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Subgroup Analyses in Clinical Trials. Stephen L George, PhD Department of Biostatistics and Bioinformatics Duke University Medical Center. Definition of Subgroup Analysis. An analysis of treatment effects within subgroups of patients enrolled on a clinical trial.

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subgroup analyses in clinical trials

Subgroup Analyses in Clinical Trials

Stephen L George, PhD

Department of Biostatistics and Bioinformatics

Duke University Medical Center

ODAC May 3, 2004

definition of subgroup analysis
Definition of Subgroup Analysis

An analysis of treatment effects within subgroups of patients enrolled on a clinical trial

ODAC May 3, 2004

frequency of subgroup analyses
Frequency of Subgroup Analyses
  • Approximately 50% of reports of randomized clinical trials contain at least one subgroup analysis (Pocock et al 1987)
  • Deciding on analysis after looking at the data is “dangerous, useful, and often done” (Good 1983)

ODAC May 3, 2004

problems with subgroup analyses
Problems with Subgroup Analyses
  • Increased probability of type I error when H0 true
  • Decreased power (increased type II error) in individual subgroups when H1 true
  • Difficulty in interpretation

ODAC May 3, 2004

general assumptions in clinical trials
General Assumptions in Clinical Trials
  • Hypotheses tested usually address an overall or ‘average’ treatment effect in the study population
  • No assumption of homogeneity of effect across subgroups
  • Direction, not magnitude, of the treatment effect is expected be the same in subgroups

ODAC May 3, 2004

implications
Implications
  • Overall treatment comparisons are of primary interest
  • Stratification or regression techniques can be used to adjust the overall comparison for subgroups or covariates
  • Subgroup analyses are generally of secondary interest as “hypothesis generating” techniques for future studies

ODAC May 3, 2004

pre planned vs unplanned subgroup analyses
Pre-planned vs Unplanned Subgroup Analyses
  • Pre-planned analyses (hypothesis driven)
    • Subgroup hypotheses specified in advance
    • Control of error rates can, in principle, be addressed
  • Unplanned analyses (exploratory)
    • Analyses suggested by the data
    • Exhaustive search for differential treatment effects by subgroups (data dredging)
    • Inflated, and generally unknown, error rates

ODAC May 3, 2004

ich guideline e3
ICH Guideline E3

Statistical Considerations (Appendix)

“… it is essential to consider the extent to which the analyses were planned prior to the availability of data…This is particularly important in the case of any subgroup analyses, because if such analyses are not preplanned they will ordinarily not provide an adequate basis for definitive conclusions.”

ODAC May 3, 2004

ich guideline e9
ICH Guideline E9

5.7 Subgroups, Interactions and Covariates

“In most cases…subgroup or interaction analyses are exploratory and should be clearly identified as such;…these analyses should be interpreted cautiously;…any conclusion of treatment efficacy (or lack thereof) or safety based solely on exploratory subgroup analyses are unlikely to be accepted.”

ODAC May 3, 2004

error rates in subgroup analyses
Error Rates in Subgroup Analyses

With k independent subgroups and no difference in treatments, the probability

of at least one ‘significant’ subgroup is:

1- (1- α)k

For example,α= 0.05, k = 10 yields

1- (1- 0.05)10 = 0.40

ODAC May 3, 2004

control of error rates in subgroup analyses
Control of Error Rates in Subgroup Analyses
  • For planned subgroup analyses, the overall type I error rate can be controlled. One conservative way is to use α* = α/k in each of the subgroup analyses
  • In this case, the power (probability of detecting real differences when present) is sharply reduced in individual subgroups
  • For unplanned subgroup analyses, k is unknown so the error rates are unknown

ODAC May 3, 2004

hypothetical example
Hypothetical Example
  • Treatments: Experimental (E) and Control (C)
  • Outcome: Overall survival
  • Null median: 12 months
  • Alt medians: 16 months (E) and 12 months (C)
  • 36 month accrual, 12 month followup, N = 500
  • α = 0.05, 1- β = 0.80
  • Subgroups: 350 males (70%), 150 females

ODAC May 3, 2004

subgroup tests no adjustment
Subgroup Tests (no α adjustment)
  • Use α* = 0.05 in each subgroup
  • Overall Type I error rate = .0975
  • Power in males ≈ 0.64, females ≈ 0.33
  • Probability that correct conclusion is reached in both subgroups (males, females) under the alternative hypothesis ≈ (0.64)(0.33) ≈ 0.21

ODAC May 3, 2004

subgroup tests adjusted
Subgroup Tests (adjusted α)
  • Use α* = 0.05/2 = 0.025 in each subgroup
  • Overall Type I error rate = .04875
  • Power in males ≈ 0.54, females ≈ 0.24
  • Probability that correct conclusion is reached in both subgroups (males, females) under the alternative hypothesis ≈ (0.54)(0.24) ≈ 0.13

ODAC May 3, 2004

aspirin example
Aspirin Example
  • A randomized trial of aspirin and sulfinpyrazone in threatened stroke. The Canadian Cooperative Study Group. N Engl J Med 299: 53-59, 1978.
  • “Among men the risk reduction for stroke or death was 48 per cent … whereas no significant trend was observed among women…We conclude that aspirin is an efficacious drug for men with threatened stroke.”

ODAC May 3, 2004

antiplatelet meta analysis 1988
Antiplatelet Meta-analysis (1988)
  • Secondary prevention of vascular disease by prolonged antiplatelet treatment. Antiplatelet Trialists' Collaboration. British Medical Journal 296: 320-331, 1988.
  • “Overall, allocation to antiplatelet treatment …reduced vascular mortality by 15% … and non-fatal vascular events (stroke or myocardial infarction) by 30% …”

ODAC May 3, 2004

guidelines for assessing reported subgroup differences oxman and guyatt 1992
Guidelines for Assessing Reported Subgroup Differences(Oxman and Guyatt 1992)
  • A priori hypotheses stated
  • Clinical importance of the difference
  • Proper assessment of statistical significance
  • Consistency across studies
  • Indirect supporting evidence

ODAC May 3, 2004

treatment covariate interactions a generalization of subgroup concepts
Treatment-Covariate Interactions:AGeneralization of Subgroup Concepts
  • A treatment-covariate interaction exists when the treatment effect is not the same for all values of a covariate (e.g., gender, age, etc.)
  • Quantitative interactions: Treatment effects in the same direction, but of different magnitude in some subgroups (common and even expected)
  • Qualitative interactions: Treatment effects in opposite direction (rare)

ODAC May 3, 2004

treatment covariate interactions
Treatment-covariate Interactions
  • Treatment X (0 for control, 1 for experimental)
  • Covariate Z (e.g., Z = 0 for female, 1 for male)
  • Outcome Y = β0 + β1X + β2Z + β3XZ

ODAC May 3, 2004

some strategies
Some Strategies
  • Design for overall hypotheses but test within pre-defined subgroups:
    • High overall error rates
    • Low power in subgroups
    • Biased estimates
  • Design for overall hypotheses but test for pre-specified treatment-covariate interactions:
    • Low power to detect interactions

ODAC May 3, 2004

some strategies continued
Some Strategies (continued)
  • Design for overall hypotheses and conduct unplanned (exploratory) analyses of subgroup differences:
    • Higher, but unknown, error rates
    • Hypothesis generating exercise for future study
  • Design for pre-specified subgroups or interactions:
    • Control of error rates
    • Large sample sizes

ODAC May 3, 2004

conclusions
Conclusions
  • Pre-planning is key
  • Larger studies required for proper subgroup analyses
  • Exploratory analyses are good for hypothesis generating but are not convincing alone
  • More than one study important for validation

ODAC May 3, 2004