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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.
Fleming et al. (Thu,) studied this question.