ESRI Research Note No.34

Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -Shigeru Sugihara, Koichi Kawabuchi,
Yasuko Ikemoto, and Ikumi Imamura

July 2017

Economic and Social Research InstituteCabinet Office
Tokyo, JapanThe views expressed in “ESRI Research Note” are those of the authors and not those of
the Economic and Social Research Institute, the Cabinet Office, or the Government of Japan.
(Contact us: https://form.cao.go.jp/esri/en_opinion-0002.html)

ESRI Research Note No.34

Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -Shigeru Sugihara, Koichi Kawabuchi,
Yasuko Ikemoto, and Ikumi Imamura

July 2017

Economic and Social Research InstituteCabinet Office
Tokyo, JapanThe views expressed in “ESRI Research Note” are those of the authors and not those of
the Economic and Social Research Institute, the Cabinet Office, or the Government of Japan.
(Contact us: https://form.cao.go.jp/esri/en_opinion-0002.html)

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis † -Shigeru Sugihara ‡Koichi Kawabuchi§
Yasuko Ikemoto **Ikumi Imamura ††July 2017

This paper was originally presented at the ESRI seminor held on 30 March, 2011. Achange of positions for one of the authors just after the meeting resulted in the delay in
its revision.
‡ Social and Economic Research Institute, Cabinet Office.
§ Tokyo Medical and Dental University.
** Social and Economic Research Institute, Cabinet Office.
†† Northern Territories Affairs Administration, Cabinet Office.
†1

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"Abstract
Quality relative to cost is important in any field of economics. Health care is not an
exception. If quality is superb relative to cost, it is worth incurring the cost. If quality ispoor, cheap care is of little use. Cost-benefit analysis has been performed on a lot of
individual treatments. It is unclear, however, whether health care expenditures of acountry as a whole is worth spending specifically in Japan. Virtually no attempts are
made to measure the benefits of health care for the country. We quantify the trade-off
between quality and cost of health care in Japan and perform cost-benefit analysis forthe country as a whole. Due to data availability, our analysis is restricted to AMI
patients in a small number of hospitals. The results are suggestive, however. We findstrong evidence that there is a positive trade-off: higher quality requires a higher cost, or,a lower cost induces lower quality. Whether the cost is worth it depends the value of life,of course. With the value of life of reasonable range, lower mortality more thancompensates higher costs.

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ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"1. Introduction
Quality relative to cost is important in any field of economics. Health care is not an
exception. If quality is superb relative to cost, it is worth incurring the cost. If quality ispoor, cheap care is of little use.
Cost-benefit analysis has been performed with respect to a lot of individual
treatments. It is unclear, however, whether health care expenditures of a country as awhole is worth spending specifically in Japan. Virtually no attempts are made tomeasure the benefits of health care for the total health system.
We quantify the trade-off between quality and cost of health care in Japan andperform a cost-benefit analysis for the care of AMI patients. Although the methods areapplicable to the health care system as a whole, due to data limitation, we restrict ouranalysis to a small sample of Japanese hospitals.
In examining the quality-cost trade-off, it is important to recognize the endogeneity or
simultaneous determination of quality and cost. A simple regression of quality on cost
will generate a biased estimate of the effect of cost on quality. Basically following
Timbie and Normand (2008), we will examine three models to accommodate theendogeneity: the cost-in-regression model with instrumental variables, the simultaneous
equations model and the two-part model.
The structure of the paper is as follows. Section 2 gives an overview of the method andpresents three types of models incorporating the endogeneity of quality and cost.
Section 3 describes the data used and descriptive statistics. Sections 4, 5 and 6 estimate
the cost-in-regression model, the hierarchical model and the two-part model,
respectively. Section 7 concludes.

2. Methods
In examining the relationship between quality and cost, simple comparison of outcome
and cost is not appropriate. Quality and cost are endogenous variables so that we should
control for the endogeneity.
For example, low quality of care may manifest itself in increased complications
which result in higher costs. Alternatively, low quality of care may induce early death
thereby shorten length of stay which implies lower costs.

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ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"We examine three ways to model the relationship between quality and cost:
cost-in-regression model with instrumental variables, the simultaneous equations modeland the two-part model.
Timbie and Normand (2008) proposed three methods for combining quality andefficiency measures including univariate models, regression and cost-effectivenessanalysis which uses two-part model. Our analysis follow their approach with a slight
modification that we replace their univariate models with simultaneous equations modelby allowing random errors of mortality and cost equations to be correlated.
Cost-effectiveness analysis:
We perform standard cost-effectiveness analysis just as Timbie and Normand (2008).
Incremental net benefit is defined as change in benefits multiplied by the value of unit
benefit minus change in cost.
Incremental Net Benefit= λ ⋅ ∆E − ∆C ,where λ is the value of life (quality of life), ∆E is the change in benefits and ∆C
is the change in costs. Since how much life is worth is controversial, we calculate
various levels of incremental net benefits by changing the value of life.

The remainder of this section will outline the three approaches to modeling joint
determination of quality and cost.
(a) Regression of quality on cost
A simple way to examine the relationship between quality and cost is to regress quality
on cost. We try simultaneous estimation of mortality and cost equations instead of single
mortality equation with cost as an explanatory variable. In other words, we explicitly
model determination of cost in conjunction with determination of mortality. We allow
correlation between error terms in mortality and cost equations.
To identify the effect of cost on mortality, we need an exogenous variable which isincluded in the cost equation but excluded from the mortality equation. As instrumental
variables we use variables which indicate whether a hospital is participating in the DPC
arrangement. As is explained below, the DPC system is analogous to the DRG systemand provides a strong incentive to reduce costs.

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ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"(b) Simultaneous equations: Correlation between random effects
In this approach, we directly model joint determination of quality and cost. Cost is
excluded from the mortality equation.

Figure 1

Joint Determination of Quality and Cost
Quality

State of patient( Risk factors )Choice ofTreatment

Correlation

Costs

There are two hospital-specific random effects, one which adversely affects outcomes
and the other which increases costs. If higher costs reduce mortality, these random
effects will be negatively correlated. Hence, by examining the correlation between two
random effects, we can infer the quality-cost trade-off.
Simultaneous estimation of mortality and cost equations require instrumental
variables to distinguish two equations. Here, again, we use variables which represent
DPC statuses as instruments.
(c) Two-part model
The third way to model correlation between mortality and cost is the two-part model.
The two-part model decomposes the joint distribution of mortality and cost into twoparts. One is the distribution of mortality and the other the distribution of costconditional on mortality.

p( yit , l cos tit ) = p( yit ) ⋅ p (l cos tit | yit )We first estimate the mortality equation and second estimate cost equation according as
the patient dies or not. For each part, we estimate excess mortality and excess costs.
Since risk factors change from year to year, proper risk adjustment is needed. Risk
adjustment is done by estimating a logistic regression model to measure the influence of5

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"risk factors on mortality. We re-transform the linear predictor in the logistic regression
back to the probability scale for individuals. Then, we average across all patients withineach year to obtain the predicted outcome.
To adjust for case mix differences across years, we follow Timbie, et al.
(2009:Cost-Effectiveness paper) who adopted indirect standardization. We estimate
counterfactual outcomes for each year assuming underlying quality levels of the entire
population while conditioning on each year’s case mix. We take the difference between
this expected outcome and the predicted outcome to yield an excess mortality for eachyear.
More concretely, in the indirect standardization, patient mix (distribution of risk
factors) is fixed at actual mix in each year for both predicted and expected outcomes.
We compare mortality rates of the following two cases for each year. Outcome 1 uses
realized quality of care with the relationship between risk factors and outcome being
actual one for each year. Outcome 2 uses average quality of care with the hypothetical
relationship between risk factors and outcome being estimated by supposing that eachyear’s quality of care is the same as the total year. Then, excess mortality is calculated
as the difference between two outcomes.

Figure 2

Indirect Standardization

Quality of carein a specific year

Outcome 1β̂ t
Excess mortality

Risk factors
in each year

βt

Outcome 2

Average quality of care

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ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"3. Data and basic statistics
Data were collected on AMI patients in 9 hospitals with a record of hospitalization atsome period of time from 2004.4.1 to 2007.3.31. These hospitals had agreed tocooperate in the research for the consecutive years upon approval of in-hospital ethicalcommittee.
We created structured questionnaires for data collection. Questionnaire I asked for
detailed clinical information on the patient as well as information on the treatment thepatient received. Claim data and physicians profile were collected by Questionnaire II.
Questionnaire III collected overall information on AMI treatment at the hospital, such as
the annual total number of CABG conducted. A part-time lecturer with physician’s
license in Thoracic-Cardiovascular Surgery Section of Tokyo Medical and Dental
University stayed throughout the research to fill Questionnaire I from patient medical
records including nursing records and discharge summary at each hospital.
Questionnaire II and III were filled by hospital staffs who were approved of the accessto claim data at each hospital.
Sample is restricted to ST-Elevation AMI in the following analyses. This choice isintended to secure homogeneity in the sample as is epitomized by the separate
compilation of ACC/AHA guidelines for the management of patients with ST-Elevation
myocardial infarction from those for
Non-ST-Elevation myocardial infarction.

themanagementofpatients

with

Nine hospitals were included in the data set. Only the hospitals with more than ten
STEMI patients in every year are retained in the analysis. Observations are 2631 in total,of which 598 are in 2004, 612 in 2005, 672 in 2006 and 749 in 2007.
Table 1 shows basic statistics of patients for all hospitals. The Average age is 68.9
years old and a little less than a third patients is female. About a half of patients are in
the Killip class 1, a quarter in the class 2 and a little less than 15% in classes 3 andfurther 14% in the class 4. Occlusion of the left main trunk, left bundle branch blockand ventricular fibrillation account for around 4 to 6% of patients, respectively. Morethan a half of patients are with hypertension and a little less than 40% and a little morethan a third are with hyperlipidemia and diabetes mellitus. 8% of patients suffer fromheart failure and 10% from renal failure. The share of patients with cancer is 8%.
Table 2 exhibits characteristics of sample hospitals. Three out of nine hospitals aredesignated as tertiary critical care hospitals and all except one hospitals are designatedas teaching hospitals. The average number of beds is 434. Hospitals in the sample arelarge in general, but the size varies. One hospital holds nearly 1000 beds while two

7

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"hospitals have less than 200 beds. The average number of AMI patients is 86, but thevariation is large. Two hospitals admitted more than 150 AMI patients while two
hospitals admitted only around 20. The average number of PCI performed is 297, which
is a large number in the Japanese standard. Again, there is a great variation amonghospitals. A hospital performed more than 700 PCI while two hospitals performed only
a little more than 100 PCI.
Cost is charge billed either to the Social Insurance Funds if the medical activity iscovered by the social insurance or to individuals if not. Of course, this is not a true cost,
but a cost to the patients or taxpayers. The use of this concept of cost could be justified
because this is the cost the society has to pay in order to obtain better quality of healthcare.

Figure 3 depicts crude mortality and cost over time. In 2004, crude mortality rate is alittle above 9 % while mean cost is a little less than 2.6 million yen. In 2005, mean costdeclined by around 0.1 million yen with a rise in mortality rate. The year 2006 saw adramatic fall of cost to nearly 2.1 million yen together with a commensurate rise inmortality rate to more than 12 %. Then, in 2007, mortality rate declined with virtually
no change in cost.
The decline in cost parallels with a decline in average length of stay (Figure 4). During
this period, heavy pressures to reduce medical expenditures are felt by hospitals. The
introduction of the DPC system may have been especially powerful to induce hospitals
to reduce length of stay.
The Diagnosis Procedure Combination (DPC) system was introduced in 2003 as aprospective payment system for acute care of patients treated by the Specific Function
Hospitals. Thereafter, the DPC system has been expanded to include other eligible
hospitals. As of July 2010, the DPC system covers 1,391 hospitals and around 460,000
beds, which account for 50.4% of total beds.
The classification of patients starts with the diagnosis which absorbed resources themost among their diagnoses. Patients are further classified by whether specified
operations are performed or not. Then, the final classification is reached according as
whether the patient has comorbidities or not.
The DPC system is intended for use in a Prospective Payment System. But it
retains characteristics of fee-for-service. For example, payments are per diem, not for8

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"the whole hospitalization episode, and the system does not apply to operations and someother costly procedures. Therefore, it provides incentives to reduce LOS as well as
incentives to increase operations. Overall, the former effect is larger than the latter
effect as is verified in the estimation result of, for example, the cost-in-regression model
shown in Appendix Table A1.
In 2004, of nine hospitals in the sample, one was applied the DPC system, six werein preparation for it and two were neither applied nor in preparation. In 2006, seven
were applied, one was in preparation and one was neither applied nor in preparation.
Figure 5 shows crude mortality and cost by hospital. Mortality represented by bar chartdiffers substantially among hospitals. Hospital 3 has the highest mortality rate of morethan 18 % while hospital 5 has the lowest mortality rate of only a little more than 6 %.
Average cost represented by line graph also varies substantially. Hospital 9 has
the highest cost of nearly 300 million yen while hospital 3 has the lowest cost of muchless than 200 million yen. Overall, it seems that hospitals with higher mortality tend tohave lower costs. The relationship between mortality and cost will be examined in detailbelow.
Risk factors used in the regressions are shown in Table 1. Risk factors include age,female, Killip classes 2, 3 and 4, occlusion of the left main trunk, Left Bundle Branch
Block, ventricular fibrillation(VF), history of myocardial infarction, history of PCI,
history of CABG, hypertension, diabetes mellitus, hyperlipidemia, chronic obstructive
pulmonary disease (COPD), bleeding tendencies, renal failure, cerebrovascular diseases
and cancer.

4. Cost-in-regression model
We start with the estimation of cost-in-regression model. Since cost is endogenous
variable, we explicitly model the determination of cost and to better identify the effectof cost on mortality, we include instrumental variables in the cost equation as is
explained below.
We estimate simultaneous equations for the sample of all years assuming that the
impact, γ , of cost on mortality is the same for all years. Since costs are very muchskewed, we take log-transformation to make them more “normal”.

9ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"K

yij = 1[α + ∑ β k ⋅ xij + γ ⋅ l cos tij + ciy + uij > 0]
k =1

Kl cos tij = κ + ∑ ϕ k ⋅ xij + δ ⋅ zij + cilc + vij ,k =1

where yij denotes the outcome of the j-th patient in the i-th hospital. The outcome
variable, yij takes the value 1 if a patient dies during the hospitalization and 0 if she
survives. 1[.] represents an indicator function which takes the value 1 if the condition
within the square bracket is true and 0 otherwise.

l cos tij denotes logarithms of costs of the j-th patient in the i-th hospital.
xij ’s are risk factors of a patient listed above.
zij denotes instrumental variables which sill be detailed below.
ciy is an unobserved random effect specific to i-th hospital which affects yij .
cilc is an analogous random effect which affects l cos tij

As was pointed out above, cost is an endogenous variable so that in the mortality
equation l cos tij is correlated with the error term uij .
We chose to model the simultaneous determination of mortality and cost. We
estimate the mortality equation and cost equation simultaneously allowing error terms

uij and vij to be correlated.
To identify the impact of cost on mortality, we searched for instrumental variables
which are correlated with cost but uncorrelated with the error term, uij . Variables whichindicate whether a hospital is participating in the DPC program should be goodcandidates for IVs because it can be assumed that DPC participants have strong
incentives to reduce costs by way of reducing the length of stay while affecting
mortality only through cost. In reality, the DPC system may induce hospitals to perform

10

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"operations more aggressively. However, the net effects can be assumed to be reduced
medical expenditures. This assumption is validated by the estimation results shown
below.
We have two variables which show participation in the DPC program according todiffering status. “DPC preparation” indicates that the hospital is in preparation ofparticipating in the DPC program. “DPC participation” indicates that the hospital isreimbursed by the DPC program.
Prior specifications are as follows. Correlated random intercepts are assumed to bebivariate normal with mean zero and precision matrix Σ −1 : ci ~ N (0, Σ −1 ) with

 ciy ci ≡  lc  . The random effect, ci , for each hospital comes from the same normal
 ci 
distribution so that shrinkage toward the overall mean is expected.
The precision matrix is assumed to follow Wishart distribution with scale matrix
and 2 degrees of freedom: Σ −1 ~ Wishart (Ω,2) . The choice of the 2 degrees ofΩ
freedom is intended to represent vague prior. Ω is, in turn, specified as I 2 .
The coefficient, γ , on lcost is assumed to follow a normal distribution with mean

zero and variance σ 2 : γ ~ N (0,σ 2 ) . A uniform prior on the standard deviation, σ , isadopted: σ ~ Uniform(0,100 ) . The choice of the variance of 100 is intended torepresent a diffuse prior. Gelman and Hill (2007) give a thoughtful discussion on theappropriateness of this value in the context of the logistic models or log-transformed
regressors. They argue that in logistic and logarithmic regressions, typical changes inoutcomes are on the scale of 0.1 or 1, but not 10 or 100, so that one would not expect tosee coefficients much higher than 10 in absolute values as long as the regressors are also
on a reasonable scale. Although their choice of the value of variance is 1002 , webelieve that their argument applies to our choice, 100. In fact, mean estimates of γ
obtained below is -0.82.
The model was estimated with Markov chain Monte Carlo methods using
WinBUGS software. To check the convergence, three parallel chains were run tocalculate the Gelman-Rubin statistic. A burn-in of 10,000 iterations for each chain wasallowed for the model to converge. Additional 20,000 samples for each chain weredrawn from the joint posterior distribution for the estimation of all model parameters.
Table 2 shows estimate of the coefficient on cost. Full results are in Appendix
Table A1. The mean is -0.820 and the standard error is 0.092. The 95 % credible interval

11

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"is from -1.006 to -0.643. The probability of the coefficient being positive is zero. Hence,
it is very likely that higher cost reduces mortality.
From 2004 to 2007, the average cost decreased by 16.9 % which corresponds to a
decline of around 432 thousand yen. Plugging this change into the mortality equation
reveals that this decline in costs raised mortality rate (i.e. reduced survival rate) by
0.57 % points from 9.20 % to 9.76 %. (The actual mortality rate increased to 10.8 %,which is influenced by random fluctuations and factors other than decreased costs.)
We can perform incremental cost-benefit analysis from this relationship. Recall thefollowing formula:
Incremental Net Benefit= λ ⋅ ∆E − ∆C ,where λ is the value of life, ∆E is incremental benefit (change in survival rate) and∆C is incremental cost.
First, we calculate the break-even value of life, which is the critical value of λthat equates the incremental gross benefit and incremental costs. We reversed the signsof the actual changes in survival rate and costs so that ∆E = +0.57% increase insurvival rate corresponding to ∆C = 432,042 yen increase in costs. INB is calculated
as

λ* =

∆C
432042= 76,357 thousand yen.
=∆E 0.005658

Hence, if we value life at around 76.4 million yen, a 432 thousand-yen increase in costs
is compensated by a 0.57 % increase in survival rate (decrease in mortality rate). If wevalue life more than 76.4 million yen, the 0.57 % increase in mortality more thancompensate the 432 thousand-yen increase in costs.
Second, we estimate incremental net benefits according as the value of life changes.
How much life is worth is controversial, at best. It is nearly impossible to pin down
exact value of life, although Viscusi and Aldy(2007) find that half of the studies of the
U.S. labor market reveal a value of a statistical life ranges from $5 million to $12
million and the median is $7 million when converted into year 2000 dollars. (In terms ofyen, the range is from 550 million yen to 1 billion and 320 million yen with a median of
770 million yen at the exchange rate of 110 yen per dollar.) Therefore, it is common to

12

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"calculate incremental net benefits by changing the value of life.
We can draw a diagram which shows the incremental net benefit as a function of
the value of life. Figure 6 shows this relationship between the value of life andincremental net benefit. As the value of life increases, the net benefit from an increase incosts and corresponding decrease in mortality (increase in survival rate) becomes larger.

5. Simultaneous equations model
In this approach, we directly model joint determination of quality and cost. Comparedwith the cost-in-regression model, cost is excluded from the mortality equation. For t-th
year, we checked correlation between cty and ctlc in the mortality and cost equations.
The outcome variable, yit , takes the value one if a patient i in time t dies and zero
if she is discharged alive.
K

yit = 1[α + ∑ β k ⋅ xit + cty + uit > 0]
k =1

Kl cos tit = κ + ∑ ϕ k ⋅ xit + δ ⋅ zit + ctlc + vit
k =1

Since costs are very much skewed, we take log-transformation to make them more
“normal”. Notations for variables are the same as the cost-in-regression model.
Instrumental variables are also the same.
The model was estimated with Markov chain Monte Carlo methods using WinBUGS
software. The number of chains, check of convergence, burn-in and samples for
estimation are the same as the cost-in-regression model.
Prior specifications are also similar. Namely, correlated random intercepts are
assumed to be bivariate normal with mean zero and precision matrix

Σ −1 :

 cy 
ct ~ N (0, Σ −1 ) with ct ≡  tlc  . The random effect, ct , for each year comes from the ct 
same normal distribution so that shrinkage toward the overall mean is expected.
The precision matrix is assumed to follow Wishart distribution with scale matrixΩand 2 degrees of freedom: Σ −1 ~ Wishart (Ω,2) . Ω is, in turn, specified as I 2 .
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ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"Results of the estimation of simultaneous equations model are shown in Appendix Table
A2. The upper part of Table 3 presents overall correlation between random effects for
mortality and those for cost. The estimate is almost zero. This is because correlations
within each year are very low, which are shown in the lower part of the table.
Correlation among years seems to be high as is depicted in Figure 7. One can see
negative relationship between mortality random effects and cost random effects. Overall
picture is the similar to Figure 3 of crude mortality and cost. A remarkable difference isthat mortality random effect in 2005 is lower than that in 2004. Estimates of random
effects are after adjustment for risk factors.

The case of hospital random effects
As an alternative viewpoint, we checked the correlation between hospital random
effects of mortality and cost for hospital. Namely, for i-th hospital and j-th patient, we
checked correlation between ciy and cilc in the mortality and cost equations.

K

yij = 1[α + ∑ β k ⋅ xij + ciy + uij > 0]
k =1

Kl cos tij = κ + ∑ ϕ k ⋅ xij + δ ⋅ zij + cilc + vij
k =1

When we replace year random effects with hospital random effects in the estimation of
the simultaneous equations model, we obtain correlation between mortality and costrandom effects of hospitals. Full results are shown in Appendix Table A2.
The upper part of Table 4 shows overall correlation. Again, the correlation is low
and this is because of low correlation within hospital. Once again, correlation amonghospitals seems to be high. A clear downward-sloping line is observable in Figure 8.
This line would represent the trade-off between mortality and cost. Rather surprisingly,
almost all hospitals lie on the line although hospitals 4 and 5 may have slightly better
survival rate with lower costs.
How much confidence can we place on these estimates of random effects? Figure 9shows mean level of random effects for mortality together with 95 % credible intervals.
These random effects are not exponentiated. Overall, mortality random effects are
significantly above or below zero. The probability that the random effect is above zero

14

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"is shown at the bottom of the figure. Except hospitals 3, 7 and 9, the probabilities are
more than 0.9 or less than 0.1.
Figure 11 shows mean level of random effects for cost together with 95 % credibleintervals. Cost random effects are above or below zero less significantly than mortality
random effects. The probability that the random effect is above zero is again shown at
the bottom of the figure. Four hospitals out of nine have probabilities more than 0.9 orless than 0.1 and the probabilities of other hospitals are not so different from these.

6. Two-part model
The two-part model decomposes the joint distribution of mortality and cost into twoparts. One is the distribution of mortality and the other the distribution of costconditional on mortality.

p( yit , l cos tit ) = p( yit ) ⋅ p (l cos tit | yit )The outcome variable, yit , takes the value one if a patient i in time t dies and zero if
she survives. We proceed in following steps.
First, as for the p ( yit ) part, we estimate the mortality equation:
logit [ p( yit = 1 | xit )] = α t + β t ⋅ xit ,where xit is severity index. We follow Timbie, et al. (2008:Cost-Effectiveness paper)in creating a measure of disease severity, severity index, for each patient. A logistic
regression was used to model the effect of demographic and clinical risk factors on
in-hospital mortality. Risk factors are selected by checking statistical significance andsigns of estimated coefficients. Risk factors are the same as those used in the
cost-in-regression model or the simultaneous equations model. Estimation result isshown in Appendix Table A3. The severity index is estimated as a linear predictor usingP

the coefficients from the estimated logistic regression: severityit = ∑ βˆ p ⋅ xitp , wherep =1

xitp denotes p-th covariate of i-th patient at time t.

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ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"Then, we obtain predicted mortality.

p ( yit = 1 | xit ) =exp(α t + β t ⋅ xit )≡ Λ(α t + β t ⋅ xit ) ,1 + exp(α t + β t ⋅ xit )Second, as for the p (l cos tit | yit ) part, we estimate cost equations separately
according as yit = 1 or 0.

l cos tit = κ + ϕ ⋅ xit + δ ⋅ zit + vit
Since costs are very much skewed, we take log-transformation to make them more
“normal”. We should be careful when retransforming log-cost into the original scalebecause expected log-cost is not equal to log of expected cost. We utilize smearing
estimator proposed by Duan (1983) just as Timbie and Normand (2008).
The model was estimated with Markov chain Monte Carlo methods using WinBUGS
software. The number of chains, check of convergence, burn-in and samples for
estimation are the same as the cost-in-regression model.
Prior specifications are as follows. Two random effects are assumed to follow bivariate
α 
normal with mean µ and precision matrix Σ −1 : ct ~ N ( µ , Σ −1 ) with ct ≡  t  . The βt 

random effect, ct , for each year comes from the same normal distribution so thatshrinkage toward the overall mean is expected.
Overall mean, µ , is assumed to follow a normal distribution with mean 0 andvariance 100: µ ~ N (0,100 ) . The precision matrix is assumed to follow Wishart
distribution with scale matrix Ωand 2 degrees of freedom: Σ −1 ~ Wishart (Ω,2) . The

choice of the 2 degrees of freedom is intended to represent vague prior. Ω is, in turn,specified as I 2 .

Now, we give a detailed account of indirect standardization. As is explained above, we
compare mortality rates of the following two cases for each year: Outcome 1 which uses
realized quality of care and Outcome 2 which uses average quality of care.

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ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"(i) Estimation of the mortality equation: Indirect standardization
First, we estimate the mortality equation adjusting for risk factors by indirect
standardization. To standardize case mixes, we compared two outcomes, actual andhypothetical.
Outcome 1 utilizes actual relationship between risk factors and outcome for eachyear so that parameters are estimated using the sample of each year separately.
Parameters, α t and β t , depend on time t.
We estimate a logit regression model for each year,
logit [ p( yit = 1 | xit )] = α t + β t ⋅ xit
to obtain estimates, α̂ t and β̂ t . We re-transform back into the original probability
scale: p ( yit = 1 | xit ) =exp(α t + β t ⋅ xit )≡ Λ(α t + β t ⋅ xit ) .
1 + exp(α t + β t ⋅ xit )Then, we average individual probabilities of death for each year: t = 2004, 2005, 2006
and 2007.
nt

1
Dˆ t = ∑ Λ (αˆ t + βˆt ⋅ xit )nt i =1
Then survival rate is Eˆ t = 1 − Dˆ t .

Outcome 2 sets up a hypothetical relationship between risk factors and outcome foreach year by supposing that each year’s quality of care is the same as the total year.
Parameters are estimated using the sample from all years so that parameters, α and β ,do not depend on t: common parameters for all years.
We estimate a logit regression model for all years,
logit [ p( yit = 1 | xit )] = α + β ⋅ xit
to obtain estimates, α and β . We re-transform back into the original probability
scale: p ( yit = 1 | xit ) = Λ (α + β ⋅ xit ) .

17

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"Again, we average individual probabilities for each year: t = 2004, 2005, 2006 and
2007.
1 nt
Dt = ∑ Λ (α + β ⋅ xit )nt i =1
Then survival rate is E t = 1 − Dt .

Excess mortality is the difference between Outcome 1 and Outcome 2, Êt − Et .

The first column of Table 5 shows the incremental benefit derived from the estimatedexcess mortality for each year and from 2004 to 2007.
Incremental benefit is a small positive in 2005, a large negative in 2006 and amoderate positive in 2007.
From 2004 to 2007, the incremental benefit is slight negative.

(ii) Estimation of cost equations separately according as yit = 0 or 1.
Second, we estimate cost equations conditional on whether the patient died or not.

l cos tit = κ t + ϕt ⋅ xit + vit(a) Corresponding to yit = 1 : Expirer
Case1: Use realized quality of care
Parameters, κ̂ 1t and ϕ̂1t , are estimated using the sample of each year separately. By∧

re-transforming the estimated log-cost, l cos t 1it = κˆ1t + ϕˆ1t ⋅ x1it , into the original scale
and averaging, we obtain for each year, t = 2004, 2005, 2006, 2007,
n1 t

1Cˆ1t =∑ (κˆ1t + ϕˆ1t ⋅ x1it )n1t i =1
Cost has been transformed into logarithms. When re-transforming lcost back into the18

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"natural scale, smearing estimator is applied to avoid biases due to non-linearity oflog-transformation.
Suppose that cost is log-transformed, l cos ti = log(cos ti ) , and the model isl cos ti = κ + ϕ ⋅ xi + ui . The expected cost of individual 0 is, even with E (u | x) = 0 ,E (cos t0 | x0 ) = E[exp(κ + ϕ ⋅ x0 + u )] ≠ exp(κ + ϕ ⋅ x0 )Smearing estimator proposed by Duan (1983) is:

E (cos t0 | x0 ) = E[exp(κˆ + ϕˆ ⋅ x0 + uˆi )] =1 n
∑ exp(κˆ + ϕˆ ⋅ x0 + uˆi ) ,n i =1

where uˆi ≡ l cos ti − (κˆ + ϕˆ ⋅ xi )Case2: Use average quality of care: Common parameters
Parameters are estimated using the sample of all years to obtain κ 1 and ϕ1 . Then,l cos t 1it = κ 1 + ϕ1 ⋅ x1it . We re-transform back to the original scale using smearing
estimator. Finally, we average for each year: t = 2004, 2005, 2006 and 2007.
C1t =

1 n1t
∑ (κ1 + ϕ1 ⋅ x1it + u1t )n1t i =1(b) Corresponding to yit = 0 : Survivor
Case1: Use realized quality of care
Parameters, κ̂ 0 t and ϕ̂ 0 t , are estimated using the sample of each year separately. By∧

re-transforming the estimated log-cost, l cos t 0it = κˆ 0 t + ϕˆ 0 t ⋅ x0it , into the original scale
and averaging, we obtain for each year, t = 2004, 2005, 2006, 2007,
n0 t

1
Cˆ 0 t =∑ (κˆ0t + ϕˆ0t ⋅ x0it )n0 t i =1

Case2: Use average quality of care
Parameters are estimated using the sample of all years to obtain κ 0 and ϕ 0 . Then,l cos t 0it = κ 0 + ϕ 0 ⋅ x0it . We re-transform back to the original scale using smearing

19

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"estimator. Finally, we average the re-transformed costs for each year: t = 2004, 2005,
2006 and 2007.
C0 t =

1 n0 t∑ (κ 0 + ϕ 0 ⋅ x0it )n0 t i =1

Excess cost is weighted average of costs for expirers or survivors with mortality rates as
weights.

∆Ct = Cˆ1t × Eˆ t + Cˆ 0 t × (1 − Eˆ t ) − {C1t × E t + C0 t × (1 − E t )}Excess mortality and excess cost calculated from the two-part model are shown in
Figure 11. Overall picture is similar to Figure 7 which shows year random effects in thesimultaneous equation model with a main difference being that excess mortality in 2007
is below zero.

We can perform incremental cost-benefit analysis using estimates from this relationship.
Recall that the following formula.
Incremental Net Benefit= λ ⋅ ∆E − ∆C ,where λ is the value of life, ∆E is incremental benefit (change in survival) and ∆C
is incremental cost. The excess survival rate decreased from 0.21% in 2004 to 0.05% in
2007. The excess cost decreased from 253562 yen in 2004 to -184646 yen in 2007. Thechange in the excess survival is 0.16 % while the change in the excess cost is 438,208
yen resulting in the break-even value of life of 2billion and 7810 million yen (27.8
million dollar).

7. Conclusion
This paper quantitatively examined the trade-off between quality and cost of health carein Japan and performed cost-benefit analysis for the country as a whole. Due to data

20

ESRI Research Note No.34"Quality and Cost of Health Care in Japan- Quality-Cost Trade-off and Cost-Benefit Analysis -"availability, our analysis was restricted to AMI patients in a small number of hospitals.
The results are suggestive, however. We find strong evidence that there is apositive trade-off: higher quality requires a higher cost, or, a lower cost induces lower
quality. Whether the cost is worth it depends the value of life, of course. With the valueof life of reasonable range, lower mortality more than compensates higher costs.
In the sequel of this paper, we are planning to investigate into the determinants ofquality of care. From our data, quality measures can be calculated for each hospital suchas Door-to-Balloon time and drug therapies at arrival or discharge. By contrasting
quality measures and quality of each hospital, we can examine the question: what
determines the quality? For example, Figure 12 shows the relationship between
Door-to-Balloon time and hospital-specific random effects for mortality. Whether
quality measures are related to outcomes are hotly debated. A small sample of theliterature includes Granger, et al. (2005), Bradley, et al. (2006) and Peterson, et al.
(2006). Only after we identify the determinants of quality of care can we take steps toimprove the quality of health care.
Quality-cost trade-off and cost-benefit analysis are similar but not identical to theconcept of productivity. We are planning to measure productivity of health care more inline with economics tradition as proposed by Castelli, et al. (forthcoming).

21

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30

Table 1 Basis Statistics of Risk Factors
Age
FemaleKillip1
Killip2
Killip3
Killip4
Left main trunk occluded
LBBB
Ventricular fibrillation
Hypertension
Hyperlipidemia
Diabetes mellitus
Heart failure
History of myocardial infarction
History of PCI
History of CABG
CancerBleeding
Renal failure
Cerebrovascular diseases
Aneurysm
COPD
Severity index

Average
68.9
0.296
0.482
0.237
0.147
0.135
0.051
0.067
0.044
0.539
0.375
0.348
0.078
0.108
0.095
0.015
0.076
0.019
0.102
0.123
0.025
0.021
-3.663

2004
68.9
0.298
0.527
0.199
0.124
0.151
0.042
0.057
0.030
0.587
0.375
0.370
0.100
0.100
0.107
0.007
0.060
0.020
0.119
0.097
0.027
0.023
-3.786

2005
68.8
0.289
0.430
0.288
0.119
0.163
0.052
0.072
0.031
0.565
0.355
0.364
0.078
0.127
0.101
0.018
0.056
0.029
0.090
0.124
0.023
0.028
-3.575

2006
69.0
0.275
0.510
0.211
0.153
0.125
0.058
0.061
0.064
0.487
0.360
0.351
0.063
0.112
0.095
0.022
0.098
0.015
0.116
0.125
0.030
0.018
-3.647

2007
69.0
0.320
0.462
0.248
0.183
0.107
0.052
0.075
0.048
0.525
0.405
0.314
0.075
0.093
0.081
0.013
0.087
0.015
0.085
0.140
0.023
0.015
-3.653

Table 2

hpid
1
2
8
9
10
15
16
17
26

1
2
3
4
5
6
7
8
9

Critical
Care
◎
○
○
○
○
◎
◎
○
○

Teaching
○
○
○
○
○
○
○
○
Average

Number of Number of Number of Number ofbeds
inpatients AMI patients
PCI
956
304,183164
483
524
89,224
69
103
322
7,839
19
109
530
1,601
81
299
202
72,410
186
712
592
187,73989
253
469
159,961
93
185
151
27,275
22
163
165
3,198
50
367
434

94,826

86

DPC

297

(note) In the column 'Critical Care' ○ indicates second and ◎ tertial critical care designation.

Owenership

Table 3 Simultaneous Equations Model
Year Random Effetcs
Overall correlation
node
mean
sd
rho.beta[1,2]-0.01838
0.4333
Correlation within year
2004
-0.0252005-0.0252006-0.0242007-0.025

Table 4 Simultaneous Equations Model
Hospital Random Effetcs
Overall correlation
node
mean
sd
rho.beta[1,2] -0.3728
0.2891
Correlation within hospital
Hospital 1
Hospital 2
Hospital 3
Hospital 4
Hospital 5
Hospital 6
Hospital 7
Hospital 8
Hospital 9-0.197-0.193-0.156-0.178-0.190-0.172-0.191-0.152-0.175

Figure 3 Crude Mortality and Mean Cost

Crude Mortality
0.13

0.125

2006

0.12

0.115

0.11

2007

0.105

2005

0.1

0.095

2004

0.09

0.085
200

210

220

230

240
Mean Cost

250

260

270

Figure 4 Mean and Median Costs and LOS
300

25

250
20

200
15
LOS
150

Mean
Median
10

100

5
50

0

0
2004

2005

2006

2007

Figure 5 Crude Mortality and Cost by Hospital
0.2

3500000

0.18
3000000
0.16

2500000

0.14

0.12
2000000
Mortality

0.1

Cost
1500000
0.08

0.06

1000000

0.04
500000
0.02

0

0
1

2

3

4

5

6

7

8

9

Figure 6 Net benefits by Value of Life

(Thousand yen)
400

300

200

100

0
5

-100

-200

-300

-400

-500

10

20

30

40

50

60

70

80

90

100

110

120

130

140

Value of life
(Million yen)

Figure 7 Random Effects for Mortality and Cost

Mortality RE
1.1

2006
1.08

1.06

1.04

1.02

2007

1

0.98

0.96

2004

0.94

0.92

2005
0.9
0.9

0.92

0.94

0.96

0.98

1
Cost RE

1.02

1.04

1.06

1.08

Mortality RE(Exponentiated)

Figure 8 Random Effects in the Simulataneous Eqautions Model

2.5

8
2

1
3

1.5

2

7

1

9
6
4
0.5

5

0
0.2

0.4

0.6

0.8

1

Cost RE (Exponentiated)

1.2

1.4

1.6

1.8

Figure 9 Random Effect for Mortality

Simultaneous Eqautions

box plot: beta[, 1]

2.0
[8,1]

[1,1]

[2,1]

[3,1]
[7,1]

1.0

[9,1]
[6,1]
[4,1]

0.0

[5,1]

-1.0

-2.0

Hospital
Probability

1
0.958

2
0.924

3
0.782

4
0.016

5
0.002

6
0.086

7
0.789

8
0.952

9
0.300

Figure 10 Random Effect for Cost

Simultaneous Eqautions

box plot: beta[, 2]

1.0
[9,2]
[6,2]
[4,2]

[5,2]

[7,2]

0.5
[2,2]
[1,2]
[3,2]

0.0
[8,2]

-0.5

-1.0

Hospital
1
Probability 0.187

2
0.330

3
0.046

4
5
0.844 0.863

67
0.975 0.869

8
0.000

9
0.992

Excess Mortality

Figure 11 Excess Mortality and Excess Cost in Two-Part Model

0.006

2006
0.004

0.002

0

2007

2004

-0.002-0.0042005-0.006-25000-20000-15000-10000

-5000

0

5000
Excess Cost

10000

15000

20000

25000

30000

Mortality RE

Figure 12 Door-to-Balloon Time and Moratlity Random Effects

2.5

2

1.5

1

0.5

0
40

60

80

100
120
Door-to-Balloon Time

140

160

180

Table A1 Cost in Regression
Mortality equation
Constant
Age
Bleeding
History of CABG
Cancer
COPD
Cost
Diabetes mellitus
Heart failure
Hypertension
Killip2
Killip3
Killip4
Hyperlipidemia
LBBB
History of myocardial Infarction
Cerebrovascular diseases
Left main trunk occluded
History of PCI
Renal failure
Aneurysm
FemaleVentricular fibrillation
Cost equation
Constant
Age
FemaleHistory of CABG
Cancer
COPD
Diabetes mellitus
DPC preparation
DPC applied
Heart failure
Hypertension

mean

sd

2.50%

97.50%

4.493
0.041
0.644
0.714
0.818
0.753
-0.8200.179
0.230-0.287
1.835
3.315
4.299
-0.9820.392
0.083-0.0470.833-0.187
0.665
0.795
0.489
0.879

1.115
0.009
0.479
0.558
0.256
0.445
0.092
0.186
0.257
0.180
0.382
0.359
0.374
0.258
0.253
0.288
0.213
0.306
0.364
0.210
0.408
0.179
0.280

2.309
0.025
-0.307-0.4060.313-0.128-1.006-0.188-0.279-0.639
1.100
2.632
3.585
-1.497-0.106-0.481-0.4710.227-0.9200.253-0.025
0.135
0.332

6.729
0.058
1.569
1.776
1.318
1.619
-0.643
0.543
0.723
0.067
2.597
4.037
5.048
-0.488
0.886
0.644
0.367
1.425
0.510
1.075
1.580
0.838
1.430

12.320-0.007-0.069-0.131-0.165-0.0440.110-0.396-0.499-0.008
0.054

0.186
0.001
0.105
0.120
0.056
0.103
0.031
0.059
0.070
0.056
0.031

11.930-0.009-0.277-0.364-0.275-0.2470.051-0.512-0.636-0.119-0.006

12.670-0.0040.136
0.105-0.0560.158
0.170-0.280-0.361
0.102
0.114

Killip2
Killip3
Killip4
Hyperlipidemia
LBBB
History of myocardial Infarction
Cerebrovascular diseases
Left main trunk occluded
History of PCI
Renal failure
Aneurysm
FemaleVentricular fibrillation
Random effects
Hospital 1
Mortality
Cost
Hospital 2
Mortality
Cost
Hospital 3
Mortality
Cost
Hospital 4
Mortality
Cost
Hospital 5
Mortality
Cost
Hospital 6
Mortality
Cost
Hospital 7
Mortality
Cost
Hospital 8
Mortality
Cost
Hospital 9
Mortality
Cost
Correlation coefficient of constant and coefficient
Variance of constantCorrelation of constant and coefficient
Variance of coefficient
Number of observations

0.075
0.104
0.183
0.054
0.048
-0.092-0.0770.471-0.0060.083
0.015-0.074-0.174

0.038
0.046
0.052
0.032
0.061
0.056
0.045
0.065
0.059
0.049
0.091
0.034
0.077

0.000
0.012
0.081
-0.009-0.072-0.202-0.1660.341-0.120-0.014-0.164-0.140-0.326

0.151
0.195
0.285
0.117
0.166
0.017
0.012
0.599
0.110
0.179
0.194
-0.008-0.0220.508-0.1640.394-0.0850.150-0.320-0.7580.166-0.9230.178-0.341
0.329
0.291
0.185
0.528
-0.5930.112
0.410-0.2720.564-0.113
0.271

0.305
0.180
0.334
0.182
0.406
0.192
0.361
0.182
0.325
0.180
0.376
0.184
0.322
0.180
0.429
0.195
0.369
0.184
0.310
0.382
0.182
0.176

-0.091-0.510-0.263-0.430-0.659-0.686-1.501-0.180-1.597-0.165-1.103-0.016-0.344-0.157-0.304-0.969-0.6200.058-0.7820.176-0.535
0.096

1.113
0.216
1.055
0.300
0.947
0.079
-0.0840.553-0.315
0.557
0.379
0.722
0.925
0.569
1.392
-0.192
0.840
0.800
0.395
1.542
0.158
0.719

2631

Table A2 Simultaneous Equations
Mortality equation
Constant
Age
Bleeding
History of CABG
Cancer
COPD
Diabetes mellitus
Heart failure
Hypertension
Killip2
Killip3
Killip4
Hyperlipidemia
LBBB
History of myocardial infarction
Cerebrovascular diseases
Left main trunk occluded
History of PCI
Renal failure
Aneurysm
FemaleVentricular fibrillation
Cost equation
Constant
Age
FemaleHistory of CABG
Cancer
COPD
Diabetes mellitus
DPC Preparation
DPC Applied
Heart failure
Hypertension
Killip2

mean

sd

2.50%

97.50%-5.163
0.055
0.750
0.877
0.898
0.697
0.130
0.211
-0.384
1.835
3.164
4.023
-1.016
0.318
0.078
0.068
0.395
-0.184
0.547
0.760
0.530
0.995

0.453
0.008
0.438
0.528
0.245
0.427
0.178
0.243
0.171
0.384
0.358
0.367
0.247
0.242
0.278
0.203
0.295
0.358
0.202
0.388
0.173
0.269

-6.0840.039-0.120-0.1880.414-0.151-0.220-0.274-0.719
1.108
2.495
3.329
-1.511-0.160-0.469-0.334-0.195-0.9000.148-0.011
0.192
0.467-4.305
0.072
1.601
1.884
1.376
1.522
0.479
0.682
-0.047
2.611
3.902
4.766
-0.544
0.789
0.618
0.463
0.965
0.498
0.937
1.506
0.871
1.524

12.310-0.007-0.069-0.131-0.165-0.0440.110-0.397-0.501-0.009
0.054
0.075

0.179
0.001
0.106
0.119
0.056
0.103
0.031
0.060
0.070
0.056
0.030
0.038

11.950-0.009-0.276-0.366-0.274-0.2450.050-0.514-0.639-0.119-0.0060.000

12.650-0.0040.139
0.102-0.0550.158
0.170-0.280-0.364
0.102
0.114
0.151

Killip3
Killip4
Hyperlipidemia
LBBB
History of myocardial infarction
Cerebrovascular diseases
Left main trunk occluded
History of PCI
Renal failure
Aneurysm
FemaleVentricular fibrillation
Random effects
Hospital 1
Mortality
Cost
Hospital 2
Mortality
Cost
Hospital 3
Mortality
Cost
Hospital 4
Mortality
Cost
Hospital 5
Mortality
Cost
Hospital 6
Mortality
Cost
Hospital 7
Mortality
Cost
Hospital 8
Mortality
Cost
Hospital 9
Mortality
Cost
Correlation coeffcient of constant and coefficient
Variance of constantCorrelation of constant and coefficient
Variance of coefficient
Number of observations

0.104
0.183
0.053
0.047
-0.092-0.0770.470-0.0060.083
0.016-0.074-0.174

0.046
0.052
0.032
0.061
0.056
0.045
0.066
0.058
0.049
0.092
0.034
0.077

0.013
0.080
-0.010-0.072-0.202-0.1650.340-0.120-0.014-0.165-0.140-0.325

0.195
0.285
0.117
0.166
0.018
0.012
0.598
0.109
0.179
0.195
-0.008-0.0230.553-0.1550.489-0.0760.320-0.312-0.7830.178-1.0050.189-0.517
0.340
0.263
0.195
0.717
-0.585-0.1950.421-0.3730.679-0.167
0.268

0.327
0.173
0.351
0.174
0.422
0.185
0.378
0.174
0.342
0.171
0.388
0.177
0.339
0.173
0.442
0.188
0.385
0.177
0.289
0.469
0.200
0.163

-0.084-0.488-0.185-0.409-0.509-0.673-1.557-0.156-1.704-0.138-1.3030.001-0.400-0.134-0.127-0.954-0.9630.082-0.8200.215-0.642
0.098

1.212
0.183
1.201
0.268
1.161
0.050
-0.0700.521-0.352
0.525
0.226
0.690
0.943
0.537
1.623
-0.218
0.561
0.772
0.285
1.870
0.112
0.690

2631

Table A3 Creating Severity Index
Logistic regression
Log likelihood = -551.31298
death

Number of obs =Pseudo R2=
Coefficient

Age
FemaleKillip2
Killip3
Killip4
Left main trunk occluded
LBBB
Ventricular fibrillation
Hypertension
Hyperlipidemia
Diabetes mellitus
Heart failure
History of myocardial infarction
History of PCI
History of CABG
CancerBleeding
Renal failure
Cerebrovascular diseases
Aneurysm
COPD
Constant

0.051
0.475
1.663
2.993
3.668
0.230
0.300
0.965
-0.409-1.012
0.149
0.040
0.232
-0.349
0.901
0.728
0.564
0.478
0.014
0.574
0.435
-4.809Number of observations

2631

2631
0.3789Standard Error t statistics
0.008
0.166
0.369
0.351
0.355
0.278
0.225
0.251
0.162
0.232
0.168
0.230
0.262
0.338
0.494
0.226
0.405
0.195
0.192
0.372
0.407
0.349

6.500
2.860
4.500
8.530
10.330
0.830
1.340
3.850
-2.530-4.360
0.890
0.170
0.880
-1.030
1.820
3.230
1.390
2.450
0.070
1.540
1.070
-13.800

p-value
0.000
0.004
0.000
0.000
0.000
0.408
0.182
0.000
0.011
0.000
0.374
0.861
0.377
0.302
0.068
0.001
0.164
0.014
0.941
0.123
0.285
0.000

Table A4 Two-Part Model
mean
Mortality equation
2004 Constant-4.079Severity
1.150
2005 Constant-4.063Severity
1.128
2006 Constant-3.677
Severity
1.0342007 Constant-3.284
Severity
0.839
Cost equation for expirer
2004 Constant
12.370
Severity-0.1692005 Constant
11.810
Severity
0.032
2006 Constant
10.790
Severity
0.151
2007 Constant
11.960
Severity-0.194
Cost equation for survivors
2004 Constant
12.260
Severity
0.064
2005 Constant
12.200
Severity
0.039
2006 Constant
12.170
Severity
0.045
2007 Constant
12.120
Severity
0.037
Overall mean of random effects
Mortality equation
Constant-3.767
Severity
1.036
Cost equation for expirer
Constant
11.690
Severity-0.039
Cost equation for survivors
Constant
12.170
Severity
0.044
Correlation coefficient of constant and coefficient

sd

2.50%

97.50%

0.353
0.125
0.333
0.117
0.287
0.097
0.236
0.085

-4.8250.919-4.7670.910-4.2620.849-3.7630.677-3.4441.411-3.4531.372-3.1401.229-2.836
1.012

0.241
0.071
0.251
0.075
0.201
0.057
0.166
0.054

11.900-0.31011.320-0.114
10.3900.039
11.630-0.30012.850-0.03012.3000.179
11.1800.263
12.290-0.090

0.033
0.017
0.032
0.017
0.031
0.015
0.029
0.014

12.2000.031
12.1400.006
12.1100.015
12.0600.009

12.3200.097
12.2600.072
12.2300.075
12.170
0.065

0.493
0.372

-4.7350.303-2.824
1.775

0.581
0.365

10.540-0.74912.760
0.690

0.359
0.353

11.440-0.65712.8700.746

Mortality equation
Cost equation for perishers
Cost equation for survivors
Mortality equation
Variance of constantCorrelation of constant and coefficient
Variance of coefficient
Cost equation for expirer
Variance of constantCorrelation of constant and coefficient
Variance of coefficient
Cost equation for survivors
Variance of constantCorrelation of constant and coefficient
Variance of coefficient-0.146-0.176
0.001

0.443
0.439
0.449

-0.869-0.875-0.811

0.743
0.728
0.818

0.846
-0.114
0.537

1.697
0.785
0.928

0.132
-1.288
0.098

3.653
0.712
2.223

1.286
-0.151
0.542

4.249
1.042
1.409

0.204
-1.577
0.098

5.262
0.825
2.228

0.511
0.000
0.494

1.011
0.555
0.830

0.091
-0.716
0.089

2.145
0.741
2.072

Number of observations
2004
2005
2006
2007

598
612
672
749

Total

2631