Generalized Rank Tests for Progressive Censoring Procedures

In clinical trials and life testing problems the responses are time-sequential in nature and a compl~t~ experimentation may involve a prohibitive amount of time and cost •. • Fo't "this reason, progressive· censoring schemes (PCS) are often advocated with a view to terminating the experimentation at the earliest possible stage if the accumulated statistical evidence warrants to do so. In this dissertation we propose some progressively censored tests for grouped and ungrouped data and study their asymptotic properties. For batch-arrival models (BAM) relating to categorical data under time-&equential studies, we develop four PCS chi-square type statistics. The necessary (asymptotic) distribution theory is derived for the null as well as local alternative hypotheses situations, in each case. For grouped and ungrouped data from"time-sequential experiments, we propose a general class of progressively censored rank order tests for the multiple regression model and s~~~Yn~ir asymptotic properties through the formation of suitable sampl~ processes. }or grouped data we develop, in addition, PCS rank order tests for simple regression model. We show that, under suitable regularity conditions, the distributions of the proposed statistics converge weakly to those of some functionals of the standard Brownian motion process under the null hypothesis and to those of the drifted Brownian motion process under contiguous alternatives. As the available statistical tools do not provide us with the necessary analytical expressions for the exact null distribution of these processes, we derive their empirical distributions through simulation. Two numerical examples using simulated data from exponential populations are given, illustrating the PCS chi-square type tests and PCS rank order tests when the responses are recorded on an ordered categorical set, ina two-sample problem. We empirically show that, for the negative exponential survival time distributions one often encounters in life testing problems, the rank order tests are much superior to the chi-square type tests from both power and mean stopping time considerations. Finally extensions of the proposed tests in three directions are suggested as topics for further research. ACKNOWLEDGMENTS It is a pleasure to express my sincere appreciation to my adviser, Dr. P. K. Sen, for his patience, continued guidance, and advice during the course of this research. I am also indebted to the other committee members, Drs. to Chapel Hlll af~er a lapse of four years. The financial support for this research and graduate study was through a graduate research assistantship from the Department of Biostatistics. I wish to place on records …