Flexible shrinkage estimation of subgroup effects through Dirichlet process priors

ABSTRACT

The paradigm shift towards precision medicine reignited interest in determining whether there are differential treatment effects in subgroups of trial participants. Intrinsic to this problem is that any assessment of a differential treatment effect is predicated on being able to estimate the treatment response accurately while satisfying constraints of balancing the risk of overlooking an important subgroup with the potential to make a decision based on a false discovery. While shrinkage models have been widely used to improve accuracy of subgroup parameter estimates by leveraging the relationship between them, there is still a possibility that it can lead to excessively conservative or anti-conservative results. This can possibly be due to the use of the normal distribution as prior, which forces outlying subjects to have their means over-shrunk towards the population mean, and the data from such subjects may be excessively influential in estimation of both the overall mean response and the mean response for each subgroup, or a model misspecification due to unaccounted variation or clustering. To address this issue, we investigate the use of nonparametric Bayes, particularly Dirichlet process priors, to create a flexible shrinkage model. This model represents uncertainty in the prior distribution for the overall response while accommodating heterogeneity among individual subgroups. We simulated data to compare estimates when there is no differential subgroup effect and when there is a differential subgroup effect. In either of these scenarios, the flexible shrinkage model does not force estimates to shrink excessively when similarity of treatment effects is not supported but still retains the attractiveness of improved precision given by the narrower credible intervals. We also applied the same method to a dataset based on trials conducted for an antimicrobial therapy on several related indications.

KEY WORDS:

• Dirichlet process prior
• exchangeability
• heterogeneity
• model selection
• shrinkage
• subgroups

Additional information

Notes on contributors

Margaret Gamalo-Siebers

Margaret Gamalo-Siebers, PhD, is currently a Principal Research Scientist at Eli Lilly & Co., Indianapolis, IN, 46225.

Ram Tiwari

Ram Tiwari, PhD, is an Associate Director.

Lisa LaVange

Lisa LaVange, PhD, is Director of the Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, MD, 20993-0002.

This work was completed while Dr. Gamalo-Siebers was a Mathematical Statistician, Division of Biometrics IV, Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug Administration. The views expressed in this paper are those of the authors and not necessarily those of the U.S. Food and Drug Administration or the authors’ employers.