Adaptive Designs - Evaluation and New Applications

In the last few years there has been an extensive discussion of adaptive (flexible) designs to be applied in medical studies, e.g. clinical trials. Whereas classical sequential designs have to be planned in most of the details a-priori, flexible designs allow for mid-trial design modifications based on all information collected up to an adaptive interim-analysis. In the adaptive interim analysis misspecifications from the planning phase can be revised without inflating the false positive error rate of the statistical test applied for inference from the experiment. The adaptation rules need not to be specified a-priori so that one can deal with the unexpected. Most emphasis has been put on reassessment of the sample size during an experiment. In this situation the experimenter recalculates the chances to achieve his goal in the planned statistical analysis given the results up to the interim-analysis (the conditional power). Statistical properties of adaptive designs with sample size reassessment have been investigated in recent research. Little work has been done on the problem of estimation in this context. Therefore we will compare statistical properties of existing estimation procedures and propose improved estimates. Another important issue for flexible designs is to deal with dropping of treatments due to problems of safety and/or lack of efficacy (which in clinical trials may be done by, e.g., Data Safety and Monitoring Committees). Strategies for testing and estimation when treatments are (unforeseeably) dropped during an experiment will be proposed and investigated. Medical treatments tend to be more and more tailored to specific patients characteristics (e.g. genetic variables). Therefore it becomes important to identify specific subgroups of patients which profit from a treatment and others which do not. Adaptive designs in clinical trials have the potential to look for such subgroups in an interim-analyses and to limit the focus to specific subgroups. Analyses of micro-array data and gene association data are becoming standard in medical research. These types of problems involve a large number of statistical tests applied in samples of generally small size. The concept of two stage designs can be used to drop nullhypotheses without promising first stage result and to reallocate the saved sample size among the selected ones. We will construct (cost-optimal) two stage-designs which control the (positive) false discovery rate.

Adaptive study designs allow for performing mid-trial design modifications based on data from inside or outside an ongoing trial without inflating the probability of producing false positive test decisions. This advantage as compared to conventional experiments, where the design specifications have to be strictly fixed a priori, has attracted a lot of research activities and applications over the last years particularly in the biostatistics community. This is a follow up project to FWF P15853-N04 addressing open questions and new applications of the adaptive design methodology. One goal of the project was to deal with the problem of estimation following adaptive designs since it is generally agreed on that quantifying the effects is an important task beyond statistical test decisions. Here we have proposed new point estimates when design adaptations are restricted to sample size reassessment. Under this restriction also new concepts of constructing confidence intervals have been introduced using different orderings of the sample space. An important achievement has been to define confidence intervals when adaptations are extended to treatment selection by using the duality of multiple testing and confidence intervals in adaptive testing procedures. Here the work in the adaptive field has been stimulating research on new graphical tools for multiple testing procedures and on new methods to shorten the amount of calculations required to perform specific multiple testing procedures. The issue of mid-trial treatment selection meanwhile has become a burning issue in the scientific community and several statistical problems related to it have been investigated by our group including the comparison of different selection strategies and multiple comparisons following selection. Subgroup selection within a trial - as it is a crucial issue for the concept of personalized medicine - has been considered. Fundamental problems, e.g., how to decide a priori how many treatments should be included in a trial, have come up through the research work and have been treated as well. The concept of adaptive selection designs has also been applied to the rapidly growing field of genetic markers. Different multi-stage designs have been proposed applying different concepts for the control of the probability of false positive decisions, e.g., the Family Wise Error Rate or the False Discovery Rate, also allowing for costs differing between stages. Some fundamental results on sequential procedures controlling the false discovery rate without any adjustment for multiple interim analyses have been achieved for the case that the number of candidate markers gets very large. Also some research on the scientific foundations of adaptive designs has been done in order to participate in the international exchange of arguments related to the methodology.