Synthesis of "Statistical Innovations for Cost-Effectiveness Analysis"

Agency for Healthcare Research and Quality Working Paper No. 08002 January 2008

Suggested citation: . Synthesis of "Statistical Innovations for Cost-Effectiveness Analysis".

Agency for Healthcare Research and Quality Working Paper No. 08002, January 2008,

http://gold.ahrq.gov.

AHRQ Working Papers provide preliminary analysis of substantive, technical, and methodological

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Synthesis of “Statistical Innovations for Cost Effectiveness Analysis” 

Translating Research into Policy and Practice (TRIPP) 

Melford J. Henderson 

January 2008 

ABSTRACT 

Cost-effectiveness analysis (CEA) has been promoted as a useful tool in the effort to prioritize 

expenditures on health care programs. By quantifying the trade-offs between resources that need 

to be deployed and health benefits that accrue from use of alternative interventions, CEA offers 

guidance in decision-making by structuring comparisons between these interventions. The core 

of Dr. Gardiner's research was the recognition that both costs and benefits were stochastic in 

nature and thus summary measures such as the cost-effectiveness ratio would have inherent 

variability that should be quantified. His research was also designed to produce new and more 

advanced statistical models that improve the assessment of costs and patient outcomes. 

Melford J. Henderson 

Agency for Healthcare Research and Quality 

Division of Socio-Economic Research 

Center for Financing, Access, and Cost Trends 

540 Gaither Road 

Rockville, MD 20850 

Melford.Henderson@ahrq.hhs.gov 

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Synthesis of “Statistical Innovations for Cost Effectiveness Analysis” 

Translating Research into Policy and Practice (TRIPP) 

EXECUTIVE SUMMARY 

The Agency for Healthcare Research and Quality (AHRQ) continues to be a leader in 

advancing the use and science of cost-effectiveness analysis (CEA) in health care. AHRQ 

supports extramural research in CEA and advances the science of clinical economic evaluation. 

AHRQ has also acted as a facilitator for other agencies within the Federal Government to 

develop and use CEA for the enhancement of their goals and objectives. During the period of 

1997-2003, Dr. Joseph Gardiner, Ph.D., of Michigan State University, College of Human 

Medicine, was awarded an original grant and continuation to study "Statistical Innovations for 

Cost-Effectiveness Analysis" (AHRQ Grant Number HS09514). The major goals of this 

research were to develop new statistical models and methods that fill methodological gaps, and 

resolve inconsistencies in current cost-effectiveness analysis. 

The purpose of this manuscript was to synthesize Dr. Gardiner's research developments 

related to Translating Research into Policy and Practice (TRIPP). As a result of developing and 

testing new methods and models for cost-effectiveness studies, and demonstrating their 

application in several ongoing clinical studies, this research not only offers an array of promising 

techniques, but also bridges the gap between methodological development and implementation. 

All statistical derivations such as equations and formulae were omitted in an effort to synthesize 

and highlight significant and relevant research findings, and applications related to TRIPP. 

Cost-effectiveness analysis (CEA) has been promoted as a useful tool in the effort to 

prioritize expenditures on health care programs. By quantifying the trade-offs between resources 

3
 
 

that need to be deployed and health benefits that accrue from use of alternative interventions, 

CEA offers guidance in decision-making by structuring comparisons between these 

interventions. The core of Dr. Gardiner’s research was the recognition that both costs and 

benefits were stochastic in nature and thus summary measures such as the cost-effectiveness 

ratio would have inherent variability that should be quantified. His research was also designed to 

produce new and more advanced statistical models that improve the assessment of costs and 

patient outcomes. 

The specific aims of their research were: 

1. To specify stochastic models for costs and health outcome measures; 

2. To assess the development of new models and procedures; 

3. To test and validate statistical procedures; and 

4. To apply and test procedures on existing data sets. 

Markov models provide a natural setting to describe the evolution of event histories of 

patients through different health states. They are used in clinical decision analyses and costeffectiveness analyses. Using this longitudinal framework, Gardiner et al describe stochastic 

models that reflect the experience of patients in sustained and changing states of health. Costs are 

engendered at random amounts at random points in time during the course of a health care 

intervention. By compiling these expenditure streams at the individual level into costs per unit 

time of sojourn in a health state, and in transition between health states, Gardiner et al were able 

to estimate the distribution of present value of all expenditures, and summary statistics such as 

mean and median costs. They then estimated health outcome measures such as life expectancy, 

median survival and survival rates, all discounted where appropriate at a constant rate and 

adjusted for quality of life. 

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With AHRQ’s support, the research team led by Dr. Gardiner identified major 

problematic areas in CEA and has taken several steps in addressing these issues. 

•	 Despite the rapid development of techniques for conducting economic evaluation studies 

in medicine and health, the statistical methodology to support these studies is in the 

developmental stages. Gardiner's research formulates statistical models that inform 

identification of patient characteristics and resource-use elements that influence both 

costs and outcomes. 

•	 Recognizing the natural setting in which cost and health outcomes would manifest over 

time, his current research addresses development of longitudinal models that incorporate 

covariate information and permit estimation of their impact on summary measures such 

as the cost-effectiveness ratio (CER) and net health cost (NHC). 

•	 Gardiner's interdisciplinary team of statisticians, health economists, health services 

researchers and clinical investigators has built a repertoire of publications addressing 

both applied and methodological issues in CEA. 

•	 Many methodological developments are theoretically sound and can be tested on 

simulated data. In practice, these sophisticated methods have limited use unless they 

address the inherent problems in data sets commonly available to researchers from 

clinical and epidemiologic studies. Gardiner's research team recognizes the natural setting 

in which health outcomes and costs arise in practice, accounting for issues of censoring, 

truncation, and sample selection. 

•	 The longitudinal framework that underlies their analytic techniques can be used to 

provide a complete specification of alternative models for estimating health care costs 

and outcomes. 

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Gardiner's research methods and models offer practitioners of CEA a powerful set of tools 

for the improvement of statistical analysis of cost, health care utilization and costeffectiveness data. 

Summary and Significance of Gardiner's Research Findings Related to Translating 

Research into Policy and Practice (TRIPP) 

•	 A comprehensive review38 was published in 2004 addressing statistical issues in 

assessing statistical power and sample size for cost-effectiveness studies. This was at the 

request of the editors of Expert Review of Pharmacoeconomics & Outcomes Research 

following their earlier work in Health Economics.

37 Their work in this area has led to 

collaboration with an international team of researchers in designing a study for evaluating 

the effectiveness and cost-effectiveness of treatment strategies for decreasing the burden 

of depression in developing nations. 

•	 The issue of testing of hypotheses on cost-effectiveness ratios (CER) and assessing 

statistical power and sample size is addressed in an article in Health Economics. 

Following the pioneering work of O'Brien et al32 this was the first attempt to place 

hypothesis testing on CERs on a formal statistically sound framework. 

•	 Gardiner's method incorporates the correlation between cost and effectiveness measures, 

and leads to substantially lower sample size requirements than methods that ignore the 

correlation. It extends work by several other researchers.39-41,73 

•	 An important element in reporting the results of CEA is to gauge the precision of 

estimates such as the CER. Gardiner's work compares three of the popular parametric 

techniques for constructing confidence intervals for the CER.17 This work demonstrates 

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relationships between the three approaches and shows how the interpretation of the CER 

can be compromised when the incremental effectiveness is not statistically significant. 

•	 In recognition of the work of their on statistical inference for CEA and its potential use in 

public health policy, the editors of the critically acclaimed Handbook of Statistics invited 

their contribution to a volume addressing Bioenvironmental and Public Health 

Statistics.

11 A summary is presented of how uncertainty in estimated parameters can be 

assessed by their sampling error and conventional statistical inferential techniques. These 

techniques can then be applied to problems of estimation, tests of hypotheses, sample 

size, and power determinations in planning economic evaluation studies of health care 

programs. 

•	 Gardiner's statistical method for assessing the cost-effectiveness of the ICD was the first 

to address construction of statistical confidence intervals for the CER from survival 

data.25-27 His articles in the American Heart Journal and Medical Decision Making have 

received over 55 citations in professional literature. 

•	 Gardiner's team continues their research in CEA to address the formulation of regression 

models that could inform identification of patient characteristics and resource-use 

elements that influence both costs and outcomes, and the cost-effectiveness of competing 

interventions. Applications are contemplated in cardiovascular studies and in cancer 

treatments studies. The methods could ultimately improve standardization in reporting 

the results of economic evaluation studies, and provide objective means for assessing 

subgroups in which an intervention could be cost-effective. 

•	 Through experience with analyses of length of stay and cost in hospitalizations for heart 

failure, Gardiner et al have developed methods20,23,24 to estimate the cumulative cost of 

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health interventions over a specified duration while controlling for a mix of patientspecific variables. This method blends statistical and econometric techniques to address 

issues in the analysis of health care costs and allows for a greater use of total cost data, 

typically found in hospitalization records and claims files, that has not been previously 

attempted. 

•	 Gardiner's research proposes a unified framework to estimate summary measures 

commonly used in cost analyses and CEA. These include life-expectancy, qualityadjusted life years, net present values, cost effectiveness ratios, net health cost and net 

health benefit. Since patient demographics, clinical variables and intervention 

characteristics can affect these summary measures, regression models have been 

developed that incorporate covariate information into structural equations for cost and 

outcome measures. 

•	 These regression models are uniquely designed to account for costs engendered at 

transition times between health states (e.g., changes in health state that trigger resource 

use), and costs of sojourn in health states (e.g., resource use while in remission, relapse, 

or different treatment phases). For health outcomes such as quality of life assessments, 

their longitudinal models incorporate patient heterogeneity and address the issue of 

censoring commonly found in these types of studies. 

In summary, several aspects and complexities in the analyses of health care costs and 

outcomes are incorporated into these models, and collectively these new methods promise 

useful application in CEA. Demonstration of their methods in practice with clinical and 

epidemiologic data is an equally important goal of their endeavors. 

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Introduction 

Rapid increases in health care costs continue to concern the public, federal and state 

agencies, and private industry. Publicly funded insurance programs such as Medicare and 

Medicaid are continually faced with difficult decisions in allocating health care dollars. Private 

industries are similarly challenged in providing health care benefits to their employees. 

Expenditures on health care now account for 16 percent of the U.S. gross national product.1 

Given the high and growing cost of health care in the U.S, the need to contain health care 

costs forces us to consider which interventions produce the greatest value. CEA offers a 

structured approach for making economic evaluations of health care programs. It can be used for 

optimizing health benefits from a specified health care budget, or in finding the lowest cost 

strategy for a specified health effect.2 

Faced with pressures to contain costs while optimizing value, policymakers world-wide 

have turned to evidence of cost-effectiveness in addition to evidence of health benefit in 

allocating resources for health care services. In Australia, the Pharmaceutical Benefits Advisory 

Committee makes recommendations, based on effectiveness and cost-effectiveness evidence, on 

drug products that should be subsidized and placed in the Pharmaceutical Benefits Scheme.3

 In 

the United Kingdom, the National Institute of Clinical Excellence makes similar requirements 

for use of new healthcare technologies in the National Health Service, and in Ontario, Canada, 

the Drug Benefits Plan uses economic data when supporting new additions to its formulary.4,5 

Additionally, the U.S. Preventive Services Task Force and the Panel of Cost-Effectiveness in 

Health and Medicine have urged consideration of cost-effectiveness in addition to clinical 

effectiveness to help inform investment of health care dollars.6,7 

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Improvement of health is an important objective of social policy. In welfare economics, 

output is judged according to the extent to which it contributes to overall welfare, as determined 

by individual preferences over health, relative to other considerations in utility functions.2,8,9 The 

perspective of the welfarist calls for judging output of health care according to its contribution to 

health itself, and therefore requires careful assessment of health outcome as it affects an 

individual's well-being. By defining health as a state of "complete mental, physical, and social 

well-being and not merely the absence of disease," the World Health Organization in 1948 

endorsed the broader perception of health as it is viewed today.10 

Components of Cost-Effectiveness Analysis 

Measuring Costs 

An important step in CEA is the identification of all relevant cost items followed by their 

measurement and estimation. The Panel on Cost-Effectiveness in Health and Medicine 

recommended that costs in economic evaluation studies consist of both direct and indirect 

costs.7 The direct medical costs of an intervention are those incurred in providing care, such as 

payments for drugs, medical/surgical supplies and professional services from nurses, physicians 

or other health care providers associated with intervention. These include the costs of treating 

side effects and complications resulting from the intervention. Direct non-medical costs include 

costs incurred because of the illness or the need to seek care such as caregiver costs, 

transportation and child-care expenses incurred by patients and their families. Indirect costs, also 

called productivity costs, represent costs not associated with the transactions for goods or 

services, such as morbidity that results in time lost from work, or the inability to participate in 

leisure activities. 

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Measuring Benefit 

The next component of the CEA is the measurement of health benefit resulting from 

adoption of a specific treatment or intervention. Depending on the context one could use any 

clinically meaningful measure such as improvement in life expectancy, deaths averted, or 

number of toxic side effects prevented. Since the goal of any health care intervention is much 

broader than simply treating the disease condition or preventing death, the use of qualityadjusted life years (QALYs) in CEA has been advocated. A precursor to CEA was cost-benefit 

analysis which attempted to quantify in monetary terms the effect of the disease.7 Health care 

programs designed to prevent disease could be compared relative to their costs and benefits on 

the same scale. However, the difficulty of placing a monetary value on health outcomes has 

prevented its widespread adoption. 

A cost-identification analysis is often conducted for treatments and procedures that are 

believed to be equivalent in their clinical efficacy. For example, if two competing programs do 

not differ on average in their health benefits, then the one with the lower average cost will be 

preferred. This is the argument cited for the promotion of generic drugs because they offer the 

same therapeutic benefits as more expensive brand-name versions of the same drugs. On the 

other hand, if the costs of two programs are judged equivalent, the intervention with the greater 

health benefit will be preferred. A decision has to be made when one program has both higher 

cost and greater benefit than does its competitor. Is there a critical value below which society 

would consider the more costly intervention still “cost-effective”? 

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Quality-Adjusted Life Years 

A quality-adjusted life year (QALY) represents a patient's perception of the reduction in 

value of one year in perfect health due to pain, disability, and suffering caused by illness. It can 

be viewed as the proportional decrement in quality of life in the state of ill health, multiplied by 

years of expected life. Formally, for each unit of time spent in some health state, a quality 

weight is the relative value placed on that health state against the state of perfect health. Perfect 

health has a quality weight of 1, while death (or states judged equivalent to death), get a quality 

weight of 0. All other health states receive a quality weight between 0 and 1. Quality of life 

studies seek to measure the impact of health conditions on patients' functional status, including 

their physical, mental and social functioning, as well as their emotional well-being.14,15 

In CEA, use of the QALY to quantify health outcomes provides a common metric across 

different diseases. For example, the decision maker facing resource allocation can compare costeffectiveness of coronary artery bypass surgery versus percutaneous coronary intervention, the 

cost-effectiveness of lipid lowering therapies for the prevention of cardiovascular disease, and 

the cost–effectiveness of different regimens of screening women for their susceptibility to breast 

cancer. 

Cost-Effectiveness Ratio 

The cost–effectiveness ratio (CER) is an important summary statistic for comparing the 

costs and effectiveness of competing interventions. The CER is the additional cost at which the 

new or alternative intervention delivers one unit of additional health benefit, relative to the 

standard intervention to which the new intervention is being compared. In cost-effectiveness 

12
 
studies, the CER is a useful statistical aid in decision-making processes and in the allocation of 

health care resources. 

The CER is computed as the ratio of the net difference in costs of two interventions 

relative to the net difference in their effectiveness.11 Since the CER is assessed from inputs on 

cost and effectiveness that are subject to variation, sensitivity analyses are used to assess the 

extent of uncertainty in the CER. However, with patient-level data collected on costs and 

benefits in clinical trials, the CER may be viewed as a function of the parameters of the 

distribution of cost and effectiveness. Thus, given a probability model for sampling costs and 

health benefits, the CER can be estimated from available data and formal statistical inference can 

be applied to assess the variability in the estimated CER. 

As a ratio the CER presents some difficulties in its statistical analysis. In addition, 

problems of interpretation arise with negative values of the ratio, and using the ratio alone can 

lead to very different conclusions.16 Several investigators have also cautioned using the CER 

when the incremental effectiveness is not statistically significant.17,18 In order to overcome these 

difficulties another summary measure, the net health cost (NHC) or net health benefit (NHB) has 

been proposed.18 The NHC, denominated in monetary units, is the incremental cost minus the 

incremental benefit. The incremental benefit is converted into monetary units using the 

maximum value of the CER—the upper limit of what society is willing-to-pay to gain one unit of 

effectiveness The NHB is analogously defined in terms of effectiveness units.19 

Stochastic Variation 

A common aspect of cost and benefit measures is their stochastic nature. When measured 

at the level of the individual patient, cost and health outcome measures will vary across the 

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population of patients. These outcomes will depend on demographic factors such as age, gender, 

ethnicity, socioeconomic variables such as income and education, lifestyle factors such as 

smoking, alcohol consumption, physical activity, and health conditions as well as comorbidities. 

Incorporating stochastic variation in outcomes and covariables involves notions of probabilities. 

This allows the analyst to express and quantify the degree of uncertainty in estimates of cost and 

benefit.11,16 

Another important feature of cost and benefit comes is that they accrue longitudinally. 

When an intervention is deployed costs are incurred through resource use over time. The basic 

framework that Gardiner et al have adopted recognizes that over the course of an intervention, a 

patient's event history unfolds as transitions between different health states and that sojourns in 

these states, as well as transitions between health states, are associated with costs. The ending 

state is usually death or some other terminal state which ends the evolution of the patient's event 

history. Because costs that might be incurred in the future are valued less at the present time, all 

future costs are discounted at a fixed rate. The discounted total cost of the intervention over a 

finite time horizon is then the net present value (NPV) of all expenditures incurred in transitions 

between health states, and during sojourn in health states.11 As recommended by the Panel on 

Cost-Effectiveness in Health and Medicine, this time horizon must be sufficiently long to capture 

all costs of the intervention and the health benefits that accrue over time.7 

Specific Research Design: Goals, Aims and Objectives 

Description: Motivated by the need for new techniques for analyses of health care costs 

from clinical and epidemiological studies, the goal of this research was to develop new statistical 

techniques that fill methodological gaps in current CEA models. When a health care 

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intervention is deployed, cost is engendered through the use of resources. These occur in 

random amounts at random times that may differ by patient attributes, as well as clinical and 

intervention characteristics. Study design and sampling may lead to incomplete observation of 

key outcomes in some patients. By incorporating these components into statistical models that 

accurately reflect the experience of the patients as their health histories manifest over time 

permits consideration of health outcomes and costs jointly. This research was designed to 

produce newer and more advanced statistical models that improve the assessment of costs and 

patient outcomes. Gardiner et al use a Markovian regime to model the dynamics of movement 

of patients through different health states, accounting for costs incurred at transitions between 

states and sojourns between states. Applying a constant discount rate where appropriate, they 

estimated summary health outcome measures (i.e. life expectancy, quality-adjusted life years, net 

present value, net health care cost and benefit, and cost-effectiveness ratios). In addition, they 

assessed the impact of various factors on these statistical parameters and provided a uniform 

framework for statistical inference. They tested the performance and sensitivity of the 

procedures with real and simulated data. 

The specific aims of the research were: 

1.	 To specify stochastic models for costs and health outcome measures. 

Longitudinal stochastic models were utilized that reflect the experience of patients in 

changing states of health. Costs are engendered in random amounts at random times 

during the course of a health intervention. By compiling these expenditures at the 

individual level into costs per unit time of sojourn in a health state, and in transition 

between health states, the researchers estimated the distribution of present value of all 

expenditures, and summary statistics such as mean and median costs. Using Markov 

15
 
models to describe the evolution of patient histories over time, they were able 

estimate health outcome measures such as life expectancy, median survival and 

survival rates, all discounted at a constant rate and adjusted for quality of life. 

2. To assess the development of new models and procedures. The researchers 

exploited the capability of the proposed models and new procedures for assessment of 

health care costs and outcomes. For CEA, the proposed methods yielded estimates of 

intervention effects adjusted for variables that might have impact on measures of cost 

and effectiveness. The research team then formulated procedures for statistical 

inference on summary statistics used in CEA such as cost-effectiveness ratios, net 

benefit and net cost measures. 

3. To test and validate statistical procedures. A useful tool in evaluating the 

performance of the estimators of effectiveness, cost and cost-effectiveness is to 

perform a simulation study. Since a patient event history is manifested over time by 

the occurrence of discrete events (i.e., transition between health states, cost at 

transition times) the principle of discrete event simulation (DES) may be used to track 

the flow of patients through health states and gather the relevant observations for 

estimating the summary measures of interest. Simulation studies were used to assess 

the performance of their models with regard to sensitivity to assumptions made in 

their specification. Scenarios for these studies were taken from published costeffectiveness studies that are often framed under a decision-theoretic model with 

numerous assumptions on the inputs of utilization and effectiveness. The performance 

16
 
 

of the competing procedures was studied for estimating cost-effectiveness ratios, net 

benefit and net cost measures in CEA. 

4. To apply and test procedures on existing data sets. The investigators utilized the 

Michigan Inter-Institutional Collaborative heart (MICH) study, which is a prospective 

investigation of health care utilization and patient outcomes in admissions for acute 

myocardial infarction (AMI) to 5 mid-Michigan hospitals during the period January 

1, 1994, through April 30, 1995. A second phase of the study was conducted in 1997 

which examined similar outcomes after changes in medical management and 

treatment options for AMI were instituted in these hospitals. The primary objective of 

this study was to assess sources of variability by race and gender in the use of 

invasive cardiac procedures-cardiac catheterization (CATH), percutaneous 

transluminal coronary angioplasty (PTCA), and coronary artery bypass grafting 

(CABG), in the treatment of AMI. Analyses have been conducted to detect changes 

in long term-survival between patients in each phase.22 The same study was also used 

to analyze hospital charges and length of stay by cardiac procedures, accounting for 

variations in patient characteristics such as age, gender, race, comorbidities and 

ejection fraction.23,24 

Using data from previous published studies, the researchers also evaluated the 

effectiveness and cost-effectiveness of the implantable cardiac defibrillator (ICD). Estimates of 

life-expectancy of ICD patients have been compared with patients treated under electrophysiology guided therapy.25-27 

17
 
Methodology for Analysis of Health Care Costs and Outcomes 

With increasing attention being given to gathering and compiling economic data 

alongside clinical investigations, there is a need to develop rigorous statistical models and 

techniques to jointly analyze both costs and patient outcomes. Current methods generally focus 

on a single measure of cost or health outcome and do not fully exploit the longitudinal dynamic 

mechanisms that engender cost and outcome data. It is critical to understand how individual 

characteristics might impact summary measures, such as the cost-effectiveness ratio, as well as 

median cost and survival. This is paramount in predicting resource utilization and informing 

policy on allocation of health care dollars. 

Gardiner et al apply a stochastic framework for estimation of summary measures in costeffectiveness analyses. Stochastic modeling of patient health and cost outcomes is a useful tool 

in identifying and assessing the important individual characteristics that influence these 

outcomes. It is a critical step in cost-effectiveness analysis which aims to structure comparisons 

between competing health care interventions on both health outcomes and costs. Gardiner et al 

use a Markov process to describe the occurrence of patient events that unfold over time. States of 

the process represent health conditions or health states (i.e. well, ill, or dead). Commonly used 

measures in cost-effectiveness analyses, such as net health benefit, net health cost, costeffectiveness ratio, life expectancy and quality-adjusted survival, are defined in terms of 

expected values of functions of the process. Costs are incurred through medical resource while 

sojourning in health state, and in transitions between health states. By combining these 

expenditures, Gardiner et al define net present value for expected total cost over a specified 

period of time. In this longitudinal framework, they describe statistical models for estimation of 

these summary statistics and quantifying the impact of important variables in the process. 

18
 
Although more general processes can be utilized, Markov processes have been the main 

choice in decision analyses and CEA.20,28-31 Markov models have become the paradigm for 

studying the progression of patients through various states following an intervention of 

treatment. The Markov property restricts the dependence of the future evolution of the process 

given the past, only to the most recent past. It is sufficiently flexible to permit modeling of both 

observable and unobservable patient-specific characteristics through the transition intensities, 

and assessing their impact on costs and outcomes. 

In order to be useful in practice, data arising from cost measures and health outcomes 

must incorporate the dynamics of health care utilization as it manifests over time. There are 

several advantages of using a longitudinal model. Apart from its accurate description of an 

evolving patient history, it incorporates many of the critical elements that are needed to carry out 

cost-effectiveness analyses of interventions. A Markov process used to describe a patient's 

evolving history provides a rigorous basis for quantifying variation in costs and health outcomes. 

Another advantage of the approach of Gardiner et al is that it separates the time dynamics 

of transition between health states and costs as they become known over time. From a statistical 

point of view, this allows for modeling costs using modifications of regression methodology 

applied to longitudinal correlated data. This also permits analyses of differential covariate effects 

on costs and transitions between health states. 

Research Accomplishments & Impact on Translating Research into Policy and Practice 

(TRIPP) 

 Gardiner’s research team has produced 25 peer-reviewed publications in health services 

research and clinical journals, invited presentations at professional meetings, and opportunities to 

19
 
collaborate in new research ventures. Dr. Gardiner has demonstrated the application of his 

methods in practice with clinical and epidemiologic data. His methodological advances in CEA 

continue to be cited by other researchers with collectively over 250 citations. In the year 2006, 

the American Statistical Association honored Dr. Joseph Gardiner by inducting him as Fellow 

with the citation: 

“For development of statistical methodologies for cost-effectiveness analyses and health services 

research; for significant collaborations in public health, epidemiology, and health services 

research.” 

Dr. Gardiner is an Elected Member of the International Statistical Institute. 

Cost-Effectiveness of the implantable cardioverter defibrillator 

In a series of articles Gardiner et al developed the fundamentals for statistical inference on 

the cost-effectiveness ratio. The initial investigation was motivated by their study of the costeffectiveness of the implantable cardioverter defibrillator (ICD). The ICD is an effective medical 

device in treating patients with severe ventricular arrhythmias and therefore at the risk of sudden 

death. These devices can detect ventricular tachycardia or ventricular fibrillation and restore 

normal heart rhythm, either through rapid pacing or by delivery of appropriate electrical shock. 

Improvements in ICD technology have increased the reliability and life of the ICD generator, 

reduced its size through micro-circuitry, and added features such as the capability of 

reprogramming of the device to individualize treatment, and memory to store information on 

time and level of electrical discharges. Delivery of the ICD technology is relatively expensive. 

The researchers’ study of the cost-effectiveness of the ICD was led by the prominent 

cardiologist Joel Kupersmith, MD. It followed their comprehensive study of cost-effectiveness 

20
 
of treatments in heart disease. Four articles have to date been cited in over 165 publications. 

1. Kupersmith J, Hogan A, Guerrero P, Gardiner J, Mellits ED, Baumgardner R, et al. Evaluating 

and Improving the Cost-Effectiveness of the Implantable Cardioverter-Defibrillator. 

American Heart Journal 1995;130(3):507-515. 

2. Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-Effectiveness 

Analysis in Heart-Disease. 1. General- Principles. Progress in Cardiovascular Diseases 

1994;37(3):161-184. 

3. Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-Effectiveness 

Analysis in Heart-Disease. 2. Preventive Therapies. Progress in Cardiovascular Diseases 

1995;37(4):243-271. 

4. Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-Effectiveness 

Analysis in Heart-Disease. 3. Ischemia, Congestive-Heart-Failure, and Arrhythmias. 

Progress in Cardiovascular Diseases 1995;37(5):307-346. 

The research team continues to be actively engaged in studies related to newer technological 

improvements to the ICD and their impact on patient survival. Two recent publications in the 

area are 

5. Evonich RF, Maheshwari A, Gardiner JC, Khasnis A, Kantipudi S, Ip JH, et al. Implantable 

cardioverter defibrillator therapy in patients with ischemic or non-ischemic cardiomyopathy 

and nonsustained ventricular tachycardia. Journal of Interventional Cardiac 

Electrophysiology 2004;11(1):59-65. 

6. Soundarraj D, Thakur RK, Gardiner JC, Khasnis A, Jongnarangsin K. Inappropriate ICD 

therapy: Does device configuration make a difference? Pace-Pacing and Clinical 

Electrophysiology 2006;29(8):810-815. 

Methodological studies in estimation of the cost-effectiveness ratio 

When the CER is estimated from patient-level data it is important to gauge the precision of 

the estimate. Statistically this can be achieved by estimating the standard error of the estimated 

CER or providing a confidence interval for the CER. An enormous literature has been built to 

address this problem. The CER of a test treatment compared to its next best alternative (called 

the referent treatment or standard), is the ratio of its incremental cost relative to its incremental 

benefit. When comparing two treatments on their costs and health benefits, the significance of 

21
 
the incremental benefit is often of primary importance followed by the significance of the 

incremental cost. Gardiner et al compare three popular parametric techniques for constructing 

confidence intervals for the CER. They demonstrate relationships between the three approaches 

and show how interpretation of the CER could be compromised when the incremental 

effectiveness of treatment is not statistically significant. Indeed, some researchers have argued 

that cost-effectiveness considerations should be postponed until the significance of effectiveness 

of a treatment compare to its competitor has first been established. 

Their six publications in this area continue to draw the attention of researchers and have been 

cited in over 50 articles and research reports. 

7. Gardiner J, Hogan A, Holmes-Rovner M, Rovner D, Griffith L, Kupersmith J. ConfidenceIntervals for Cost-Effectiveness Ratios. Medical Decision Making 1995;15(3):254-263. 

8. Gardiner J, Holmes-Rovner M, Goddeeris J, Rovner D, Kupersmith J. Covariate-adjusted 

cost-effectiveness ratios. Journal of Statistical Planning and Inference 1999;75(2):291-

304. 

9. Gardiner JC, Huebner M, Jetton J, Bradley CJ. Power and sample size assessments for tests of 

hypotheses on cost-effectiveness ratios. Health Economics 2000;9(3):227-234. 

10. Gardiner JC, Huebner M, Jetton J, Bradley CJ. On parametric confidence intervals for the 

cost-effectiveness ratio. Biometrical Journal 2001;43(3):283-296. 

11. Indurkhya A, Gardiner JC, Luo ZH. The effect of outliers on confidence interval procedures 

for cost-effectiveness ratios. Statistics in Medicine 2001;20(9-10):1469-1477. 

12. Gardiner JC, Indurkhya A, Luo Z. The performance of estimation procedures for costeffectiveness ratios. In: Balakrishnan N, editor. Advances on Methodological and Applied 

Aspects of Probability and Statistics. New York: Taylor & Francis, 2002:547-559. 

Design of cost-effectiveness studies 

The recent growth in conducting economic evaluation studies alongside traditional 

investigation of efficacy of treatments has led inevitably to considerations of appropriate sample 

size for demonstrating cost-effectiveness. For example, several recent randomized clinical trials 

on the ICD have collected the requisite patient-level data that would allow for subsequent 

economic analyses. Several researchers have proposed techniques for assessing sample size and 

22
 
 

power for cost-effectiveness studies. Gardiner et al’s formal statistically rigorous approach to 

this problem provides a framework for deriving statistical power and sample size expressions for 

testing different hypotheses on the CER. 

Gardiner et al’s manuscript # 9 was the groundwork for this approach. Tests of hypotheses 

on the CER were constructed from the net cost and incremental effectiveness measures. Their 

methods account for the correlation between cost and effectiveness and lead to smaller sample 

size requirements than comparative methods that ignore the correlation. Their arguments indicate 

that in commonly encountered circumstances, a study powered to demonstrate cost-effectiveness 

would require a substantially larger number of patients than that needed to show effectiveness 

alone. In the context of treatment trials this raises the ethical dilemma of continuing a study to 

gather data to test economic hypotheses after there is evidence of a statistically significant and 

clinically meaningful difference in treatment efficacy. Because the researchers’ methods permit 

hypothesis testing on the CER in a trial powered for effectiveness, they can be used to compute 

the power for tests on the CER. The practical implication of these findings is that large scale 

clinical trials should collect whenever feasible pertinent data for economic information to 

conduct modest cost-effectiveness studies. Post-marketing surveillance studies used by most 

pharmaceutical companies and administrative databases on utilization maintained by insurance 

companies could be valuable resources for carrying out cost-effectiveness studies. However, the 

challenge is what methodological principles and practices should be applied so that the ensuing 

inference would be reliable and valid. 

Gardiner et al recently updated and critically appraised the currently available techniques for 

assessing sample size and power for cost-effectiveness studies. Their review #13 below was 

23
 
deemed one of the most read papers with over 95 full-text downloads from the website futuredrugs.com maintained by the publishers Future Drugs Ltd of the Expert Review.{accessed 

10/27/2006 http://www.future-drugs.com/action/showMostReadArticles} 

13. Gardiner JC, Sirbu CM, Rahbar MH. Update on statistical power and sample size 

assessments for cost-effectiveness studies. Expert Review of Pharmacoeconomics & 

Outcomes Research 2004;4(1):89-98. 

Methodological studies for costs and health outcomes in longitudinal studies 

Longitudinal epidemiologic and clinical studies record events occurring in individuals over 

time. As a typical individual’s history unfolds, one observes the time of occurrence of events and 

their type. Multi-state models are commonly used in this context to describe the evolution of 

longitudinal data. States defined as “well”, “ill” or “dead” are the simplest description of a 

person’s health history and forms the basis of illness-death models. In studies of survival one 

recognizes just two states, a starting state “well” and the final destination state, “death”. 

Multi-state models are well suited to study the dynamics of change in patient health over a 

period of time. They have also been advocated in analyses of quality of life data where multiple 

assessments of an individual’s functioning are made (eg, physical and mental health functioning 

using the SF-36). The statistical framework for multi-state modeling is a stochastic process that 

describes the health states that a patient may visit. Typically, there are several transient states and 

one or more absorbing states. A transient state is one if visited would be exited after a finite 

sojourn, whereas an absorbing state is never exited once entered. To describe the dynamics of 

movement between transient states and sojourns, Markov models have been gainfully applied in 

several biomedical studies. The biostatistics and epidemiology literature is replete with 

24
 
applications of these flexible models especially in evaluating treatment effects while adjusting 

for the influence of confounding explanatory variables. 

Gardiner et al have used this same framework to incorporate costs. Costs may emanate from 

two streams. First, costs that are incurred at transition times. This would occur when there is a 

change in health condition that requires an additional use of resources. This change is often 

represented in the model by a transition from one transient state to another. An example from 

cancer follow up studies is a patient who previously was in remission but has now relapsed and 

requires additional surgery. A second type of cost is incurred while sojourning in a health state. 

The typical example here is a hospital stay. A patient may sojourn through several care units in 

the hospital (eg, ED, ICU, CCU, Recovery unit) before being discharged. The cost incurred is 

each unit would be different as different resources would be used. 

In a series of articles Gardiner et al have discussed different aspects of this unified 

framework to carry out inference for cost-effectiveness studies. First, they built upon expanding 

the definitions of the commonly used measures in cost-effectiveness analysis to this new 

framework. These include life-expectancy, net present value, quality adjusted life years, net 

health cost, net health benefit and the cost-effectiveness ratio. The research team is hopeful that 

their recent publication (#23) would be useful to theorists and well as to practitioners of the craft 

of cost-effectiveness analysis. 

14. Gardiner JC, Bradley CJ, Huebner M. The cost-effectiveness ratio in the analysis of health 

care programs. In: Rao CR, Sen PK, editors. Handbook of Statistics, Bioenvironmental and 

Public Health Statistics. New York: North-Holland, 2000:841-869. 

15. Gardiner JC, Luo Z, Bradley CJ, Polverejan E, Holmes-Rovner M, Rovner D. Longitudinal 

assessment of cost in health care interventions. Health Services & Outcomes Research 

Methodology 2002;3:149-168. 

25
 
16. Gardiner JC, Polverejan E. Longitudinal models for the analysis of health care costs and 

outcomes. Proceedings of the American Statistical Association, Section on Health Policy 

Statistics [CD-ROM] 2002. 

17. Polverejan E, Gardiner JC, Bradley CJ, Holmes-Rovner M, Rovner D. Estimating mean 

hospital cost as a function of length of stay and patient characteristics. Health Economics 

2003;12(11):935-947. 

18. Baser O, Bradley CJ, Gardiner JC, Given CW. Testing and correcting for non-random 

selection bias due to censoring: An application to medical costs. Health Services & 

Outcomes Research Methodology 2003;4:93-107. 

19. Bradley CJ, Given CW, Baser O, Gardiner JC. Influence of surgical and treatment choices on 

the cost of breast cancer care. European Journal of Health Economics 2003;4:96-101. 

20. Baser O, Gardiner JC, Bradley CJ, Given CW. Estimation from censored medical cost data. 

Biometrical Journal 2004;46(3):351-363. 

21. Bradley CJ, Gardiner J, Given CW, Roberts C. Cancer, Medicaid enrollment, and survival 

disparities. Cancer 2005;103(8):1712-1718. 

22. Baser O, Gardiner JC, Bradley CJ, Yuce H, Given CW. Longitudinal analysis of censored 

medical costs data. Health Economics 2006;15(5):513-525. 

23. Gardiner JC, Luo Z, Liu L, Bradley CJ. A stochastic framework for estimation of summary 

measures in cost-effectiveness analyses. Expert Review of Pharmacoeconomics & 

Outcomes Research 2006;6(3):347-358. 

24. Gardiner JC, Luo Z, Bradley CJ, Sirbu CM, Given CW. A dynamic model for estimating 

changes in health status and costs. Statistics in Medicine 2006, 25:3648-3667. 

25. Gardiner JC, Liu L, Luo Z. Estimation of medical costs from a transition model. IMSLecture Notes-Collection Series 2007 (1): 350-363, In press. 

26. Gardiner JC, Luo Z, Liu L. Analysis of Multiple Failure Times Using SAS Software. In: R. 

Khattree, Naik D, editors. Computational Methods in Biomedical Research. New York, 

NY: Taylor & Francis, 2007. In press. 

27. Luo Z, Goddeeris J, Gardiner JC, Lyles JS, Smith RC. Cost of a primary care intervention 

for patients with medically unexplained symptoms – a randomized controlled trial. 

Psychiatric Services 2007;58:1079-1086. 

In (#24) Gardiner et al demonstrate the application of a dynamic model for estimation costs 

following treatments given to cancer patients. During the 2 year follow-up period, patients 

experienced episodes of normal physical function interspersed with periods of impaired physical 

function, before succumbing to death. The underlying process is modeled as a 3-state Markov 

process with states: normal function, impaired function, and dead. The researchers found that 

sojourns in the transient states were associated with different costs that also depend on the type 

of cancer (breast, colon, lung, or prostate) and the initial stage of their cancer diagnosis. In their 

26
 
article (#25) the investigators provide mathematical details on how multi-state models can 

subsume many of the previously published analytic models for assessing cost and effectiveness. 

In (#26) they provide details on how standard statistical software can be used in estimation of 

multi-state models, and in (#27) they report on the relative cost of an intervention delivered in a 

primary care setting to patients with medically unexplained symptoms. The efficacy of this 

intervention had been previously published.74 

Identification of Major Problematic Areas in CEA and How Gardiner's Research Is 

Addressing These Issues 

As a result of my review of the literature, I have identified what I consider to be the major 

problematic areas in CEA. These are: 

•	 The central problem seems to be a lack of standardization in CEA. 

•	 CEAs can be complex and difficult to conduct due to inadequate representation of cost 

and effectiveness data. Many cost-effectiveness studies use complex models that rely on 

numerous assumptions where evidence is lacking or inconsistent. 

•	 Current methods generally focus on a single measure of cost or health outcome and do 

not fully exploit the longitudinal character of data needed for CEAs and its impact on 

summary measures such as the CER as well as median cost and survival rates. These 

measures are paramount to predicting resource utilization and informing policy on the 

allocation of health care dollars. 

•	 CEAs are often reported in a way that makes it difficult for users to understand how 

results are obtained. 

27
 
•	 There are many difficulties in statistical analysis for CEA. Rigorous statistical 

techniques must be developed to analyze jointly both costs and patient outcomes. 

•	 When differences in approach, assumptions, methods, and quality lead to conflicting 

conclusions, potential users may be confused and credibility of the CEA undermined. 

•	 Inadequate attention to the design of cost-effectiveness studies can lead to 

inconsistencies. 

With AHRQ's support, the research team led by Gardiner has taken several steps in 

addressing these issues: 

•	 Despite the rapid development of techniques for conducting economic evaluation studies 

in medicine and health, the statistical methodology to support these studies is in the 

developmental stages. Gardiner's research formulates statistical models that inform 

identification of patient characteristics and resource-use elements that influence both 

costs and outcomes. 

•	 Recognizing the natural setting in which cost and health outcomes would manifest over 

time, his current research addresses development of longitudinal models that incorporate 

covariate information and permit estimation of their impact on summary measures such 

as the CER and NHC. 

•	 The Australian Pharmaceutical Benefits Advisory Committee guidelines on conduct of 

CEA3

 advise adoption of methods that are "responsive in differences in health states 

between individuals and to changes in health states over time experienced by any one 

individual." In addition, they also advise consideration of the impact of patient 

heterogeneity and sensitivity on results of a CEA. Gardiner's interdisciplinary team of 

statisticians, health economists, health services researchers and clinical investigators has 

28
 
built a repertoire of publications addressing both applied and methodological issues in 

CEA. 

•	 Many methodological developments are theoretically sound and can be tested on 

simulated data. In practice, these sophisticated methods have limited use unless they 

address the inherent problems in data sets commonly available to researchers from 

clinical and epidemiologic studies. These include problems with patient heterogeneity, 

skewness in cost distributions, incomplete follow up, truncation, censoring and sample 

selection. Gardiner's research team uses multi-state models for the dynamics of 

movement of patients through health states. They recognize the natural setting in which 

health outcomes and costs arise in practice, accounting for issues of censoring, 

truncation, and sample selection. 

•	 The longitudinal framework that underlies their analytic techniques can be used to 

provide a complete specification of alternative models for estimating health care costs 

and outcomes. 

•	 Gardiner's research methods and models offer practitioners of CEA a powerful set of 

tools for the improvement of statistical analysis of cost, health care utilization and costeffectiveness data. 

The flexible framework for stochastic CEA being developed by Gardiner and colleagues draw 

upon the following features: 

•	 Recognizes that costs are stochastic and incurred at random times in random amounts as 

patients' transition between health states and sojourn in health states. 

•	 Exhibits the role of discounting costs as they manifest over time. 

29
 
•	 Defines all the summary measures used in CEA as functions of statistical parameters 

arising from the underlying probability model. These include, net present value, qualityadjusted life years, cost-effectiveness ratio, net health benefit and net health cost. 

•	 Incorporates patient-specific explanatory variables (covariates) into the analysis, allowing 

for the assessment of their influence of summary measures used in CEA. 

•	 Addresses the impact of sampling plans under which the data on costs and outcomes 

ensue in the longitudinal model, including the role of censoring and outcomes. 

•	 Formalizes statistical inference on net present value, quality-adjusted life years, costeffectiveness ratio, and net health cost by providing a rigorous basis for their estimation, 

as well as derivation of their statistical distributions. This allows for quantifying 

uncertainty in estimates through standard errors and confidence intervals. 

•	 Permits testing of hypotheses on net present value, quality-adjusted life years, costeffectiveness ratio, and net health cost. Given the data gathering mechanisms for costs 

and outcomes, this provides a comprehensive scheme for statistical inference based on 

these entities. 

•	 Addresses design issues in CEA such as assessment of statistical power and sample size 

for planning of cost-effectiveness studies. 

Summary and Significance of Gardiner's Research Findings Related to Translating 

Research into Policy and Practice (TRIPP) 

•	 A comprehensive review38 was published in 2004 addressing statistical issues in 

assessing statistical power and sample size for cost-effectiveness studies. This was at the 

request of the editors of Expert Review of Pharmacoeconomics & Outcomes Research 

30
 
 

following their earlier work in Health Economics.

37 Their work in this area has led to 

collaboration with an international team of researchers in designing a study for evaluating 

the effectiveness and cost-effectiveness or treatment strategies for decreasing the burden 

of depression in developing nations. 

•	 The issue of testing of hypotheses on cost-effectiveness ratios and assessing statistical 

power and sample size is addressed in an article in Health Economics. Following the 

pioneering work of O'Brien et al,

32 this was the first attempt to place hypothesis testing 

on CERs on a formal statistically sound framework. 

•	 Gardiner's method incorporates the correlation between cost and effectiveness measures, 

and leads to substantially lower sample size requirements than methods that ignore the 

correlation. It complements the work by several other researchers.39-41,73 

•	 An important element in reporting the results of CEA is to gauge the precision of 

estimates such as the CER. Gardiner's work compares three of the popular parametric 

techniques for constructing confidence intervals for the CER.17 His work demonstrates 

relationships between the three approaches and show how the interpretation of the CER 

can be compromised when the incremental effectiveness is not statistically significant. 

•	 In recognition of the work of Gardiner et al on statistical inference for CEA and its 

potential use in public health policy, the editors of the critically acclaimed Handbook of 

Statistics invited their contribution to a volume addressing Bioenvironmental and Public 

Health Statistics.

11 A summary is presented of how uncertainty in estimated parameters 

can be assessed by their sampling error and conventional statistical inferential 

techniques. These techniques can then be applied to problems of estimation, tests of 

31
 
hypotheses, sample size, and power determinations in planning economic evaluation 

studies of health care programs. 

•	 Gardiner's statistical method for assessing the cost-effectiveness of the ICD was the first 

to address construction of statistical confidence intervals for the CER from survival 

data.25-27 His articles in the American Heart Journal and Medical Decision Making have 

received over 55 citations in professional literature. 

•	 Gardiner's team continues their research in CEA to address the formulation of regression 

models that could inform identification of patient characteristics and resource-use 

elements that influence both costs and outcomes, and the cost-effectiveness of competing 

interventions. Applications are contemplated in cardiovascular studies and in cancer 

treatments studies. The methods could ultimately improve standardization in reporting 

the results of economic evaluation studies, and provide objective means for assessing 

subgroups in which an intervention could be cost-effective. 

•	 Through experience with analyses of length of stay and cost in hospitalizations for heart 

failure, Gardiner et al have developed methods20,23,24 to estimate the cumulative cost of 

health interventions over a specified duration while controlling for a mix of patientspecific variables. This method blends statistical and econometric techniques to address 

issues in the analysis of health care costs and allows for a greater use of total cost data, 

typically found in hospitalization records and claims files, that has not been previously 

attempted. 

•	 Gardiner's research proposes a unified framework to estimate summary measures 

commonly used in cost analyses and CEA. These include life-expectancy, qualityadjusted life years, net present values, cost effectiveness ratios, net health cost and net 

32
 
health benefit. Since patient demographics, clinical variables and intervention 

characteristics can affect these summary measures, regression models have been 

developed that incorporate covariate information into structural equations for cost and 

outcome measures. 

•	 These regression models are uniquely designed to account for costs engendered at 

transition times between health states (e.g., changes in health state that trigger resource 

use), and costs of sojourn in health states (e.g., resource use while in remission, relapse, 

or different treatment phases). For health outcomes such as quality of life assessments, 

their longitudinal models incorporate patient heterogeneity and address the issue of 

censoring commonly found in these types of studies. 

•	 In summary, several aspects and complexities in the analyses of health care costs and 

outcomes are incorporated into these models, and collectively these new methods 

promise useful application in CEA. Demonstration of these methods in practice with 

clinical and epidemiologic data is an equally important goal of their endeavors. 

Future Plans related to Translating Research into Policy and Practice (TRIPP) 

The methods that Gardiner et al described can be of considerable benefit in assessing patient 

health and cost outcomes stemming from new health initiatives such as economic evaluations of 

the implementation of Medicare Part D. The Medicare Prescription Drug Improvement and 

Modernization Act (MMA) was signed into law by President Bush in 2003. The MMA offers 

prescription drug benefits to Medicare beneficiaries and is the first substantial expansion of 

Medicare benefits in nearly 4 decades. With this expansion comes considerable cost—it is 

estimated that people aged 65 years and older spend approximately $2300 each year on 

prescription drugs. The net federal cost of the benefit is projected to be about $37 billion in 2006 

33
 
and $724 billion from 2006 to 2015. Currently, prescription drugs account for about 17% of 

overall healthcare expenditures. 

As new prescription drugs are approved by the Federal Drug Administration, costeffectiveness considerations would be important. The Centers for Medicare and Medicaid 

Services (CMS) will continue to monitor the need to include specific drugs to in its Part D 

coverage. Plans now cover at least two drugs in each therapeutic class or category and provide 

access to a “broad range of medically appropriate drugs,” including a majority of drugs within 

the following classes: antidepressants, anti-psychotics, anti-convulsants, anti-retrovirals, 

immuno-suppressants, and anti-neoplastics. Other countries that provide similar benefits to its 

citizens have adopted formal guidelines for the conduct of cost-effectiveness analysis. It is likely 

that prescription drug plans in the United States will also find it necessary to engage in methods 

of cost-effectiveness analysis in order to select drugs for its formularies. 

Recently CMS has provided researchers informed access to the Medicare Part D Prescription 

Drug Event (PDE) database. The PDE is similar to an administrative pharmacy record database. 

It contains recipient-specific claim records submitted by Part D plans for each filled prescription. 

In addition to the standard information on insurance, coverage status and beneficiary copays, 

service and payment dates, the PDE identifies the drugs dispensed (from National Drug Codes), 

its quantity, and chemical compound codes. With some recipient identifiers, the PDE can be 

linked to demographic factors (eg, patient date of birth and gender), other Medicare service 

utilization and diagnoses. However, due to the sensitive nature of PDE the CMS requires 

researchers to have a formal data use agreement for specific analyses. 

34
 
The methods that Gardiner et al have advanced can be of considerable benefit in assessing 

patient health and cost outcomes stemming from new health initiatives such as the MMA. The 

non-homogeneous Markov process can be used to develop a credible model of patients’ 

longitudinal costs and health outcomes. This model is well-suited to inputs from administrative 

data such as Medicare claim files, which contain claims for health care services from inpatient 

and outpatient facilities, skilled nursing facilities, home health care, health care providers, and 

hospice providers. Claims data—particularly if combined with disease registries such as the 

Surveillance, Epidemiology, and End Results (SEER) cancer registry—can be neatly subdivided 

into disease states and health outcomes. An advantage of using the methods Gardiner et al 

describe along with claims data is it allows for the evaluation of costs and benefits in a dynamic 

framework where costs incurred in one area (eg., prescription drugs) may be offset by benefits in 

another area (eg., inpatient utilization). 

In a limited capacity, the formal evaluation of pharmaceutical benefits is currently underway 

in many private health care plans. Policy initiatives such as the MMA will dramatically increase 

the demand for evaluation of health costs and outcomes data along with methods appropriate for 

the formal assessment of new health care interventions. We anticipate that benefit managers and 

policy analysts will become skilled experts at evaluating the methodological quality of costeffectiveness studies. These experts will require methodological rigor along with model 

sophistication, which recognizes that health care costs and outcomes rarely occur in a 

deterministic environment. Sophistication in methodological development to meet these 

challenges via a copulation of statistical and econometric techniques seems inevitable. Markov 

models can serve as a basis of a longitudinal model for patient costs and health outcomes that 

35
 
meets both methodological rigor and sophistication required to make decisions regarding the 

relative value of health care interventions. 

The usefulness and versatility of cost-effectiveness analyses is not restricted to health care 

and medicine. In the regulatory environment policy makers have used cost-benefit analyses to 

assess the likely impacts of alternative regulatory strategies on human health and safety. Since 

2003, the US Office of Management and Budget (OMB) has required agencies to supplement 

cost-benefit analyses with cost-effectiveness analyses when recommending changes to health and 

safety regulations. A recent report from the Institute of Medicine highly recommends the use of 

cost-effectiveness analyses for regulatory analyses in environmental, health, and safety 

regulation. One may conclude with some degree of conviction that the development of new 

methodologies for cost-effectiveness analyses will continue unabated. The challenge that lies 

ahead is their implementation and translation into practice that could ultimately benefit our 

society by optimally deploying our resources in the most efficient manner. 

Research Products 

Dr. Gardiner has produced several publications in peer-reviewed journals, abstracts and invited 

presentations at professional meetings. Listed below are the research products. 

Publications 

1.	 Gardiner J, Hogan A, Holmes-Rovner M, Rovner D, Griffith L, Kupersmith J. 

Confidence-Intervals for Cost-Effectiveness Ratios. Medical Decision Making 1995;15 

(3):254-63. 

2.	 Kupersmith J, Hogan A, Guerrero P, Gardiner J, et al. Evaluating and Improving the 

Cost-Effectiveness of the Implantable Cardioverter-Defibrillator. American Heart 

Journal 1995;130 (3):507-15. 

3.	 Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-effectiveness 

analysis in heart-disease. 1. General principles. Progress in Cardiovascular Diseases 

1994;37 (3):161-184. 

36
 
4.	 Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-effectiveness 

analysis in heart-disease. 2. Preventive therapies. Progress in Cardiovascular Diseases 

1995;37(4):243-71. 

5.	 Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-effectiveness 

analysis in heart-disease. 3. Ischemia, congestive-heart-failure, and arrhythmias. Progress 

in Cardiovascular Diseases 1995;37(5):307-46. 

6.	 Rahbar MH, Gardiner JC. Nonparametric estimation of regression parameters from 

censored data with a discrete covariate. Statistics & Probability Letters 1995;24(1):13-20. 

7.	 Gardiner J, Holmes-Rovner M, Goddeeris J, Rovner D, Kupersmith J. Covariate-adjusted 

cost-effectiveness ratios. Journal of Statistical Planning and Inference 1999;75 (2):291-

304. 

8.	 Gardiner JC, Huebner M, Jetton J, Bradley CJ. Power and sample size assessments for 

tests of hypotheses on cost-effectiveness ratios. Health Economics 2000;9 (3):227-34. 

9.	 Gardiner JC, Bradley CJ, Huebner M. The cost-effectiveness ratio in the analysis of 

health care programs. In: Rao CR, Sen PK, eds. Handbook of Statistics, 

Bioenvironmental and Public Health Statistics. New York: North-Holland, 2000: 841-69. 

10. Gardiner JC, Huebner M, Jetton J, Bradley CJ. On parametric confidence intervals for the 

cost-effectiveness ratio. Biometrical Journal 2001;43 (3):283-96. 

11. Indurkhya A, Gardiner JC, Luo Z. The effect of outliers on confidence interval 

procedures for cost-effectiveness ratios. Statistics in Medicine 2001;20 (9-10):1469-77. 

12. Gardiner JC, Indurkhya A, Luo Z. The performance of estimation procedures for costeffectiveness ratios. In: Balakrishnan N, ed., Advances on Methodological and Applied 

Aspects of Probability and Statistics. New York: Taylor & Francis, 2002: 547-59. 

13. Gardiner JC, Polverejan E. Longitudinal models for the analysis of health care costs and 

outcomes. Proceedings of the American Statistical Association, Section on Health Policy 

Statistics [CD-ROM] 2002, New York, NY. 

14. Gardiner JC, Luo Z, Bradley CJ, Polverejan E, Holmes-Rovner M, Rovner D. 

Longitudinal assessment of cost in health care interventions. Health Services & Outcomes 

Research Methodology 2002;3:148-69. 

15. Polverejan E, Gardiner JC, Bradley CJ, Holmes-Rovner M, Rovner D. Estimating mean 

hospital cost as a function of length of stay and patient characteristics. Health Economics 

2003;12:935-47. 

16. Bradley CJ, Given CW, Baser O, Gardiner JC. Influence of surgical and treatment 

choices on the cost of breast cancer care. European Journal of Health Economics 

2003;4:96-101. 

17. Baser O, Bradley CJ, Gardiner JC, Given CW. Testing and correcting for non-random 

selection bias due to censoring: An application to medical costs. Health Services & 

Outcomes Research Methodology 2003;4:93-107. 

18. Rahbar MH, Sikorski A, Gardiner JC. Regression analysis of medical costs with right 

censored data in the presence of discrete covariates. Proceedings of the American 

Statistical Association: Biometrics Section [CD-ROM] 2003, Alexandria, VA: American 

Statistical Association. 

19. Baser O, Bradley CJ, Gardiner JC. Estimation from censored medical costs. Biometrical 

Journal 2004; 46:351-63. 

37
 
20. Gardiner JC, Sirbu CM, Rahbar MH. Update on sample size and power assessments for 

cost-effectiveness studies. Expert Review of Pharmacoeconomics & Outcomes Research 

2004 4(1):89-98. 

21. Rahbar MH, Gardiner JC. Nonparametric modeling of the mean survival time in a multifactor design based on randomly right-censored data. Biometrical Journal 

2004;46(5):497-502. 

22. Evonich RF, Maheshwari A, Gardiner JC, Khasnis A, Kantipudi S, Ip JH, et al. 

Implantable cardioverter defibrillator therapy in patients with ischemic or non-ischemic 

cardiomyopathy and nonsustained ventricular tachycardia. Journal of Interventional 

Cardiac Electrophysiology 2004;11(1):59-65. 

23. Bradley CJ, Gardiner JC, Given CW, Roberts CR. Cancer, Medicaid enrollment and 

survival disparities. Cancer 2005;103(8):1712-1718. 

24. Baser O, Gardiner JC, Bradley CJ, Yuce H, Given C. Longitudinal analysis of censored 

medical cost data. Health Economics 2006;15(5):513-525. 

25. Stommel M, Olomu A, Holmes-Rovner M, Corser W, Gardiner JC. Changes in practice 

patterns affecting in-hospital and post-discharge survival among ACS patients. BMC 

Health Services Research 2006;6. 

26. Soundarraj D, Thakur RK, Gardiner JC, Khasnis A, Jongnarangsin K. Inappropriate ICD 

therapy: Does device configuration make a difference? Pace-Pacing and Clinical 

Electrophysiology 2006;29(8):810-815. 

27. Gardiner JC, Luo Z, Liu L, Bradley CJ. A stochastic framework for estimation of 

summary measures in cost-effectiveness analyses. Expert Review of Pharmacoeconomics 

& Outcomes Research 2006;6(3):347-358. 

28. Gardiner JC, Luo ZH, Bradley CJ, Sirbu CA, Given CW. A dynamic model for 

estimating changes in health status and costs. Statistics in Medicine 2006;25(21):3648-

3667. 

29. Gardiner JC, Liu L, Luo Z. Estimation of medical costs from a transition model. IMSLecture Notes-Collection Series 2007 (1): 350-363, In press. 

30. Reed PL, Rosenman K, Gardiner J, Reeves M, Reilly MJ. Evaluating the Michigan 

SENSOR surveillance program for work-related asthma. American Journal of Industrial 

Medicine 2007;50(9):646-656. 

31. Gardiner JC, Luo Z, Liu L. Analysis of Multiple Failure Times Using SAS Software. In: 

R. Khattree, Naik D, editors. Computational Methods in Biomedical Research. New 

York, NY: Taylor & Francis, 2007. In press. 

32. Luo Z, Goddeeris J, Gardiner JC, Lyles JS, Smith RC. Cost of a primary care 

intervention for patients with medically unexplained symptoms – a randomized 

controlled trial. Psychiatric Services 2007;58:1079-1086. 

Abstracts and Presentations 

1.	 Guererro P, Hogan A, Gardiner J, Mellits D, Baumgardner R, Levine J, Rovner D, HolmesRovner M, Griffith L, Kupersmith J. Strategies to improve cost effectiveness of the 

implantable cardioverter defibrillator. Clinical Research 1993; 41(2):122a, presented. 

2.	 Guererro P, Hogan A, Gardiner J, Mellits D, Baumgardner R, Levine J, Rovner D, HolmesRovner M, Griffith L, Kupersmith J. New approach to determination of cost/effectiveness of 

the implantable cardioverter defibrillator. Clinical Research 1993; 41(2):234a, presented. 

38
 
3.	 Guererro P, Hogan A, Gardiner J, Mellits D, Baumgardner R, Rovner D, Holmes-Rovner M, 

McLane A, Levine J, Griffith L, Kupersmith J. Relationship of cost effectiveness of the 

transthoracic implantable cardioverter defibrillator to patient category and clinical strategy. 

Circulation Supplement 1993; 88:I-44. 

4.	 Guererro P, Hogan A, Gardiner J, Mellits D, Baumgardner R, Rovner D, Holmes-Rovner M, 

McLane A, Levine J, Saksena S, Griffith L, Kupersmith J. Improving the cost effectiveness 

of the Transvenous Implantable Cardioverter Defibrillator. Journal of the American College 

of Cardiology 1994; 23:206a. 

5.	 Gardiner J, Hogan A, Holmes-Rovner M, Rovner D, Griffith L, Kupersmith J. Estimation of 

confidence intervals for average cost-effectiveness and cost-effectiveness ratios from 

survival data. Clinical Research 1994; 42(2):224a, presented. 

6.	 Hogan A, Saksena S, Gardiner J, Mellits ED, Baumgardner RA, Rovner DR, Holmes-Rovner 

M, McLane AM, Levine J, Griffith L, Kupersmith J. The subpectoral transvenous 

implantable cardioverter defibrillator is a cost effective intervention. American College of 

Cardiology 44th Annual Scientific Session, 1994. 

7.	 Gardiner J, Hogan A, Holmes-Rovner M, Rovner D, Griffith L, Kupersmith J. Confidence 

intervals for cost-effectiveness ratios. Biometrics Society 1995, presented. 

8.	 Gardiner J, Holmes-Rovner M, Rovner D, Goddeeris J, Kupersmith J. Cost-effectiveness 

ratios in multi-state Markov models. Biometrics Society, Spring Meeting, 1996, Richmond, 

VA, presented. 

9.	 Abela G, Mitra R, Dwamena F, Gardiner J, Vasilenko P, Kroll J, Kupersmith J. Elevation in 

blood glucose is associated with complications during myocardial infarction—MICH Study. 

American Heart Association 69th Session, 1996. 

10. Dwamena F, Mitra R, Watson R, Gardiner J, Abela G, Vasilenko P, Kupersmith J. Do 

community physicians prescribe angiotensin-converting enzyme inhibitors to patients with 

acute myocardial infarction?—MICH Study. American Heart Association 69th Session 1996. 

11. Watson R, Mitra R, Dwamena F, Kroll J, Vasilenko P, McIntosh B, Gardiner J, Manfred 

Stommel, Kupersmith J. Race influences the rate of cardiac catheterization, but does not 

influence the rate of PTCA and CABG following acute myocardial infarction?—MICH 

Study. American Heart Association 69th Session 1996. 

12. Gardiner J, Holmes-Rovner M, Rovner D, Goddeeris J, Kupersmith J. Covariate-adjusted 

cost-effectiveness ratios. Biometrics Society, Spring Meeting, 1997, Memphis, TN, 

presented. 

13. Gardiner J, Holmes-Rovner M, Rovner D, Goddeeris J, Kupersmith J. Covariate-adjusted 

cost-effectiveness ratios. Society for Medical Decision Making, Annual Meeting, 1997, 

Houston, TX, presented. 

14. Gardiner J, Huebner M, Jetton J, Bradley CJ. Power assessments and confidence intervals for 

cost-effectiveness analyses. Medical Decision Making 1998;18(4):465, presented. 

15. Gardiner J, Huebner M, Jetton J, Bradley, C. Power assessments and confidence intervals for 

cost-effectiveness studies. International Indian Statistical Association, 1998, McMaster 

University, Canada, presented. 

16. Bradley CJ, Gardiner JC, Luo Z, Holmes-Rovner M, Rovner D. The Health and Activities 

Limitation Index: A means to estimate for population-based quality-adjusted life years. 

Society for Medical Decision Making. Submitted. 1999. 

39
 
17. Gardiner JC, Polverejan E, Pathak PK. Modeling costs and health outcomes jointly: 

Application to cost-effectiveness analyses. Society for Medical Decision Making: Med Decis 

Making 1999; 19 (4):542, presented 

18. Polverejan E, Gardiner JC, Holmes-Rovner M, Rovner D. Joint analysis of in-hospital length 

of stay and cost. Biometrics Society, Spring Meeting, 2000, Chicago, IL, presented. 

19. Polverejan E, Gardiner JC, Holmes-Rovner M, Rovner D. A multivariate model to assess 

jointly the correlates of length of stay and hospital cost associated with cardiac procedures. 

Society for Medical Decision Making. Submitted, 2000. 

20. Polverejan E, Gardiner JC. Estimating medical cost in longitudinal studies. Biometrics 

Society, Spring Meeting, 2001, Charlotte NC, presented. 

21. Luo Z, Rappley MD, Gardiner JC. Analyzing health care utilization with count regression 

models: application to children in Michigan Medicaid. Biometrics Society, Spring Meeting, 

2001, Charlotte NC, presented 

22. Gardiner JC, Luo Z, Polverejan E, Bradley CJ, Holmes-Rovner M, Rovner D. Longitudinal 

assessment of cost in health care interventions. Biometrics Society, Spring Meeting, 2002, 

Arlington, VA, presented. 

23. Gardiner JC, Polverejan E. Longitudinal assessment of cost in health care interventions: 

Application to cost-effectiveness analysis. Joint Statistical Meetings, American Statistical 

Association, 2002, New York, NY, presented. 

24. Bradley CJ, Given CW, Baser,O, Gardiner JC. Initial surgery determines subsequent costs of 

breast cancer care. Med Decision Making 2002:22(6);540, presented. 

25. Soundarraj D, Evonich R, Gardiner J, Mungee S, Khasnis A, Kantipudi S, Ip J, Thakur RK. 

Inappropriate therapy in patients with ischemic cardiomyopathy compared to patients with 

non-ischemic cardiomyopathy. XIIth and World Congress on Cardiac Pacing 

Electrophysiology, 2003, Hong Kong, presented. 

26. Soundarraj D, Evonich R, Gardiner J, Mungee S, Khasnis A, Kantipudi S, Ip J, Hayter G, 

Thakur RK. Do dual chamber ICDs reduce the incidence of inappropriate ICD therapy (IT)? 

XIIth and World Congress on Cardiac Pacing Electrophysiology, 2003, Hong Kong, 

submitted. 

27. Baser O, Bradley CJ, Gardiner JC, Given CW. Testing and correcting for nonrandom sample 

selection bias due to censoring. Society for Medical Decision Making, 2003, Chicago IL, 

presented. 

28. Gardiner JC, Sirbu CM. Assessing medical costs from a transition model. Symposium on 

Health Policy Analysis and Health Services Research, 2003, Portland, ME, presented. 

29. Gardiner JC. New developments in cost-effectiveness analysis. Joint Statistical Meetings, 

American Statistical Association 2003, San Francisco, CA, presented. 

30. Gardiner JC. Estimating costs and outcomes from a longitudinal model. International 

Conference on Healthcare Policy Research, 2003, Chicago, IL, presented. 

31. Sirbu CM, Gardiner JC. A transition model for assessing medical costs. Biometrics Society, 

Spring Meeting, 2004, Pittsburgh, PA, presented. 

32. Gardiner JC, Luo Z, Sirbu CM, Bradley CJ, Given CW. A multi-state stochastic model for 

assessing covariate effects on survival and cost. Society for Medical Decision Making 2004, 

Atlanta, GA. 

33. Gardiner JC, Luo Z, Sirbu CM, Bradley CJ, Given CW. A dynamic model to assess covariate 

effects on cost and health outcomes. Spring Meeting, Biometrics Society, 2005, Austin, TX. 

40
 
34. Luo Z, Gardiner JC, Bradley CJ, Given CW. Do propensity score methods overcome bias in 

estimating average treatment effects in observational studies? Society for Medical Decision 

Making, 2005, presented. 

35. Liu L, Luo Z, Gardiner JC. Comparison of estimators for average medical costs in a Markov 

model. Spring Meeting, Biometrics Society, 2006, Tampa, FL. 

36. Gardiner JC, Luo Z, Yang N. Estimation of mean response in the discrete and corner solution 

regression models with endogenous covariates. Spring Meeting, Biometrics Society, 2007, 

Atlanta, GA. 

37. Gardiner JC. Markovian models in cost-effectiveness analysis. Fourth Symposium— 

Frontiers of Statistical, Mathematical and Computational Sciences. The George Washington 

University, 2007, Washington, DC. 

38. Gardiner JC. Estimation of medical costs. Beyond Nonparametrics-Past, Present and Future 

Directions. University of South Carolina, 2007. Columbia, SC. 

41
 
Selected References 

1. Levit K, Smith C, Cowan C, Lazenby H, Sensenig A, Catlin A. Trends in U.S. health care 

spending, 2001. Health Affairs 2003;22(1):154-64. 

2. Garber AM. Advances in CE Analyses. In: Culyer AJ, Newhouse JP, editors. Handbook of 

Health Economics. Amsterdam: Elsevier Science BV, 2000:181-221. 

3. Commonwealth of Australia. Guidelines for the pharmaceutical industry on preparation of 

submissions to the Pharmaceutical Benefits Advisory Committee: including major submissions 

involving economic analyses. Canberra: Australian Government Publishing Service. 2002. 

4. Canadian Coordinating Office for Health Technology Assessment. Guidelines for economic 

evaluation of pharmaceuticals: Canada. 2nd ed. Ottawa: Canadian Coordinating Office for 

Health Technology Assessment (CCOHTA). 1997. 

5. National Institute for Clinical Excellence: Technology appraisals work programme, new 

guidance documents, 2001. 

6. U.S. Preventive Services Task Force. Guide to Clinical Preventive Services, 2nd Edition. 

Baltimore: Williams & Wilkins, 1996. 

7. Gold MR, Siegel JE, Russell LB, Weinstein MC, editors. Cost-Effectiveness in Health and 

Medicine. New York: Oxford University Press, 1996. 

8. Brouwer WBF, Koopmanschap MA. On the economic foundations of CEA. Ladies and 

gentlemen, take your positions! Journal of Health Economics 2000;19(4):439-59. 

9. Garber AM, Phelps CE. Economic foundations of cost-effectiveness analysis. Journal of 

Health Economics 1997;16(1):1-31. 

10. WHO. Constitution of the World Health Organization, Basic Documents. Geneva: World 

Health Organization, 1948. 

11. Gardiner JC, Bradley CJ, Huebner M. The cost-effectiveness ratio in the analysis of health 

care programs. In: Rao CR, Sen PK, editors. Handbook of Statistics, Bioenvironmental and 

Public Health Statistics. New York: North-Holland, 2000:841-69. 

12. Blumenschein K, Johannesson M, Yokoyama KK, Freeman PR. Hypothetical versus real 

willingness to pay in the health care sector: results from a field experiment. Journal of Health 

Economics 2001;20(3):441-57. 

13. Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-effectiveness 

analysis in heart-disease. 1. General principles. Progress in Cardiovascular Diseases 

1994;37(3):161-84. 

42
 
14. Fairclough DL. Design and Analysis of Quality of Life Studies in Clinical Trials. Boca Raton: 

Chapman & Hall/CRC, 2002. 

15. Royston P. Analysis of quality of life data in controlled clinical trials. Statistical Methods in 

Medical Research 2002;11(1):1-2. 

16. Glick HA, Briggs AH, Polsky D. Quantifying stochastic uncertainty and presenting results of 

cost-effectiveness analyses. Expert Review of Pharmacoeconomics & Outcomes Research 

2001;1(1):25-36. 

17. Gardiner JC, Huebner M, Jetton J, Bradley CJ. On parametric confidence intervals for the 

cost-effectiveness ratio. Biometrical Journal 2001;43(3):283-96. 

18. Stinnett AA, Mullahy J. Net health benefits: A new framework for the analysis of uncertainty 

in cost-effectiveness analysis. Medical Decision Making 1998;18(2):S68-S80. 

19. Lothgren M, Zethraeus N. Definition, interpretation and calculation of cost- effectiveness 

acceptability curves. Health Economics 2000;9(7):623-30. 

20. Gardiner JC, Polverejan E. Longitudinal models for the analysis of health care costs and 

outcomes. Proceedings of the American Statistical Association, Section on Health Policy 

Statistics [CD-ROM], 2002. 

21. Gardiner JC, Luo L, Liu L. Estimation of medical costs from a transition model.IMS-Lecture 

Notes-Collection Series 2007 (1): 350-363, In press. 

22. Stommel M, Olomu A, Holmes-Rovner M, Corser W, Gardiner JC. Changes in practice 

patterns affecting in-hospital and post-discharge survival among ACS patients. BMC Health 

Services Research 2006;6. 

23. Polverejan E, Gardiner JC, Bradley CJ, Holmes-Rovner M, Rovner D. Estimating mean 

hospital cost as a function of length of stay and patient characteristics. Health Economics 

2003;12(11):935-47. 

24. Gardiner JC, Luo Z, Bradley CJ, Polverejan E, Holmes-Rovner M, Rovner D. Longitudinal 

assessment of cost in health care interventions. Health Services & Outcomes Research 

Methodology 2002;3:149-68. 

25. Gardiner J, Hogan A, Holmes-Rovner M, Rovner D, Griffith L, Kupersmith J. Confidenceintervals for cost-effectiveness ratios. Medical Decision Making 1995;15(3):254-63. 

26. Gardiner J, Holmes-Rovner M, Goddeeris J, Rovner D, Kupersmith J. Covariate-adjusted 

cost-effectiveness ratios. Journal of Statistical Planning and Inference 1999;75(2):291-304. 

43
 
27. Kupersmith J, Hogan A, Guerrero P, Gardiner J, Mellits ED, Baumgardner R, et al. 

Evaluating and improving the cost-effectiveness of the implantable cardioverter-defibrillator. 

American Heart Journal 1995;130(3):507-15. 

28. Beck JR, Pauker SG. The Markov Process in Medical Prognosis. Medical Decision Making 

1983;3(4):419-58. 

29. Briggs A, Sculpher M. Markov models of medical prognosis—Commentary. British Medical 

Journal 1997;314(7077):354-5. 

30. Briggs A, Sculpher M. An introduction to Markov modeling for economic evaluation. 

Pharmacoeconomics 1998;13(4):397-409. 

31. Sonnenberg FA, Beck JR. Markov-Models in Medical Decision Making—a Practical Guide. 

Medical Decision Making 1993;13(4):322-38. 

32. O'Brien BJ, Drummond MF, Labelle RJ, Willan A. In search of power and significance— 

issues in the design and analysis of stochastic cost-effectiveness studies in health-care. Medical 

Care 1994;32(2):150-63. 

33. Willan AR, Obrien BJ. Confidence intervals for cost-effectiveness ratios: An application of 

Fieller's theorem. Health Economics 1996;5(4):297-305. 

34. Chaudhary MA, Stearns SC. Estimating confidence intervals for cost-effectiveness ratios: An 

example from a randomized trial. Statistics in Medicine 1996;15(13):1447-58. 

35. Briggs AH, Wonderling DE, Mooney CZ. Pulling cost-effectiveness analysis up by its 

bootstraps: A non-parametric approach to confidence interval estimation. Health Economics 

1997;6(4):327-40. 

36. Laska EM, Meisner M, Siegel C. Statistical inference for cost-effectiveness ratio. Health 

Economics 1997;6(3):229-42. 

37. Gardiner JC, Huebner M, Jetton J, Bradley CJ. Power and sample size assessments for tests 

of hypotheses on cost-effectiveness ratios. Health Economics 2000;9(3):227-34. 

38. Gardiner JC, Sirbu CM, Rahbar MH. Update on statistical power and sample size 

assessments for cost-effectiveness studies. Expert Review of Pharmacoeconomics & Outcomes 

Research 2004;4(1):89-98. 

39. Briggs AH, Gray AM. Power and sample size calculations for stochastic cost-effectiveness 

analysis. Medical Decision Making 1998;18(2):S81-S92. 

40. Laska EM, Meisner M, Siegel C. Power and sample size in cost-effectiveness analysis. 

Medical Decisionmaking 1999;19(3):339-43. 

44
 
41. Al MJ, Van Hout BA, Michel BC, Rutten FFH. Sample size calculation in economic 

evaluations. Health Economics 1998;7(4):327-35. 

42. Backhouse ME. Use of randomised controlled trials for producing cost-effectiveness 

evidence—Potential impact of design choices on sample size and study duration. 

Pharmacoeconomics 2002;20(15):1061-77. 

43. Briggs A, Fenn P. Confidence intervals or surfaces? Uncertainty on the cost- effectiveness 

plane. Health Economics 1998;7(8):723-40. 

44. Wakker P, Klaassen MP. Confidence-Intervals for Cost/Effectiveness Ratios. Health 

Economics 1995;4(5):373-81. 

45. Polsky D, Glick HA, Willke R, Schulman K. Confidence intervals for cost-effectiveness 

ratios: A comparison of four methods. Health Economics 1997;6(3):243-52. 

46. Willan A, O'Brien BJ. Confidence intervals for cost-effectiveness ratios: an application of 

Fieller's theorem (vol 5, pg 297, 1996). Health Economics 1999;8(6):559. 

47. Heitjan DF, Moskowitz AJ, Whang W. Bayesian estimation of cost-effectiveness ratios from 

clinical trials. Health Economics 1999;8(3):191-201. 

48. O'Hagan A, Stevens JW, Montmartin J. Inference for the cost-effectiveness acceptability 

curve and cost-effectiveness ratio. Pharmacoeconomics 2000;17(4):339-49. 

49. Gardiner JC, Indurkhya A, Luo Z. The performance of estimation procedures for costeffectiveness ratios. In: Balakrishnan N, editor. Advances on Methodological and Applied 

Aspects of Probability and Statistics. New York: Taylor & Francis, 2002:547-59. 

50. Indurkhya A, Gardiner JC, Luo ZH. The effect of outliers on confidence interval procedures 

for cost-effectiveness ratios. Statistics in Medicine 2001;20(9-10):1469-77. 

51. Jiang G, Wu J, Williams GR. Fieller's interval and the bootstrap-Fieller interval for the 

incremental cost-effectiveness ratio. Health Services & Outcomes Research Methodology 

2000;1(3-4):291-303. 

52. Briggs AH, Mooney CZ, Wonderling DE. Constructing confidence intervals for costeffectiveness ratios: An evaluation of parametric and non-parametric techniques using Monte 

Carlo simulation. Statistics in Medicine 1999;18(23):3245-62. 

53. Weintraub WS, Cole J, Tooley JF. Cost and cost-effectiveness studies in heart failure 

research. American Heart Journal 2002;143(4):565-76. 

54. Weintraub WS, Mahoney EM, Ghazzal ZMB, King SB, Culler SD, Morris DC, et al. Trends 

in outcome and costs of coronary intervention in the 1990s. American Journal of Cardiology 

2001;88(5):497-503. 

45
 
55. Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-Effectiveness 

Analysis in Heart-Disease. 3. Ischemia, Congestive-Heart-Failure, and Arrhythmias. Progress in 

Cardiovascular Diseases 1995;37(5):307-46. 

56. Kupersmith J, Holmes-Rovner M, Hogan A, Rovner D, Gardiner J. Cost-Effectiveness 

Analysis in Heart-Disease .2. Preventive Therapies. Progress in Cardiovascular Diseases 

1995;37(4):243-71. 

57. O'Brien BJ, Connolly SJ, Goeree R, Blackhouse G, Willan A, Yee R, et al. Costeffectiveness of the implantable cardioverter-defibrillator—Results from the Canadian 

Implantable Defibrillator Study (CIDS). Circulation 2001;103(10):1416-21. 

58. Larsen G, Hallstrom A, McAnulty J, Pinski S, Olarte A, Sullivan S, et al. Cost-effectiveness 

of the implantable cardioverter-defibrillator versus antiarrhythmic drugs in survivors of serious 

ventricular tachyarrhythmias—Results of the Antiarrhythmics Versus Implantable Defibrillators 

(AVID) economic analysis substudy. Circulation 2002;105(17):2049-57. 

59. Epstein AE, Conti JB, Curtis AB, Hess PG, Iansmith DH, Lott JW, et al. Antiarrhythmics 

Versus Implantable Defibrillators (Avid) —Rationale, Design, and Methods. American Journal 

of Cardiology 1995;75(7):470-75. 

60. Mushlin AI, Hall WJ, Zwanziger J, Gajary E, Andrews M, Marron R, et al. The costeffectiveness of automatic implantable cardiac defibrillators: Results from MADIT. Circulation 

1998;97(21):2129-35. 

61. Coats AJS. MADIT II, the Multi-center Autonomic Defibrillator Implantation Trial II 

stopped early for mortality reduction, has ICD therapy earned its evidence-based credentials? 

International Journal of Cardiology 2002;82(1):1-5. 

62. O'Brien B, Connolly S, Goeree R, Blackhouse G, Willan A, Yee R, et al. Cost-effectiveness 

of the implantable cardioverter defibrillator: Results from the Canadian Implantable Defibrillator 

Study (CIDS). Journal of the American College of Cardiology 2000;35(2):152A-153A. 

63. Evonich RF, Maheshwari A, Gardiner JC, Khasnis A, Kantipudi S, Ip JH, et al. Implantable 

cardioverter defibrillator therapy in patients with ischemic or non-ischemic cardiomyopathy and 

nonsustained ventricular tachycardia. Journal of Interventional Cardiac Electrophysiology 

2004;11(1):59-65. 

64. Hlatky MA, Bigger T. Cost-effectiveness of the implantable cardioverter defibrillator? 

Lancet 2001;357(9271):1817-8. 

65. Weiss JP, Saynina O, McDonald KM, McClellan MB, Hlatky MA. Effectiveness and costeffectiveness of implantable cardioverter defibrillators in the treatment of ventricular arrhythmias 

among Medicare beneficiaries. American Journal of Medicine 2002;112(7):519-27. 

46
 
66. Gardiner J, Hogan A, Kupersmith J, Holmes-Rovner M, Rovner D, Griffith L. Estimation of 

confidence-intervals for average cost-effectiveness and cost-effectiveness ratios from survivaldata. Clinical Research 1994;42(2):A224. 

67. Parmigiani G. Modeling in Medical Decision Making-A Bayesian Approach. New York: 

Wiley & Sons, Inc, 2002. 

68. Spath MA, O'Brien BJ. Cost effectiveness of implantable cardioverter defibrillator therapy 

versus drug therapy for patients at high risk of sudden cardiac death. Pharmacoeconomics 

2002;20(11):727-38. 

69. Sanders GD, Hlatky MA, Every NR, McDonald KM, Heidenreich PA, Parsons LS, et al. 

Potential cost-effectiveness of prophylactic use of the implantable cardioverter defibrillator or 

amiodarone after myocardial infarction. Annals of Internal Medicine 2001;135(10):870-83. 

70. Thompson S. Statistical issues in cost-effectiveness analyses. Statistical Methods in Medical 

Research 2002;11(6):453-4. 

71. Watson RE, Stein AD, Dwamena RC, Kroll J, Mitra R, McIntosh BA, et al. Do race and 

gender influence the use of invasive procedures? Journal of General Internal Medicine 

2001;16(4):227-34. 

72. AHCPR Guidelines Panel. Depression in Primary Care: Detection and Diagnosis. Rockville, 

MD: U.S. Department of Health and Human Services, Agency for Healthcare Policy & 

Research, Pub #93-0550, 1993. 

73. Sacristan JA, Day SJ, Navarro O, Ramos J, Hernandez JM. Use of confidence-intervals and 

sample-size calculations in health economic-studies. Annals of Pharmacotherapy 1995;29(7-

8):719-25. 

74. Smith RC, Lyles JS, Gardiner JC, Sirbu C, Hodges A, Collins C, et al. Primary care 

clinicians treat patients with medically unexplained symptoms: A randomized controlled trial. 

Journal of General Internal Medicine 2006;21(7):671-677. 

47