Statistical methods and software for clinical trials with binary and survival endpoints. Efficiency, sample size and two-sample comparison

Defining the scientific question is the starting point for any clinical study. However, even though the main objective is generally clear, how this is addressed is not usually straightforward. Clinical studies very often encompass several questions, defined as primary and secondary hypotheses, and measured through different endpoints. 

In clinical trials with multiple endpoints, composite endpoints, defined as the union of several endpoints, are widely used as primary endpoints.  The use of composite endpoints is mainly motivated because they are expected to increase the number of observed events and to capture more information than by only considering one endpoint.  Besides, it is generally thought that the power of the study will increase if using composite endpoints and that the treatment effect on the composite endpoint will be similar to the average effect of its components. However, these assertions are not necessarily true and the design of a trial with a  composite endpoint might be difficult.  

Different types of endpoints might be chosen for different research stages. This is the case for cancer trials,  where short-term binary endpoints based on the tumor response are common in early-phase trials, whereas overall survival is the gold standard in late-phase trials. In recent years,  there has been a growing interest in designing seamless trials with both early response outcome and later event times.  Considering these two endpoints together could provide a wider characterization of the treatment effect and also may reduce the duration of clinical trials and their costs.  

In this thesis, we provide novel methodologies to design clinical trials with composite binary endpoints and to compare two treatment groups based on binary and time-to-event endpoints. In addition, we present the implementation of the methodologies by means of different statistical tools. Specifically, in Chapter 2, we propose a general strategy for sizing a trial with a composite binary endpoint as primary endpoint based on previous information on its components. In Chapter 3, we present the ARE (Asymptotic Relative Efficiency) method to choose between a composite binary endpoint or one of its components as the primary endpoint of a trial. In Chapter 4, we propose a class of two-sample nonparametric statistics for testing the equality of proportions and the equality of survival functions. In Chapter 5, we describe the software developed to implement the methods proposed in this thesis. In particular, we present  CompARE, a web-based tool for designing clinical trials with composite endpoints and its corresponding R package, and the R package SurvBin in which we have implemented the class of statistics presented in Chapter 4. We conclude this dissertation with general conclusions and some directions for future research in Chapter 6.