Power Calculations for Preclinical Studies Using a K-Sample Rank Test and the Lehmann Alternative Hypothesis

Power calculations in a small sample comparative study, with a continuous outcome measure, are typically undertaken using the asymptotic distribution of the test statistic. When the sample size is small, this asymptotic result can be a poor approximation. An alternative approach, using a rank based test statistic, is an exact power calculation. When the number of groups is greater than two, the number of calculations required to perform an exact power calculation is prohibitive. To reduce the computational burden, a Monte Carlo resampling procedure is used to approximate the exact power function of a k-sample rank test statistic under the family of Lehmann alternative hypotheses. The motivating example for this approach is the design of animal studies, where the number of animals per group is typically small.

Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch, and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient. The efficient influence function for the parametric part aggress with the more general information bound calculations of Robins, Hsieh, and Newey (1995). By verifying the conditions of Murphy and Van der Vaart (2000) for a least favorable parametric submodel, we provide asymptotic justification for statistical inference based on profile likelihood.