David P. Harrington

A class of hypothesis tests for one and two sample censored survival data

This paper proposes a class of new non-parametric test statistics useful for goodness-of-fit or two-sample hypothesis testing problems when dealing with randomly right censored survival data. The procedures are especially useful when one desires sensitivity to differences in survival distributions that are particularly evident at at least one point in time. This class is also sufficiently rich to allow certain statistics to be chosen which are yery sensitive to survival differences occurring over a specified period of interest. The asymptotic distribution of each test statistic is obtained and then employed in the formulation of the corresponding test procedure. Size and power of the new procedures are evaluated for small and moderate sample sizes using Monte Carlo simulations. The simulations, generated in the two sample situation, also allow comparisons to be made with the behavior of the Gehan-Wilcoxon and log-rank test procedures.

Considerations for monitoring and evaluating treatment effects in clinical trials

The efficacies of various treatments commonly are evaluated and compared using prospective clinical trials. For ethical reasons, data from these trials are analyzed on an interim basis. The statistical test procedures used in these evaluations must be carefully selected and appropriately applied.

Procedures for Serial Testing in Censored Survival Data

Prospective studies, such as those carried out in many cancer centers throughout the world, need to be carefully monitored and subjected to interim analyses to satisfy important ethical considerations. Typically, the therapeutic effecacy and resulting survival distribution for an experimental treatment regimen are compared to the efficacy and survival obtained from a currently accepted standard regimen. These studies often give rise to the dual need to terminate as soon as possible any trial in which it ist sufficiently clear either that (1) the experimental treatment yields better results than the standard treatment or (2) the data strongly contradict the hypothesis of some minimally acceptable treatment difference. In this paper, we examine the problem of constructing closed sequential experimental designs allowing for hypothesis tests at multiple points in time when the data gathered are censored failure time data. The tests we study are useful for examining various forms of dependence of an underlying survival function S(x) on a random scalar covariate Z.

Estimation for discrete time nonhomogeneous Markov chains

Using the maximum likelihood principle, nonparametric estimators are derived for discrete time nonhomogeneous Markov chains. As the number of observed chains becomes large, asymptotic unbiasedness and strong consistency of the estimators are proved, as well as asymptotic distribution results. Finally the estimators are compared with ones which have been proposed in continuous time.

Statistical properties of estimators for continuous time Markov branching processes with varying and random environments

Abstract Asymptotic properties are established for estimators of time dependent intensities in Markov branching processes with varying and random environments. For the varying environment model, the estimators are shown to be uniformly strongly consistent on bounded intervals as the initial population size X 0 → ∞, and, when considered as empirical stochastic processes, to converge weakly to Gaussian processes with independent increments. For random environments, the estimators are shown to be asymptotically normal as t → ∞, where t is the time parameter.

A note on efficiencies for estimators in varying environments

Abstract The distribution, as the initial population size grows large, of the maximum likelihood estimator of the time average reproduction mean in a branching process with varying environments is compared with that of the classical estimator proposed under the assumption that the environments are constant in time.