Contributions to analysis of randomized multi-center clinical trials: The role of conditioning

We distinguish between "design based" versus "model based" analyses of a planned experiment. A design based analysis incorporates the main features of the planned experiment as the principal basis for making inferences. A model based analysis may ignore some features of the planned experiment and use models such as proportional hazards, logistic and linear regression as the basis for inference. Our philosophy is that all inferences should be based on design based analyses. The model based analyses are only appropriate if they are close approximations to the design based analyses. An important class of planned experiments is the multi-center randomized clinical trial. A design based analysis would rely on the permutation distribution generated by the randomization process. Ordinarily the number of patients assigned to each treatment within a center is a random variable, but is also an ancillary statistic. Another feature of multi-center randomized trials is the use of permuted blocks to allocate the treatments. The permuted blocks also generate ancillary statistics. More generally when there are covariates, the number of subjects assigned to the level of a covariate is a random variable, but is also an ancillary statistic. An important principal in frequentist inference is to condition on the ancillary statistics as the conditioning will reduce the sample space resulting in greater power. Finding the exact distribution of the appropriate test statistic under these circumstances may be difficult, if not impossible. As a result we have developed an approximation to this distribution. Simulations show that the approximation works well. We have investigated the power when the outcomes are continuous, binary, and censored in the context of multi-center trials with variation between institutions. Our investigations indicate that there is an increase in power, conditioning on the ancillary statistics, compared to ignoring the ancillary statistics for the three types of outcome data. The increase in power is a function of the variation amongst the treatment sample sizes within institutions and may be considerable if there is large variation between institutions. The methods have been extended to group sequential trials with similar increases in power.; In the second part of the thesis, we proposes a new distribution-free statistical method for testing hypotheses about covariates for survival data having simultaneously right, left and interval-censored survival times. (Abstract shortened by UMI.)...