BLINDED EVALUATIONS OF EFFECT SIZES IN CLINICAL TRIALS: COMPARISONS BETWEEN BAYESIAN AND EM ANALYSES

Abstract

Clinical trials are major and costly undertakings for researchers. Planning a clinical trial involves careful selection of the primary and secondary efficacy endpoints. The 2010 draft FDA guidance on adaptive designs acknowledges possible study design modifications, such as selection and/or order of secondary endpoints, in addition to sample size re-estimation. It is essential for the integrity of a double-blind clinical trial that individual treatment allocation of patients remains unknown. Methods have been proposed for re-estimating the sample size of clinical trials, without unblinding treatment arms, for both categorical and continuous outcomes. Procedures that allow a blinded estimation of the treatment effect, using knowledge of trial operational characteristics, have been suggested in the literature. Clinical trials are designed to evaluate effects of one or more treatments on multiple primary and secondary endpoints. The multiplicity issues when there is more than one endpoint require careful consideration for controlling the Type I error rate. A wide variety of multiplicity approaches are available to ensure that the probability of making a Type I error is controlled within acceptable pre-specified bounds. The widely used fixed sequence gate-keeping procedures require prospective ordering of null hypotheses for secondary endpoints. This prospective ordering is often based on a number of untested assumptions about expected treatment differences, the assumed population variance, and estimated dropout rates. We wish to update the ordering of the null hypotheses based on estimating standardized treatment effects. We show how to do so while the study is ongoing, without unblinding the treatments, without losing the validity of the testing procedure, and with maintaining the integrity of the trial. Our simulations show that we can reliably order the standardized treatment effect also known as signal-to-noise ratio, even though we are unable to estimate the unstandardized treatment effect. In order to estimate treatment difference in a blinded setting, we must define a latent variable substituting for the unknown treatment assignment. Approaches that employ the EM algorithm to estimate treatment differences in blinded settings do not provide reliable conclusions about ordering the null hypotheses. We developed Bayesian approaches that enable us to order secondary null hypotheses. These approaches are based on posterior estimation of signal-to-noise ratios. We demonstrate with simulation studies that our Bayesian algorithms perform better than existing EM algorithm counterparts for ordering effect sizes. Introducing informative priors for the latent variables, in settings where the EM algorithm has been used, typically improves the accuracy of parameter estimation in effect size ordering. We illustrate our method with a secondary analysis of a longitudinal study of depression.