Subgroup Analysis in Cost-Effectiveness Analysis

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

• Encyclopedia of Biostatistics
• Subgroup Analysis in Clinical Trials see
  Treatment-Covariate Interaction

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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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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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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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Test of Quantitative Interaction(Gail Simon,
1985)
Suppose there are K countries, each with mean
treatment effect Di and standard deviation Si

• Compute
• where

• Compare H to ?2 with K-1 d.f.

Large value of H implies treatment differences
exists among countries/centers
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Test of Qualitative Interaction 1(Gail Simon,
1985)

• Compute Q- and Q for positive and negative
  differences

• Test Statistic

Large value of Q implies differences exist in
direction of treatment effect among countries
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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 lt 0 and Lj gt 0
• Pan Wolfe discuss relative merit of methods

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Scandinavian Simvastatin Survival Study (4S)

• Randomized, double-blind, placebo-controlled,
  N4444 patients in Scandinavian countries.
• - Denmark (N713) - Norway (N1025)
• - Finland (N868) - Sweden (N1681)
• - Iceland (N157)
• 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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4S Proportion of Patients Dying by Country for
Placebo and Simvastatin Patients
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4S Cardiovascular Hospitalizations Per Patient
Year by Country for Placebo and Simvastatin
Patients
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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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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 lt 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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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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4S CE Ratio
? 75K
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4S Cost Per Additional Survivor
with 95 Confidence Intervals
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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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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 41361-372.
• 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 221955-1976.
• Cook JR and Heyse JF. Use of an angular
  transformation for ratio estimation in
  cost-effectiveness analysis. Statistics in
  Medicine 2000 192989-3003.