820</td>
<td>0.038</td>
<td>0.000</td>
<td>-1.871</td>
<td>0.042</td>
<td>0.000</td>
<td>-2.169</td>
<td colspan="2">0.050</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>-0.115</td>
<td>0.036</td>
<td>0.001</td>
<td>-0.121</td>
<td>0.036</td>
<td>0.001</td>
<td>-0.127</td>
<td colspan="2">0.038</td>
<td colspan="2">0.001</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-0.307</td>
<td>0.214</td>
<td>0.152</td>
<td>-0.283</td>
<td>0.209</td>
<td>0.174</td>
<td>-0.273</td>
<td colspan="2">0.222</td>
<td colspan="2">0.219</td>
</tr>
<tr class="even">
<td>AGE2</td>
<td>-0.556</td>
<td>0.158</td>
<td>0.000</td>
<td>-0.465</td>
<td>0.150</td>
<td>0.002</td>
<td>-0.499</td>
<td colspan="2">0.163</td>
<td colspan="2">0.002</td>
</tr>
<tr class="odd">
<td>AGE3</td>
<td>-0.829</td>
<td>0.089</td>
<td>0.000</td>
<td>-0.687</td>
<td>0.083</td>
<td>0.000</td>
<td>-0.751</td>
<td colspan="2">0.092</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE4</td>
<td>-0.964</td>
<td>0.061</td>
<td>0.000</td>
<td>-0.830</td>
<td>0.058</td>
<td>0.000</td>
<td>-0.907</td>
<td colspan="2">0.063</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE5</td>
<td>-0.903</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.771</td>
<td>0.041</td>
<td>0.000</td>
<td>-0.840</td>
<td colspan="2">0.044</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE6</td>
<td>-0.850</td>
<td>0.036</td>
<td>0.000</td>
<td>-0.722</td>
<td>0.035</td>
<td>0.000</td>
<td>-0.787</td>
<td colspan="2">0.037</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE7</td>
<td>-0.765</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.640</td>
<td>0.032</td>
<td>0.000</td>
<td>-0.694</td>
<td colspan="2">0.034</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE8</td>
<td>-0.591</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.500</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.537</td>
<td colspan="2">0.033</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE9</td>
<td>-0.472</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.385</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.410</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-0.308</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.238</td>
<td>0.029</td>
<td>0.000</td>
<td>-0.248</td>
<td colspan="2">0.031</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-0.212</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.153</td>
<td>0.029</td>
<td>0.000</td>
<td>-0.155</td>
<td colspan="2">0.031</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-0.072</td>
<td>0.030</td>
<td>0.015</td>
<td>-0.037</td>
<td>0.029</td>
<td>0.202</td>
<td>-0.031</td>
<td colspan="2">0.031</td>
<td colspan="2">0.315</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>0.002</td>
<td>0.031</td>
<td>0.941</td>
<td>0.021</td>
<td>0.031</td>
<td>0.492</td>
<td>0.029</td>
<td colspan="2">0.033</td>
<td colspan="2">0.367</td>
</tr>
<tr class="even">
<td>AGE15</td>
<td>0.555</td>
<td>0.366</td>
<td>0.129</td>
<td>0.469</td>
<td>0.364</td>
<td>0.197</td>
<td>0.462</td>
<td colspan="2">0.385</td>
<td colspan="2">0.230</td>
</tr>
<tr class="odd">
<td>AGE16</td>
<td>0.473</td>
<td>0.259</td>
<td>0.067</td>
<td>0.456</td>
<td>0.247</td>
<td>0.065</td>
<td>0.492</td>
<td colspan="2">0.267</td>
<td colspan="2">0.066</td>
</tr>
<tr class="even">
<td>AGE17</td>
<td>0.251</td>
<td>0.165</td>
<td>0.128</td>
<td>0.239</td>
<td>0.154</td>
<td>0.120</td>
<td>0.268</td>
<td colspan="2">0.170</td>
<td colspan="2">0.116</td>
</tr>
<tr class="odd">
<td>AGE18</td>
<td>0.277</td>
<td>0.104</td>
<td>0.008</td>
<td>0.283</td>
<td>0.097</td>
<td>0.004</td>
<td>0.302</td>
<td colspan="2">0.107</td>
<td colspan="2">0.005</td>
</tr>
<tr class="even">
<td>AGE19</td>
<td>0.278</td>
<td>0.070</td>
<td>0.000</td>
<td>0.297</td>
<td>0.065</td>
<td>0.000</td>
<td>0.323</td>
<td colspan="2">0.072</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE20</td>
<td>0.299</td>
<td>0.056</td>
<td>0.000</td>
<td>0.295</td>
<td>0.053</td>
<td>0.000</td>
<td>0.321</td>
<td colspan="2">0.058</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE21</td>
<td>0.221</td>
<td>0.049</td>
<td>0.000</td>
<td>0.210</td>
<td>0.048</td>
<td>0.000</td>
<td>0.229</td>
<td colspan="2">0.051</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE22</td>
<td>0.126</td>
<td>0.046</td>
<td>0.006</td>
<td>0.148</td>
<td>0.045</td>
<td>0.001</td>
<td>0.160</td>
<td colspan="2">0.048</td>
<td colspan="2">0.001</td>
</tr>
<tr class="even">
<td>AGE23</td>
<td>0.152</td>
<td>0.044</td>
<td>0.001</td>
<td>0.162</td>
<td>0.043</td>
<td>0.000</td>
<td>0.177</td>
<td colspan="2">0.046</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>0.057</td>
<td>0.043</td>
<td>0.180</td>
<td>0.079</td>
<td>0.042</td>
<td>0.059</td>
<td>0.084</td>
<td colspan="2">0.045</td>
<td colspan="2">0.059</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>0.070</td>
<td>0.042</td>
<td>0.094</td>
<td>0.084</td>
<td>0.041</td>
<td>0.039</td>
<td>0.089</td>
<td colspan="2">0.043</td>
<td colspan="2">0.041</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>0.034</td>
<td>0.041</td>
<td>0.408</td>
<td>0.055</td>
<td>0.040</td>
<td>0.173</td>
<td>0.058</td>
<td colspan="2">0.043</td>
<td colspan="2">0.175</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.045</td>
<td>0.043</td>
<td>0.300</td>
<td>-0.022</td>
<td>0.042</td>
<td>0.601</td>
<td>-0.028</td>
<td colspan="2">0.045</td>
<td colspan="2">0.543</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-1.333</td>
<td>0.063</td>
<td>0.000</td>
<td>-1.119</td>
<td>0.058</td>
<td>0.000</td>
<td>-1.263</td>
<td colspan="2">0.064</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-0.980</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.822</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.916</td>
<td colspan="2">0.036</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>-0.123</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.079</td>
<td>0.032</td>
<td>0.014</td>
<td>-0.088</td>
<td colspan="2">0.034</td>
<td colspan="2">0.011</td>
</tr>
<tr class="even">
<td>C4</td>
<td>0.218</td>
<td>0.041</td>
<td>0.000</td>
<td>0.275</td>
<td>0.039</td>
<td>0.000</td>
<td>0.298</td>
<td colspan="2">0.043</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>-1.340</td>
<td>0.032</td>
<td>0.000</td>
<td>-1.191</td>
<td>0.035</td>
<td>0.000</td>
<td>-1.319</td>
<td colspan="2">0.034</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C6</td>
<td>-0.658</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.576</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.634</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C7</td>
<td>0.159</td>
<td>0.035</td>
<td>0.000</td>
<td>0.169</td>
<td>0.034</td>
<td>0.000</td>
<td>0.177</td>
<td colspan="2">0.036</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C8</td>
<td>0.548</td>
<td>0.054</td>
<td>0.000</td>
<td>0.544</td>
<td>0.052</td>
<td>0.000</td>
<td>0.570</td>
<td colspan="2">0.056</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C9</td>
<td>-1.019</td>
<td>0.049</td>
<td>0.000</td>
<td>-0.939</td>
<td>0.048</td>
<td>0.000</td>
<td>-1.033</td>
<td colspan="2">0.050</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C10</td>
<td>-0.451</td>
<td>0.035</td>
<td>0.000</td>
<td>-0.379</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.415</td>
<td colspan="2">0.036</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C11</td>
<td>0.268</td>
<td>0.037</td>
<td>0.000</td>
<td>0.307</td>
<td>0.036</td>
<td>0.000</td>
<td>0.343</td>
<td colspan="2">0.038</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C12</td>
<td>0.836</td>
<td>0.041</td>
<td>0.000</td>
<td>0.860</td>
<td>0.040</td>
<td>0.000</td>
<td>0.947</td>
<td colspan="2">0.043</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C13</td>
<td>0.638</td>
<td>0.039</td>
<td>0.000</td>
<td>0.625</td>
<td>0.038</td>
<td>0.000</td>
<td>0.681</td>
<td colspan="2">0.041</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C14</td>
<td>0.491</td>
<td>0.037</td>
<td>0.000</td>
<td>0.502</td>
<td>0.036</td>
<td>0.000</td>
<td>0.555</td>
<td colspan="2">0.038</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C15</td>
<td>0.921</td>
<td>0.031</td>
<td>0.000</td>
<td>0.907</td>
<td>0.031</td>
<td>0.000</td>
<td>0.995</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C16</td>
<td>1.032</td>
<td>0.053</td>
<td>0.000</td>
<td>1.028</td>
<td>0.052</td>
<td>0.000</td>
<td>1.128</td>
<td colspan="2">0.055</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C17</td>
<td>-0.954</td>
<td>0.032</td>
<td>0.000</td>
<td>-0.933</td>
<td>0.033</td>
<td>0.000</td>
<td>-1.014</td>
<td colspan="2">0.033</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C18</td>
<td>-0.308</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.282</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.309</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C19</td>
<td>0.214</td>
<td>0.036</td>
<td>0.000</td>
<td>0.202</td>
<td>0.036</td>
<td>0.000</td>
<td>0.219</td>
<td colspan="2">0.038</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C20</td>
<td>0.628</td>
<td>0.080</td>
<td>0.000</td>
<td>0.612</td>
<td>0.079</td>
<td>0.000</td>
<td>0.652</td>
<td colspan="2">0.084</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C21</td>
<td>-0.068</td>
<td>0.028</td>
<td>0.017</td>
<td>-0.008</td>
<td>0.028</td>
<td>0.761</td>
<td>-0.010</td>
<td colspan="2">0.030</td>
<td colspan="2">0.738</td>
</tr>
<tr class="even">
<td>ρ</td>
<td colspan="3" rowspan="2"></td>
<td>0.0412</td>
<td>.</td>
<td>.</td>
<td colspan="5"></td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3"></td>
<td>0.779</td>
<td colspan="2">0.041</td>
<td colspan="2">.</td>
</tr>
</tbody>
</table>

**Table 3.6.1b Parameter Estimates from Time Trend Models fit to IQI-25
(Bilateral Cardiac Catheterization Rate)**

<table style="width:100%;">
<colgroup>
<col style="width: 12%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 0%" />
<col style="width: 8%" />
<col style="width: 0%" />
<col style="width: 9%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Parameter</strong></td>
<td colspan="3"><strong>Simple Logistic Regression Model</strong></td>
<td colspan="3"><strong>Generalized Estimating Equations
Model</strong></td>
<td colspan="5"><p><strong>Generalized Linear</strong></p>
<p><strong>Mixed Model</strong></p></td>
</tr>
<tr class="even">
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td><strong>Estimate</strong></td>
<td><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
<td colspan="2"><strong>Estimate</strong></td>
<td colspan="2"><strong>Std Err</strong></td>
<td><strong>p value</strong></td>
</tr>
<tr class="odd">
<td>Intercept</td>
<td>-1.817</td>
<td>0.038</td>
<td>0.000</td>
<td>-1.870</td>
<td>0.042</td>
<td>0.000</td>
<td>-2.167</td>
<td colspan="2">0.050</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>SEX</td>
<td>-0.116</td>
<td>0.036</td>
<td>0.001</td>
<td>-0.122</td>
<td>0.036</td>
<td>0.001</td>
<td>-0.130</td>
<td colspan="2">0.038</td>
<td colspan="2">0.001</td>
</tr>
<tr class="odd">
<td>AGE1</td>
<td>-0.298</td>
<td>0.215</td>
<td>0.165</td>
<td>-0.277</td>
<td>0.209</td>
<td>0.184</td>
<td>-0.263</td>
<td colspan="2">0.222</td>
<td colspan="2">0.236</td>
</tr>
<tr class="even">
<td>AGE2</td>
<td>-0.549</td>
<td>0.158</td>
<td>0.001</td>
<td>-0.464</td>
<td>0.150</td>
<td>0.002</td>
<td>-0.499</td>
<td colspan="2">0.163</td>
<td colspan="2">0.002</td>
</tr>
<tr class="odd">
<td>AGE3</td>
<td>-0.824</td>
<td>0.089</td>
<td>0.000</td>
<td>-0.688</td>
<td>0.083</td>
<td>0.000</td>
<td>-0.755</td>
<td colspan="2">0.092</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE4</td>
<td>-0.963</td>
<td>0.061</td>
<td>0.000</td>
<td>-0.832</td>
<td>0.058</td>
<td>0.000</td>
<td>-0.908</td>
<td colspan="2">0.063</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE5</td>
<td>-0.901</td>
<td>0.043</td>
<td>0.000</td>
<td>-0.773</td>
<td>0.041</td>
<td>0.000</td>
<td>-0.844</td>
<td colspan="2">0.044</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE6</td>
<td>-0.847</td>
<td>0.036</td>
<td>0.000</td>
<td>-0.723</td>
<td>0.035</td>
<td>0.000</td>
<td>-0.788</td>
<td colspan="2">0.037</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE7</td>
<td>-0.764</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.642</td>
<td>0.032</td>
<td>0.000</td>
<td>-0.696</td>
<td colspan="2">0.034</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE8</td>
<td>-0.589</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.500</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.539</td>
<td colspan="2">0.033</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE9</td>
<td>-0.470</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.386</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.411</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE10</td>
<td>-0.308</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.240</td>
<td>0.029</td>
<td>0.000</td>
<td>-0.250</td>
<td colspan="2">0.031</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE11</td>
<td>-0.213</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.154</td>
<td>0.029</td>
<td>0.000</td>
<td>-0.157</td>
<td colspan="2">0.031</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE12</td>
<td>-0.072</td>
<td>0.030</td>
<td>0.015</td>
<td>-0.038</td>
<td>0.029</td>
<td>0.190</td>
<td>-0.032</td>
<td colspan="2">0.031</td>
<td colspan="2">0.298</td>
</tr>
<tr class="odd">
<td>AGE13</td>
<td>0.003</td>
<td>0.031</td>
<td>0.935</td>
<td>0.020</td>
<td>0.031</td>
<td>0.503</td>
<td>0.028</td>
<td colspan="2">0.033</td>
<td colspan="2">0.384</td>
</tr>
<tr class="even">
<td>AGE15</td>
<td>0.568</td>
<td>0.366</td>
<td>0.121</td>
<td>0.475</td>
<td>0.365</td>
<td>0.192</td>
<td>0.462</td>
<td colspan="2">0.385</td>
<td colspan="2">0.230</td>
</tr>
<tr class="odd">
<td>AGE16</td>
<td>0.475</td>
<td>0.259</td>
<td>0.066</td>
<td>0.458</td>
<td>0.248</td>
<td>0.064</td>
<td>0.504</td>
<td colspan="2">0.267</td>
<td colspan="2">0.060</td>
</tr>
<tr class="even">
<td>AGE17</td>
<td>0.250</td>
<td>0.165</td>
<td>0.130</td>
<td>0.239</td>
<td>0.154</td>
<td>0.121</td>
<td>0.275</td>
<td colspan="2">0.170</td>
<td colspan="2">0.106</td>
</tr>
<tr class="odd">
<td>AGE18</td>
<td>0.279</td>
<td>0.104</td>
<td>0.008</td>
<td>0.286</td>
<td>0.097</td>
<td>0.003</td>
<td>0.301</td>
<td colspan="2">0.108</td>
<td colspan="2">0.005</td>
</tr>
<tr class="even">
<td>AGE19</td>
<td>0.281</td>
<td>0.070</td>
<td>0.000</td>
<td>0.298</td>
<td>0.065</td>
<td>0.000</td>
<td>0.328</td>
<td colspan="2">0.072</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE20</td>
<td>0.301</td>
<td>0.056</td>
<td>0.000</td>
<td>0.297</td>
<td>0.054</td>
<td>0.000</td>
<td>0.323</td>
<td colspan="2">0.058</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>AGE21</td>
<td>0.222</td>
<td>0.049</td>
<td>0.000</td>
<td>0.211</td>
<td>0.048</td>
<td>0.000</td>
<td>0.232</td>
<td colspan="2">0.051</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE22</td>
<td>0.127</td>
<td>0.046</td>
<td>0.006</td>
<td>0.149</td>
<td>0.045</td>
<td>0.001</td>
<td>0.163</td>
<td colspan="2">0.048</td>
<td colspan="2">0.001</td>
</tr>
<tr class="even">
<td>AGE23</td>
<td>0.154</td>
<td>0.044</td>
<td>0.001</td>
<td>0.163</td>
<td>0.043</td>
<td>0.000</td>
<td>0.179</td>
<td colspan="2">0.046</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>AGE24</td>
<td>0.058</td>
<td>0.043</td>
<td>0.175</td>
<td>0.080</td>
<td>0.042</td>
<td>0.056</td>
<td>0.086</td>
<td colspan="2">0.045</td>
<td colspan="2">0.053</td>
</tr>
<tr class="even">
<td>AGE25</td>
<td>0.070</td>
<td>0.042</td>
<td>0.090</td>
<td>0.084</td>
<td>0.041</td>
<td>0.038</td>
<td>0.091</td>
<td colspan="2">0.043</td>
<td colspan="2">0.037</td>
</tr>
<tr class="odd">
<td>AGE26</td>
<td>0.034</td>
<td>0.041</td>
<td>0.408</td>
<td>0.055</td>
<td>0.040</td>
<td>0.172</td>
<td>0.060</td>
<td colspan="2">0.043</td>
<td colspan="2">0.165</td>
</tr>
<tr class="even">
<td>AGE27</td>
<td>-0.045</td>
<td>0.043</td>
<td>0.303</td>
<td>-0.022</td>
<td>0.043</td>
<td>0.610</td>
<td>-0.026</td>
<td colspan="2">0.045</td>
<td colspan="2">0.573</td>
</tr>
<tr class="odd">
<td>C1</td>
<td>-1.343</td>
<td>0.063</td>
<td>0.000</td>
<td>-1.122</td>
<td>0.058</td>
<td>0.000</td>
<td>-1.266</td>
<td colspan="2">0.064</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C2</td>
<td>-0.987</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.826</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.919</td>
<td colspan="2">0.036</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C3</td>
<td>-0.128</td>
<td>0.033</td>
<td>0.000</td>
<td>-0.081</td>
<td>0.032</td>
<td>0.011</td>
<td>-0.090</td>
<td colspan="2">0.034</td>
<td colspan="2">0.009</td>
</tr>
<tr class="even">
<td>C4</td>
<td>0.215</td>
<td>0.041</td>
<td>0.000</td>
<td>0.273</td>
<td>0.040</td>
<td>0.000</td>
<td>0.298</td>
<td colspan="2">0.043</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C5</td>
<td>-1.345</td>
<td>0.032</td>
<td>0.000</td>
<td>-1.192</td>
<td>0.035</td>
<td>0.000</td>
<td>-1.320</td>
<td colspan="2">0.034</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C6</td>
<td>-0.660</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.576</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.632</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C7</td>
<td>0.158</td>
<td>0.035</td>
<td>0.000</td>
<td>0.169</td>
<td>0.034</td>
<td>0.000</td>
<td>0.177</td>
<td colspan="2">0.036</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C8</td>
<td>0.544</td>
<td>0.054</td>
<td>0.000</td>
<td>0.542</td>
<td>0.053</td>
<td>0.000</td>
<td>0.570</td>
<td colspan="2">0.056</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C9</td>
<td>-1.026</td>
<td>0.049</td>
<td>0.000</td>
<td>-0.942</td>
<td>0.048</td>
<td>0.000</td>
<td>-1.035</td>
<td colspan="2">0.050</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C10</td>
<td>-0.459</td>
<td>0.035</td>
<td>0.000</td>
<td>-0.382</td>
<td>0.034</td>
<td>0.000</td>
<td>-0.417</td>
<td colspan="2">0.036</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C11</td>
<td>0.267</td>
<td>0.037</td>
<td>0.000</td>
<td>0.307</td>
<td>0.036</td>
<td>0.000</td>
<td>0.344</td>
<td colspan="2">0.038</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C12</td>
<td>0.836</td>
<td>0.041</td>
<td>0.000</td>
<td>0.861</td>
<td>0.040</td>
<td>0.000</td>
<td>0.949</td>
<td colspan="2">0.043</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C13</td>
<td>0.633</td>
<td>0.039</td>
<td>0.000</td>
<td>0.623</td>
<td>0.039</td>
<td>0.000</td>
<td>0.682</td>
<td colspan="2">0.041</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C14</td>
<td>0.489</td>
<td>0.037</td>
<td>0.000</td>
<td>0.501</td>
<td>0.036</td>
<td>0.000</td>
<td>0.555</td>
<td colspan="2">0.038</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C15</td>
<td>0.920</td>
<td>0.031</td>
<td>0.000</td>
<td>0.907</td>
<td>0.031</td>
<td>0.000</td>
<td>0.995</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C16</td>
<td>1.034</td>
<td>0.053</td>
<td>0.000</td>
<td>1.030</td>
<td>0.052</td>
<td>0.000</td>
<td>1.129</td>
<td colspan="2">0.055</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C17</td>
<td>-0.962</td>
<td>0.032</td>
<td>0.000</td>
<td>-0.936</td>
<td>0.033</td>
<td>0.000</td>
<td>-1.017</td>
<td colspan="2">0.033</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C18</td>
<td>-0.313</td>
<td>0.031</td>
<td>0.000</td>
<td>-0.285</td>
<td>0.030</td>
<td>0.000</td>
<td>-0.311</td>
<td colspan="2">0.032</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C19</td>
<td>0.212</td>
<td>0.036</td>
<td>0.000</td>
<td>0.201</td>
<td>0.036</td>
<td>0.000</td>
<td>0.219</td>
<td colspan="2">0.038</td>
<td colspan="2">0.000</td>
</tr>
<tr class="even">
<td>C20</td>
<td>0.626</td>
<td>0.080</td>
<td>0.000</td>
<td>0.612</td>
<td>0.079</td>
<td>0.000</td>
<td>0.648</td>
<td colspan="2">0.084</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>C21</td>
<td>-0.069</td>
<td>0.028</td>
<td>0.014</td>
<td>-0.009</td>
<td>0.028</td>
<td>0.755</td>
<td>-0.009</td>
<td colspan="2">0.030</td>
<td colspan="2">0.753</td>
</tr>
<tr class="even">
<td>YEAR</td>
<td>-0.073</td>
<td>0.005</td>
<td>0.000</td>
<td>-0.072</td>
<td>0.007</td>
<td>0.000</td>
<td>-0.077</td>
<td colspan="2">0.016</td>
<td colspan="2">0.000</td>
</tr>
<tr class="odd">
<td>ρ</td>
<td colspan="3" rowspan="3"></td>
<td>0.0405</td>
<td>.</td>
<td>.</td>
<td colspan="5"></td>
</tr>
<tr class="even">
<td>σ<sup>2</sup><sub>Hosp</sub></td>
<td colspan="3" rowspan="2"></td>
<td>0.766</td>
<td colspan="2">0.042</td>
<td colspan="2">.</td>
</tr>
<tr class="odd">
<td>σ<sup>2</sup><sub>Year</sub></td>
<td>0.031</td>
<td colspan="2">0.007</td>
<td colspan="2"></td>
</tr>
</tbody>
</table>

**Table 3.6.1c Wald Test Statistics and (P-Value) Comparing Models fit
to IQI-25 (Bilateral Cardiac Catheterization Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | 466.78  | 4037.6  |         | 457.86  | 4035.7  |
|         |         |         |         |         |         |         |
|         |         | (0.000) | (0.000) |         | (0.000) | (0.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 146.63  |         | 213.69  | 145.58  |         | 214.20  |
|         |         |         |         |         |         |         |
|         | (0.000) |         | (0.000) | (0.000) |         | (0.000) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | 158.45  | 309.24  |         | 155.51  | 308.95  |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.000) | (0.000) |         | (0.000) | (0.000) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** Wald Test uses the estimated covariance matrix from the model
listed in each row

### Provider-Level Model Predictions

Table 3.6.2 below provides the mean and standard deviation of
differences between model predictions (expected rates above the
diagonal, and risk-adjusted rates below the diagonal) from a random
sample of 50 providers within the NIS reference population for IQI 17.
For example, the mean difference in expected rates between the GEE and
GLMMIX approaches for the cross sectional model was -0.016 (relative to
a national mean response rate of 0.076 from Table 3.1). This estimated
difference is quite high relative to the national mean response rate,
demonstrating that model choice could have a significant effect on
provider-level estimates.

Mean differences (and standard deviations) attributable to model
specification (simple logistic vs GEE vs GLMMIX) for the risk-adjusted
rates appear to be higher than the expected rates.

**Table 3.6.2 Estimated Differences (and Standard Deviation) in
Provider-Level Model Predictions of Expected and Risk Adjusted Rates for
IQI-25**

**(Bilateral Cardiac Catheterization Rate)**

+---------+---------+---------+---------+---------+---------+---------+
|         | **Cross |         |         | **Time  |         |         |
|         | Se      |         |         | Trend   |         |         |
|         | ctional |         |         | Model** |         |         |
|         | Model** |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | **SLR** | **GEE** | **G     | **SLR** | **GEE** | **G     |
|         |         |         | LMMIX** |         |         | LMMIX** |
+---------+---------+---------+---------+---------+---------+---------+
| **SLR** |         | -0.005  | 0.016   |         | -0.005  | 0.016   |
|         |         |         |         |         |         |         |
|         |         | (0.003) | (0.006) |         | (0.003) | (0.006) |
+---------+---------+---------+---------+---------+---------+---------+
| **GEE** | 0.008   |         | 0.021   | 0.008   |         | 0.021   |
|         |         |         |         |         |         |         |
|         | (0.008) |         | (0.003) | (0.007) |         | (0.003) |
+---------+---------+---------+---------+---------+---------+---------+
| **G     | -0.036  | -0.044  |         | -0.036  | -0.044  |         |
| LMMIX** |         |         |         |         |         |         |
|         | (0.044) | (0.049) |         | (0.045) | (0.051) |         |
+---------+---------+---------+---------+---------+---------+---------+

**\*** In each 3x3 table above, Expected Rate Differences (and Standard
Deviations) are above the diagonal, and Adjusted Rate Differences (and
Standard Deviations) are below the diagonal.

# Conclusions

This Section will be written after receiving comment and input from the
workgroup participants. Some general conclusions are as follows:

-   The potential effects of positive correlation among patients within
    the same hospital caused significant differences in the vector of
    parameter estimates in 2 of the five QI's selected for this
    investigation.

-   The simple adjustment for a linear trend over time resulted in a
    highly significant negative slope for all QI's investigated.

-   For 4 of the 5 QI's investigated, a change in the modeling approach
    did not create a meaningful difference in the expected rates
    (relative to the National mean response).

    -   However, in many cases, the differences in provider-level
        estimates of expected and risk-adjusted rates between the
        modeling approaches were significantly different than zero based
        on the random samples of 50 providers. This is suggestive of a
        subtle, yet statistically significant bias.

-   In some cases, there were significant differences between the GEE
    and GLMMIX approaches. These differences need to be more carefully
    investigated -- in order to make a more definitive recommendation on
    the appropriate methodology to recommend for adjusting the models.

-   Additional work could be done to exploit the potential added benefit
    of the distribution of random effects (from the GLMMIX modeling
    approach) to allow providers to assess where they might be located
    within the National distribution of providers (rather than a simple
    comparison of whether they are above or below the National mean
    response).

# Continuing Investigations

While the workgroup participants are reviewing this draft report,
Battelle will continue work on this investigation in the following
areas:

1.  Create Wald-Statistics based on the GEE and GLMMIX robust variance
    covariance matrices

2.  Provide a descriptive and graphical summary of the distribution of
    estimated random effects intercepts (and slopes) from the GLMMIX
    cross sectional and time-trend models.

3.  Assess model fit -- particularly for situations in which there are
    statistically significant differences between the GEE and GLMMIX
    approaches.

4.  Provide more specifics on the use of the random effects to identify
    where a provider is located within the national distribution of
    providers.

> **References**
>
> AHRQ (2005) Guide to Prevention Quality Indicators. Technical Report
> published by the U.S. Department of Health and Human Services Agency
> for Healthcare Research and Quality, accessed on 8/28/06 at
> [http://www.qualityindicators.ahrq.gov](http://www.qualityindicators.ahrq.gov/)
>
> McCullagh, P. & Nelder, J.A. (1989) Generalized Linear Models. 2^nd^
> edition. London: Chapman and Hall.
>
> Liang, K.Y. & Zeger, S.L. (1986) Longitudinal data analysis using
> generalized linear models. Biometrika. 73:13-22.
>
> Royall, R.M. (1986) Model robust inference using maximum likelihood
> estimators. International Statistical Review. 54:221-226.
>
> Zeger, S.L. & Liang, K.Y. (1986) Longitudinal data analysis for
> discrete and continuous outcomes. Biometrics. 42:121-130.
>
> Fitzmaurice, G.M., Laird, N.M., and Ware, J.H. (2004) Applied
> longitudinal analysis. John Wiley and Sons.
>
> **Risk Adjustment and Hierarchical Modeling Workgroup**
>
> **Workgroup Members**
>
> Dan R. Berlowitz, Bedford Veterans Affairs Medical Center
>
> Cheryl L. Damberg, Pacific Business Group on Health
>
> R. Adams Dudley, Institute for Health Policy Studies, UCSF
>
> Marc Nathan Elliott, RAND
>
> Byron J. Gajewski, University of Kansas Medical Center
>
> Andrew L. Kosseff, Medical Director of System Clinical Improvement,
> SSM Health Care
>
> John Muldoon, National Association of Children's Hospitals and Related
> Institutions
>
> Sharon-Lise Teresa Normand, Department of Health Care Policy Harvard
> Medical School
>
> Richard J. Snow, Doctors Hospital, OhioHealth
>
> **Liaison Members**
>
> Simon P. Cohn, National Committee on Vital and Health Statistics
> (Kaiser Permanente)
>
> Donald A. Goldmann, Institute for Healthcare Improvement
>
> Andrew D. Hackbarth, Institute for Healthcare Improvement
>
> Lein Han, Centers for Medicare & Medicaid Services
>
> Amy Rosen, Bedford Veterans Affairs Medical Center
>
> Stephen Schmaltz, Joint Commission on Accreditation of Healthcare
> Organizations
>
> **Technical Advisors**
>
> Rich Averill, 3M
>
> Robert Baskin, AHRQ
>
> Norbert Goldfield, 3M
>
> Bob Houchens, Medstat
>
> Eugene A. Kroch, Institute for Healthcare Improvement Technical
> Advisor (Carescience)
>
> **AHRQ QI Support Team**
>
> Agency for Healthcare Research and Quality:
>
> Mamatha Pancholi
>
> Marybeth Farquhar
>
> Battelle Memorial Institute:
>
> Warren Strauss
>
> Jyothi Nagaraja
>
> Jeffrey Geppert
>
> Theresa Schaaf