This project will investigate theory, methods and applications of mathematical statistics and probability, with particular emphasis on the problems with data collected by NICHD. Current focus is on 1) the analysis of data arising from longitudinal studies with repeated measurements, 2)nonparametric procedures, 3) likelihood approaches to nonparametric two-sample problem for right-censored data, 4) sequential clincial trials, and 5) general methodology for reproductive and perinatal epidemiology. Examples of NICHD projects on longitudinal studies are Successive Small-for-Gestational Age Study I and Study II in Alabama and Scandinavia, and the Longitudinal Study of Vaginal Flora. A host of statistical procedures for estimation and hypothesis testing will be proposed and investigated for the time varying coefficient models via their asymptotic properties and simulations. Applications will be developed to handle questions concerning various issues in perinatal and reproductive epidemiology. New and rigorous statistical methods and algorithms will be generated and validated through investigation of their statistical and probabilistic properties. Computer-intensive techniques such as bootstrapping methodology will be investigated for the relevant problems. Among the applications of the developed methodology are fetal growth, maternal risk factors and pregnancy outcomes. Regression models for unbalanced longitudinal ordinal data will be studied. Major motivation and application come from the Longitudinal Study of Vaginal Flora. One direction is to develop sequential methodologies for clinical trials. Particular focus will be on the estimation problems following the termination of a clinical trial. Adaptive designs in clinical trials will be studied. Also under investigation is the incorporation of partial overrruning into the final analysis of a sequential clinical trial. Longitudinal analysis for discrete data and sequential adaptive designs will be the major focus for the near future. Point and interval estimation for two-stage adaptive procedures will be studied. A two-stage adaptive procdeure will be designed for the selection of the best diagnostic biomarker. The general linear mixed models for longitudinal data will be studied. Specific attention will be focused on the simultanous optimality of least squares estimate and analysis of variance estimate, and the exact inference on contrasts in intraclass correlation models with missing data. Semi-Bayes statistical procedures will be studied in the statistical problems of hypothesis testing and model selections.