This project aims at developing predictive methodology, widening its realm of application and implementing it. Predictive inference, as expressed by prediction intervals and model selection on the basis of prediction fit, is addressed. Classes of models and statistics particularly relevant to health sciences are focused on in the development of the proposed methodology. In each case, both analytical and empirical investigations of the behavior of the methods are intended, the latter drawing upon both simulations and actual data sets. The first two components of this research program pertain to the development of a predictive approach to the selection of models for categorical and survival data with a view to helping in the elicitation of predictors and prognostic factors. The sequential aspect of the data collection is taken into account. The goal of the research is to establish sound theoretical foundations for these diagnostics and to demonstrate their practicality. The third component casts the construction of empirical Bayes confidence intervals in a predictive framework and concentrates on the development of such techniques to statistics of importance in clinical trials. The priors are chosen to embody the correlation structure between the groups under study. The construction of Bese intervals will be addressed via both analytical methods and bootstrap samples. Comparison with respect to several validation criteria will discriminate between existing and proposed techniques. Focussing on observables, the characteristics of prediction intervals based on empirical Bayes distributions will be looked into. The study of prediction intervals based on generalized linear and quasilikelihood models constitutes the fourth component of this project. As a means of predictive inference from clinical investigations, delimiting standards by which subjects can be gauged, their reliability is crucial. The behavior of the actual coverage probability, a random variable affected by parameter estimation, will be considered.
The aim i s to remove the first order bias in the overall coverage probability. Ways of improving the calibration of the constructed intervals are proposed: one is analytical and the other makes use of Monte-Carlo simulations. The properties of the bootstrap in predictive contexts is of prime interest. Lastly, all proposed methodology together with established techniques will be put to practical purposes in developing and assessing prognostic systems for primary biliary cirrhosis, with the view to determine the optimal time for liver transplantation.
| Seillier-Moiseiwitsch, F (1996) Predictive diagnostics for logistic models. Stat Med 15:2149-60 |
