Statistical Methods in Medical Research

In this paper, we consider group sequential procedures for clinical trials under variance heterogeneity. Group sequential procedures typically involve small samples at each interim analysis. We advocate Welch’s correction for variance heterogeneity, and present a natural application of the significance level method for such situations. Currently available procedures are based on a large sample method, with no allowance for corrections of heterogeneity. Unless the sample size is large, the results are not valid. On the basis of simulation studies, comparing their abilities to control Type I error rates, we recommend using Welch’s correction for sequential trials involving small samples under variance heterogeneity.

The evaluation of diagnostic agents or imaging procedures is governed by the same scientific and regulatory rules as that of other medical products. Receiver operating characteristic (ROC) curves, and especially the area under these ROC curves, are indices for the accuracy of a diagnostic test for continuous as well as ordinal data. The methodology of multivariate rank statistics for the nonparametric Behrens-Fisher problem is used to evaluate the accuracy of a diagnostic test in a complex factorial design with repeated measurements. Hypotheses are formulated by means of relative treatment effects and are tested by a multivariate extension of the Mann-Whitney statistic in a heteroscedastic model. The application of this method is demonstrated by the analysis of a data set from a diagnostic clinical trial.

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Studies of HIV dynamics in AIDS research are very important for understanding pathogenesis of HIV infection and for assessing the potency of antiviral therapies. Since the viral dynamic results from clinical data were first published by Ho et al. and Wei et al., the study of HIV-1 dynamics in vivo has drawn a great attention from AIDS clinicians and researchers. Although the important findings from HIV dynamic studies have been published in many prestigious scientific journals, statistical methods for estimating viral dynamic parameters have not been paid enough attention by HIV dynamic investigators. The estimation methods in many viral dynamic studies are very crude and inefficient. In this paper, we review the statistical methods and mathematical models for HIV dynamic data analysis developed in recent years. We also address some practical issues and share our experiences in the design and analysis of viral dynamic studies. Some principles and guidelines for the design and analysis of viral dynamic studies are provided. The methodologies reviewed in this paper are also applicable to studies of other viruses such as hepatitis B virus or hepatitis C virus. We also pose some challenging statistical problems in this area in order to stimulate further study by the statistical research community.