Bayesian hierarchical modeling of patient subpopulations: Efficient designs of Phase II oncology clinical trials

Abstract

Background

In oncology, the treatment paradigm is shifting toward personalized medicine, where the goal is to match patients to the treatments most likely to deliver benefit. Treatment effects in various subpopulations may provide some information about treatment effects in other subpopulations.

Purpose

We compare different approaches to Phase II trial design where a new treatment is being investigated in several groups of patients. We compare considering each group in an independent trial to a single trial with hierarchical modeling of the patient groups.

Methods

We assume four patient groups with different background response rates and simulate operating characteristics of three trial designs, Simon’s Optimal Two-Stage design, a Bayesian adaptive design with frequent interim analyses, and a Bayesian adaptive design with frequent interim analyses and hierarchical modeling across patient groups.

Results

Simon’s designs are based on 10% Type I and Type II error rates. The independent Bayesian designs are tuned to have similar error rates, but may have a slightly smaller mean sample size due to more frequent interim analyses. Under the null, the mean sample size is 2–4 patients smaller. A hierarchical model across patient groups can provide additional power and a further reduction in mean sample size. Under the null, the addition of the hierarchical model decreases the mean sample size an additional 4–7 patients in each group. Under the alternative hypothesis, power is increased to at least 98% in all groups.

Limitations

Hierarchical borrowing can make finding a single group in which the treatment is promising, if there is only one, more difficult. In a scenario where the treatment is uninteresting in all but one group, power for that one group is reduced to 65%. When the drug appears promising in some groups and not in others, there is potential for borrowing to inflate the Type I error rate.

Conclusions

The Bayesian hierarchical design is more likely to correctly conclude efficacy or futility than the other two designs in many scenarios. The Bayesian hierarchical design is a strong design for addressing possibly differential effects in different groups.

Get full access to this article

View all access options for this article.

References

Hamburg

Collins

. The path to personalized medicine. N Engl J Med 2010; 363(4): 301–04.

Simon

. Clinical trials for predictive medicine: New challenges and paradigms. Clin Trials 2010; 7(5): 516–24.

Berry

Carlin

Lee

Muller

. Bayesian Adaptive Methods for Clinical Trials. CRC Press, Boca Raton, FL, 2011.

Berry

. Bayesian clinical trials. Nat Rev Drug Discov 2006; 5(1): 27–36.

Stein

. Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proc Third Berkeley Symp Math Stat Probab 1956; 1: 197–206.

James

Stein

. Estimation with quadratic loss. Proc Fourth Berkeley Symp Math Stat Probab 1961; 1: 361–79.

Bernardo

Smith

AFM

. Bayesian Theory. Wiley, Chichester; New York, 1994.

Berry

. Bayesian approaches for comparative effectiveness research. Clin Trials 2012; 9(1): 37–47.

Berry

. Accounting for multiplicities in assessing drug safety: A three-level hierarchical mixture model. Biometrics 2004; 60(2): 418–26.

10.

Berry

Natarajan

. Bayesian survival analysis with nonproportional hazards: Metanalysis of combination pravastatin-aspirin. J Am Stat Assoc 2004; 99(465): 36–44.

11.

Berry

Ishak

Luce

Berry

. Bayesian meta-analysis for comparative effectiveness and informing coverage decisions. Med Care 2010; 48(6): S137–44.

12.

Berry

Stangl

. Bayesian Biostatistics. Marcel Dekker, New York, 1996.

13.

Brown

Ibrahim

. A Bayesian semiparametric joint hierarchical model for longitudinal and survival data. Biometrics 2003; 59(2): 221–28.

14.

Carlin

Louis

. Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall/CRC, Boca Raton, FL, 2000.

15.

Davis

Leffingwell

. Empirical Bayes estimates of subgroup effects in clinical trials. Control Clin Trials 1990; 11: 37–42.

16.

Dixon

Simon

. Bayesian subset analysis. Biometrics 1991; 47: 871–81.

17.

Jones

Ohlssen

Neuenschwander

Racine

Branson

. Bayesian models for subgroup analysis in clinical trials. Clin Trials 2011; 8(2): 129–43.

18.

Louis

. Estimating a population of parameter values using Bayes and empirical Bayes methods. J Am Stat Assoc 1984; 79(386): 393–98.

19.

Simon

. Bayesian subset analysis: Application to studying treatment-by-gender interactions. Stat Med 2002; 21: 2909–16.

20.

Skene

Wakefield

. Hierarchical models for multicentre binary response studies. Stat Med 1990; 9(8): 919–29.

21.

Stangl

. Prediction and decision making using Bayesian hierarchical models. Stat Med 1995; 14(20): 2173–90.

22.

Thall

Wathen

Bekele

. Hierarchical Bayesian approaches to phase II trials in diseases with multiple subtypes. Stat Med 2003; 22(5): 763–80.

23.

Chugh

Wathen

Maki

. Phase II multicenter trial of imatinib in 10 histologic subtypes of sarcoma using a Bayesian hierarchical statistical model. J Clin Oncol 2009; 27(19): 3148–53.

24.

Simon

. Optimal two-stage designs for phase II clinical trials. Control Clin Trials 1989; 10(1): 1–10.

25.

Gelman

. Prior distributions for variance parameters in hierarchical models. Bayesian Anal 2006; 1(3): 515–34.