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![Page 1: Subgroup Analysis in Cost-Effectiveness Analysis ISPOR Issues Panel May 17, 2004 Joseph Heyse John Cook Merck Research Laboratories.](https://reader035.fdocuments.us/reader035/viewer/2022072006/56649d085503460f949da090/html5/thumbnails/1.jpg)
Subgroup Analysis inCost-Effectiveness Analysis
ISPOR Issues Panel
May 17, 2004
Joseph Heyse
John Cook
Merck Research Laboratories
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ISPOR Issues Panel 2004.ppt.2
Definition
Encyclopedia of Biostatistics
Subgroup Analysis in Clinical Trials see
Treatment-Covariate Interaction
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ISPOR Issues Panel 2004.ppt.3
Treatment-Covariate Interaction
A treatment-covariate interaction exists when the effect of a treatment varies according to the value of a specific covariate.
Covariates are defined according to patient characteristics such as gender, race, age, study center country, or disease risk factors. Subgroups are sets of patients with common values of covariates.
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ISPOR Issues Panel 2004.ppt.4
Importance
Identifying and evaluating interactions is a key step in the analysis of clinical trial data.
– Assess the appropriateness of an overall estimate of treatment effect.
– Improve precision of estimated treatment effect.
– Adjust estimate of treatment effect for common value of covariates.
– Explore the consistency of the treatment among subgroups.
– Identify subgroups of patients with greater/lesser levels of treatment effect.
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ISPOR Issues Panel 2004.ppt.5
Characterizing Interaction(Gail and Simon, 1985)
Quantitative: Treatment effect varies among the subgroups of patients.
Qualitative: The direction of the true treatment differences varies among the subgroups of patients. This is sometimes called crossover interaction.
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ISPOR Issues Panel 2004.ppt.6
Test of Quantitative Interaction(Gail & Simon, 1985)
K
ii
K
iii
K
iii
ssDD
sDDH
1
2
1
2
1
22
1
– Compare H to 2 with K-1 d.f.
Large value of H implies treatment differences exists among countries/centers
Suppose there are K countries, each with mean
treatment effect Di and standard deviation Si
– Compute:
where
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ISPOR Issues Panel 2004.ppt.7
Test of Qualitative Interaction #1(Gail & Simon, 1985)
Compute Q- and Q+ for positive and negative differences:
Q D s I D
Q D s I D
i ii
K
i
i ii
K
i
2 2
1
2 2
1
0
0
Q Min Q Q C , Test Statistic:
Large value of Q implies differences exist in direction of treatment effect among countries
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ISPOR Issues Panel 2004.ppt.8
Test of Qualitative Interaction #2(Piantadosi & Gail, 1993; Pan & Wolfe, 1997)
Construct confidence intervals for each country
(Li , Ui ): Di ± Z• Si, for i = 1, 2…, K
where * = ½(1-PK)
PK = 2(1-)1/(k-1) - 1
Qualitative interaction exists if there are two countries (i and j) with intervals such that:
Ui < 0 and Lj > 0
Pan & Wolfe discuss relative merit of methods
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ISPOR Issues Panel 2004.ppt.9
Scandinavian Simvastatin Survival Study (4S)
Randomized, double-blind, placebo-controlled, N=4444 patients in Scandinavian countries.
- Denmark (N=713) - Norway (N=1025)
- Finland (N=868) - Sweden (N=1681)
- Iceland (N=157)
Patients with previous MI followed median period of 5.4 years.
Simvastatin therapy associated with 30% reduction in deaths and 34% fewer hospital days.
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ISPOR Issues Panel 2004.ppt.10
4S: Proportion of Patients Dying by Country for Placebo and Simvastatin Patients
0 .02 .04 .06 .08 .10 .12 .14 .16 .18
Placebo
0
.02
.04
.06
.08
.10
.12
.14
.16
.18
Sweden
Denmark
Overall Norway
Finland
Iceland
Unit Line
Simvastatin
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ISPOR Issues Panel 2004.ppt.11
4S: Cardiovascular Hospitalizations Per Patient Year by Country for Placebo and Simvastatin Patients
0 .02 .04 .06 .08 .10 .12 .14 .16 .18
Placebo
0
.02
.04
.06
.08
.10
.12
.14
.16
.18
Simvastatin
Iceland
Finland Norway
Overall
DenmarkSweden
Unit Line
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Testing for Interaction: CE Ratios
Homogeneity among countries in costs and effects does not imply homogeneity in the ratio
Challenges with the CE ratio
Analytic challenges:• Lack of uniqueness with ratio
• When E = 0
Conceptual challenge:• What is a qualitative interaction?
Recommend using an angular transformation of the CE Ratio.
ISPOR Issues Panel 2004.ppt.12
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ISPOR Issues Panel 2004.ppt.13
Angular Transformation
Apply angular transformation to (∆C, ∆E) to obtain the CE angle:
Tan-1 [C / SD(C) , E / SD(E)] if C 0
180o +Tan-1 [C / SD(C) , E / SD(E)] if C < 0
Construct 95% confidence limits for angle (counter clockwise and clockwise limits)
– Can use either normal theory or percentile bootstrap methods
Must reverse transform angles back to ratios!
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ISPOR Issues Panel 2004.ppt.14
Testing for Interaction: CE Ratio
What is a qualitative interaction for the ratio:
– Requires specification of CE threshold ()
• CE ratios “below” are deemed cost-effective
• CE ratios “above” are deemed not cost-effective
– Qualitative interaction exists if some countries are cost-effective, while others are not.
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ISPOR Issues Panel 2004.ppt.15
4S: CE Ratio
0.00 0.01 0.02 0.03 0.04 0.05
Incremental Survival Probability
0
500
1000
1500
2000
2500
Incremental Cost (U.S.$)
DenmarkFinland
Iceland
NorwaySweden
Overall
= 75K
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4S: Cost Per Additional Survivor with 95% Confidence Intervals
ISPOR Issues Panel 2004.ppt.16
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ISPOR Issues Panel 2004.ppt.17
Concluding Remarks
It is important to assess the consistency of treatment effects on costs, effects, and cost-effectiveness across subgroups of patients.
This analysis includes a characterization of possible interactions being quantitative or qualitative.
Available tests for interaction can be applied to cost-effectiveness ratios and net health benefits.
The results of the analysis can be used to improve the precision of the estimate and evaluate the generalizability of study conclusions.
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ISPOR Issues Panel 2004.ppt.18
Selected References
Armitage P and Colton T, Editors. Encyclopedia of Biostatistics, Volume 6, John Wiley & Sons: New York, 1998.
Gail MH and Simon R. Testing for qualitative interactions between effects and patient subsets. Biometrics 1985; 41:361-372.
Pan G and Wolfe DA. Test for qualitative interaction of clinical significance. Statistics in Medicine 1997; 16: 1645-1652.
Cook JR, Drummond MF, Glick H, and Heyse JF. Assessing the appropriateness of combining economic data from multinational clinical trials. Statistics in Medicine 2003; 22:1955-1976.
Cook JR and Heyse JF. Use of an angular transformation for ratio estimation in cost-effectiveness analysis. Statistics in Medicine 2000; 19:2989-3003.