![]() For each experimental unit we define a full data random variable and it is assumed that they are identically and independently distributed. We present a general statistical framework which allows us to study adaptive designs and estimators based on data generated by these adaptive designs from a frequentist perspective in great generality. In spite of the results on response adaptive clinical trial design as presented in Hu and Rosenberger (2006), among most practitioners there seems to be a widely accepted consensus that for formal frequentist statistical inference changing the design based on a look at the data in a clinical trial should be avoided even if it is not used for testing. This naturally raises the question: Why not learn a user supplied optimal unknown choice of the controlled components of the design based on the data collected in the previously initiated experiments, and thereby adjust/adapt these controlled components of the design for future experiments during the course of the study? Although, certain basic types of so called ”response adaptive designs” in clinical trials have been proposed and studied from a frequentist perspective (Hu and Rosenberger (2006)), allowing treatment randomization probabilities to be a function of outcomes collected in previous experiments, by far most designs in practice are static and most of the adaptive design literature has focussed on adaptive stopping times based on sequential testing or other adaptive stopping rules. The choice of these design mechanisms are typically made a priori, and, it is common that during the course of the ordered sequence of experiments the observed data suggests that the chosen design is ineffective in answering the scientific question of interest, or is dissatisfying from other perspectives, and that a much better design (i.e., choice of mechanisms) should have been selected. ![]() ![]() That is, the design of each experiment involves selecting a so called treatment mechanism/monitoring mechanism/ missingness/censoring mechanism, where these mechanisms represent a formally defined conditional distribution of one of these actions (i.e., assignment of treatment/monitoring indicator/missingness indicators/ right censoring indicators), given observed data characteristics on the unit. The design of each experiment involves making various decisions such as 1) What variables to measure on the randomly sampled experimental unit?, 2) How regularly to monitor the unit, and for how long?, 3) How to randomly assign a treatment or drug-dose to the unit?, among others. In order to answer scientific questions of interest one often carries out an ordered sequence of experiments generating the appropriate data over time.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |