Adaptive Designs and bias in treatment effects estimation

Every year a huge number of new drugs are developed against different pathologies and tested to evaluate their efficacy and safety. In clinical trials, one of the main objectives is to identify the most effective dose among several ones to obtain the maximum efficacy from a treatment. In classical Randomized Controlled Trials (RCTs), this is performed by giving different doses and a reference treatment or a placebo to a certain population, and by estimating the treatment effects via Maximum-Likelihood Estimation in order to compare them. In recent years, Adaptive Designs (ADs) have been developed to enhance clinical development. One of the main advantage of this procedure consists in the possibility, at interim analyses during the trial, to stop the evaluation of certain treatments for lack of efficacy and to focus only on the best ones. This results in improvements both in terms of resources and ethics, because it reduces the number of patients receiving non effective treatments. In Adaptive Designs, a selection of the best treatments may be performed at interim analyses. Because of this selection, the naive Maximum-Likelihood Estimation is biased. In particular, two types of biases can be identified: the always-reporting bias, a negative bias which affects the estimation of the dropped treatments, and the selection bias, a positive bias which affects the estimation of the selected treatments. In the literature, several methods have been proposed to obtain a better estimation of the treatments’ effects in such contexts. In this thesis, the main ones are compared via simulations, and applied to two case studies, one clinical trial in Alzheimer’s Disease and another in Heart Failure. We compare the Maximum-Likelihood Estimator (MLE) with Unbiased Estimators, Shrinkage Estimators and Bias-Adjusted Estimators. Unbiased Estimators are developed to find estimations which have no bias. Shrinkage Estimators attempt to reduce, but not to eradicate, the bias with low impact on the variability of the estimation, shrinking the treatments effects towards the overall mean. Bias-Adjusted Estimators, find an estimation of the bias that can be iteratively subtracted from the original naive estimation; we analyse the Single-Iteration procedure and the Multi-Iteration procedure. The performances are evaluated in terms of Bias, Variance and Mean Squared Error (MSE). A comparison of the previously discussed methods is also carried out in the context of adaptive designs with sub-population selection, i.e. when the aim is to identify at interim analyses the population that benefits the most from the treatment. Following the analyses, the Unbiased Estimator and the Single-Iteration Bias-Adjusted Estimator are recommended for a general application: the former completely eradicates the bias, but is highly variable with respect to a naive estimation; the latter is less biased than a naive estimation, but only slightly more variable.