Urn Sampling and the Proportional Hazard Model

This paper investigates the urn sampling analogue for the score statistic relating survival to covariates assuming a proportional hazard model. The exact permutation distribution can be calculated as well as the exact low order moments for arbitrary censoring patterns. The asymptotic distribution of the score statistic is an easy consequence. The method is naturally extended to deal with the multivariate case, time varying covariates and interval censoring. Finally the relationship between the censoring process, the survival times and covariates are studied considering different reference sets for the distribution of the score statistic. Some assumptions about the censoring process are investigated and as a consequence the effect of censoring is clarified.     

Comparing the Survival of Two Groups with an Intermediate Clinical Event

Consider a subject entered on a clinicaltrial in which the major endpoint is a time metric such as deathor time to reach a well defined event. During the observationalperiod the subject may experience an intermediate clinical event.The intermediate clinical event may induce a change in the survivaldistribution. We consider models for the one and two sample problem.The model for the one sample problem enables one to test if theoccurrence of the intermediate event changed the survival distribution.This models provides a way of carrying out non-randomized clinicaltrial to determine if a therapy has benefit. The two sample problemconsiders testing if the probability distributions, with andwithout an intermediate event, are the same. Statistical testsare derived using a semi-Markov or a time dependent mixture model.Simulation studies are carried out to compare these new procedureswith the log rank, stratified log rank and landmark tests. Thenew tests appear to have uniformly greater power than these competitortests. The methods are applied to a randomized clinical trialcarried out by the Aids Clinical Trial Group (ACTG) which comparedlow versus high doses of zidovudine (AZT).     

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Lifetime Data Analysis -     

Intermediate clinical events,surrogate markers and survival

This paper investigates one- and two-sample problems comparing survival times when an individual may experience an intermediate event prior to death or reaching some well defined endpoint. The intermediate event may be polychotomous. Patients experiencing the intermediate event may have an altered survival distribution after the intermediate event. Score tests are derived for testing if the occurrence of the intermediate event actually alters survival. These models have implications for evaluating therapies without randomization as well as strengthening the log rank test for comparing two survival distributions. The exact distribution of the score tests can be found by conditioning on both the waiting time and occurrence of the intermedate event.Deceased