Subgroup Analysis in Cost-Effectiveness Analysis ISPOR Issues Panel May 17, 2004 Joseph Heyse John Cook Merck Research Laboratories

Subgroup Analysis inCost-Effectiveness Analysis

ISPOR Issues Panel

May 17, 2004

Joseph Heyse

John Cook

Merck Research Laboratories

ISPOR Issues Panel 2004.ppt.2

Definition

Encyclopedia of Biostatistics

Subgroup Analysis in Clinical Trials see

Treatment-Covariate Interaction


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.


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.


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.


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


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


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


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.


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


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

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.



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!


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.


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

4S: Cost Per Additional Survivor with 95% Confidence Intervals



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.


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.

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Subgroup Analysis in Cost-Effectiveness Analysis ISPOR Issues Panel May 17, 2004 Joseph Heyse John Cook Merck Research Laboratories