When Is Stratification Detrimental to a Clinical Trial Design? Part I

1. When Is Stratification Detrimental to a Clinical Trial Design?Part I Gretchen Marcucci, M.S. Biostatistician, Rho, Inc. and Katherine L. Monti, Ph.D. Rho, Inc. and University of North Carolina

2. Outline • Introduction • Motivation for the literature search • Why stratify? Advantages • Why not stratify? Disadvantages • If you want to stratify …

3. Outline • How many strata? • Alternatives • Limitations of the literature • Conclusions

4. Introduction • This paper presents the results of a literature search on the use of stratified randomization, with particular interest in clinical trials.

5. Introduction • Stratification in clinical trials is different from classical stratification in survey sampling, or from blocking in experimental design. • In stratified sampling, “the population is divided into subgroups, or strata, each of which is sampled randomly with a known sample size.” • In experimental design, treatments are assigned within blocks, which are defined by factors that are largely determinable and controllable (e.g., temp, water level in a greenhouse setting). Again, the sample size in each block is part of the design.

6. Introduction • In clinical trials, stratification refers to the assignment of treatment to homogeneous groups defined by patient-related characteristics that may affect outcome. • These factors are generally not controllable (e.g., stage of disease, age within the allowable range). • Until the end of the study, the sample size of each factor level is generally unknown.

7. Introduction • Sometimes stratification is beneficial. • Some trialists maintain that it is never harmful. • Is that the case?

8. Motivation • A drug company’s design: • 120 subjects • 4 treatments (placebo, three drug doses) • 30 sites • 1 prognostic factor with 2 levels (hi and low levels, continuous covariate) • Randomization: • At each site, NOT centralized • In blocks of 4 within factor level within site

9. Motivation • Those designing the study thought that randomizing within factor level • would increase balance in the design, • “couldn’t hurt”. • Others argued that randomizing within factor level would increase theimbalance in the design.

10. Motivation • 120 subjects / (30 sites) = 4 subjects per site Perfect balance with 4 treatments. • 120 subjects / (30 sites x 2 levels) = 2 subjects per site for each levelBalance not assured with 4 treatments.

11. Motivation • Although 2 subjects/level/site is not a realistic enrollment pattern, it is unlikely that stratification would help balance the design.

12. Motivation • What does the literature have to say about stratification in clinical trials? • When is stratification beneficial? • When is stratification harmful? • Is it true that it “couldn’t hurt”?

13. Why stratify? Advantages • To keep variability of subjects within strata as small as possible and between-strata variability as large as possible in order to have the most precision of the treatment effect. (Chow and Liu, 1998) • Avoid imbalance in the distribution of treatment groups within strata. • Increase efficiency. • Protect against Type I and Type II errors.

14. Why stratify? Advantages • Avoid confounding. • Satisfy prevailing investigator assumptions. • Provide credibility to choice of analysis covariates.

15. Why not stratify? Disadvantages • More costly and complicated trial. • More opportunity to introduce error. • Power loss from unstratified randomization may be very small in many cases. • Gain in precision of estimates is small once (number of subjects) / (treatment) > 50.

16. If you want to stratify …

17. Consider • If the covariates are imprecisely assessed, then may introduce error. • If there are too many covariates, • then there is a higher chance of imbalance, or • the effect is the same as simple randomization. • If covariates are not related to outcome, then the gain in efficiency will be small or negative. • If there are too many strata with small number of subjects / stratum, the analysis model may be overparameterized.

18. Consider How many strata depends on: • Total number of subjects in the trial. • Expected number to be in each stratum. • Importance of prognostic factors. • Type of allocation scheme (permuted blocks vs. dynamic allocation).

19. Consider • The number of strata should be less than (total sample size) / (block size). (Hallstrom and Davis, 1988) • In our case, N=120, B=4, • Recommendation: < 30 strata • Design: 60 strata • Stratification begins to fail (in terms of balance) if the total number of strata is greater than approximately N/2 (for 2 treatments). (Therneau, 1993) • or N/k, k= number of treatments

20. Number of strata: notes • “One can inadvertently counteract the balancing effects of blocking by having too many strata.” “…, most blocks should be filled because unfilled blocks permit imbalances.” (Piantadosi,1997)

21. Number of strata: notes • “If ‘institution effect’ were to be introduced as a further prognostic factor, …, the total number of strata may then be in the hundreds and one would have achieved little more than purely random treatment assignment.” (Pocock and Simon, 1975)

22. Alternatives • Dynamic allocation / adaptive stratification • Minimization by Taves. • Pocock and Simon’s method. • Zelen’s method. • Begg and Iglewics. • Others. • Post-stratification (ANCOVA).

23. Minimization • Keeps track of the current imbalance and assigns the treatment that reduces the imbalance. • Advantages: • Produces less imbalance than conventional stratification. • Canaccommodate more factors.

24. Minimization • Disadvantages: • Need to keep track of current imbalance. • None of the assignments are completely random. • Since it only aims to balance marginal totals, precision is only increased if the interaction between prognostic factors is not pronounced. (Tu et. al., 2000)

25. Post-stratification If stratification is not done at randomization, covariate analysis can be performed. • Easier and less costly to implement. • Often nearly as efficient. • May be less convincing, in particular if covariate was not mentioned in the protocol. • Cannot correct for cases of extreme imbalance.

26. Limitations of the literature • Literature refers mostly to trials of two treatments. • Little attention is paid to operational disadvantages of more complex designs.

27. Conclusions Consider stratifying only if: • Prognostic factors are known to be related to the outcome and are easy to collect prior to randomization. • Operational costs justify any gain. • Sample size is small ( N < 100), but the stratified design does not induce imbalance. • The number of strata should be less than (total sample size) / (block size).(Hallstrom and Davis, 1988)

28. Conclusions Authors are still (1999) concluding that “Stratification is … harmless always, useful frequently, and important rarely”. (Kernan et. al., 1999) The preconception that stratification would improve the balance and could not hurt should be reconsidered.

29. Contact Information GMarcucc@RhoWorld.Com Slides: www.rhoworld.com

30. References • Begg CB, Iglewicz B. A treatment allocation procedure for sequential clinical trials. Biometrics36: 81-90, 1980 • Chow SC, Liu JP. Design and Analysis of Clinical Trials. John Wiley and Sons; 1998. • Hallstrom A, Davis K. Imbalance in treatment assignments in stratified block randomization. Control Clin Trials 1988; 9:375-382. • Kernan WN, Viscoli CM, Makuch RW, et al. Stratified randomization for clinical trials. J Clin Epidemiolol 1999; 52: 19-26. • Piantadosi, S. Clinical Trials. A methodologic perspective. John Wiley and Sons; 1997.

31. References • Pocock SJ, Simon R. Sequential tretment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 1975; 31:103-115. • Taves DR. Minimization: A new method in assigning patient to treatment and control group. Clinical Pharmacology and Therapeutics 15: 443-453, 1974. • Therneau TM. How many stratification factors is "too many" to use in a randomization plan? Control Clinical Trial 14: 98-108, 1993. • Tu D, Shalay K, Pater J Adjustment of treatment effect for covariates in clinical trials: Statistical and Regulatory Issues Drug Info Journal 34:511-523, 2000. • Zelen M. The randomization and stratification of patients to clinical trials. Journal of Chronic Dis, 27:365-375, 1974 .