Blinded Sample Size Re-estimation for Longitudinal Overdispersed Count Data in Randomized Clinical Trials with an Application in Multiple Sclerosis

Abstract

In many clinical experiments, particularly in randomized clinical trials, the sample size required needs to be assessed and justified. For calculating a clinical trial’s sample size, assumptions have to be made regarding the clinical trial’s outcome data. These assumptions are based on prior clinical trials or merely on expert knowledge and always subject to some degree of uncertainty. To cope with this uncertainty in sample size estimation, adaptive designs were developed to re-estimate the sample size within a running trial. Especially adaptive designs for blinded sample size re-estimation, also referred to as non-comparative adaptive designs, have gained popularity, as these generally do not require an adjustment of the significance level to maintain type I error rates. In the first part of this thesis, we will consider developing sample size re-estimation methods for longitudinal overdispersed count data. As a first step, such data is modeled by a negative binomial counting process, and techniques for inference, sample size estimation and sample size re-estimation are provided. In a second step, presented methods are extended to handle time trends, which may occur during the course of a clinical trial. These trends are modeled by a gamma frailty model, for which inference, sample size estimation and sample size re-estimation techniques are also described in detail. As an application, we consider lesion counts measured by magnetic resonance imaging (MRI), which play an important role in phase II multiple sclerosis (MS) trials for measuring disease progression. These lesion counts are generally overdispersed and often measured multiple times per patient during a running trial, therefore resembling the statistical model. Methods are kept general to allow for applications outside of MS, whenever similar data arise, and shown to preserve type I error rates while correcting the sample size, such that a desired power level is reached, in extensive simulation runs. The second part of this thesis will consider univariate negative binomial data with baseline covariates. For example, such data arise in MS when the total number of lesions at the end of a clinical trial, corrected for the number of lesions at baseline or other baseline variables, is taken as an endpoint. Developed sample size re-estimation techniques are also shown to preserve type I error rates while correcting the sample size such that a desired power level is reached. The summarized results are made available as R-functions and extend current methodology in the field of non-comparative adaptive designs.