Aspects of analysis of small-sample right censored data using generalized Wilcoxon rank tests

The estimated bias and variance of commonly applied and jackknife variance estimators and observed significance level and power of standardised generalized Wilcoxon linear rank sum test statistics and tests, respectively, of Gehan and Prentice are compared in a Monte Carlo simulation study. The variance estimators are the permutational-, the conditional permutational- and the jackknife variance estimators of the test statistic of Gehan, and the asymptotic- and the jackknife variance estimators of the test statistic of Prentice. In unbalanced small sample size problems with right censoring, the commonly applied variance estimators for the generalized Wilcoxon rank test statistics of Gehan and Prentice may be biased. In the simulation study it appears that variance properties and observed level and power may be improved by using the jackknife variance estimator. To establish the sensitivity to gross errors and misclassifications for standardised generalized Wilcoxon linear rank sum statistics in small samples with right censoring, the sensitivity curves of Tukey are used. For a certain combined sample, which might contain gross errors, a relatively simple method is needed to establish the applicability of the inference drawn from the selected rank test. One way is to use the change of decision point, which in this thesis is defined as the smallest proportion of altered positions resulting in an opposite decision. When little is known about the shape of a distribution function, non-parametric estimates for the location parameter are found by making use of censored one-sample- and two-sample rank statistics. Methods for constructing censored small sample confidence intervals and asymptotic confidence intervals for a location parameter are also considered. Generalisations of the solutions from uncensored one-sample and two-sample rank tests are utilised. A Monte-Carlo simulation study indicates that rank estimators may have smaller absolute estimated bias and smaller estimated mean squared error than a location estimator derived from the Product-Limit estimator of the survival distribution function. The ideas described and discussed are illustrated with data from a clinical trial of Head and Neck cancer.digitalisering@um