Subset Selection Based on Order Statistics from Logistic Populations

Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Paul van der Laan, Department of Mathematics and Computing Science, Eindhoven University of Technology, The Netherlands


Consider k equal size treatment groups and let the outcome of interest be a survival time. Suppose that a known monotone transformation of the survival times is logistically distributed and that the treatment only affects the location parameter. We obtain exact results for the problem of selecting a subset of treatments, based on the i-th ordered survival times, which contains with specified probability P* the optimal treatment. Since the distribution of the median of a small logistic i.i.d. sample is shown to approximate very well the normal distribution our exact results for the median can also be used for subset selection based on estimates of location parameters which are normally or approximately normally distributed. Statistics, 00, pp. 1-9