Repeated measures studies arise in all areas of Public Health, and the responses are often categorical (such as sick or well), and not continuous (such as blood pressure). In repeated measures studies, the basic sampling unit is a group or cluster of subjects; a measurement is made on each subject within the cluster. For example, in a toxicological study, the cluster is a litter, and the fetuses or newborns are the subjects within the litter; in a longitudinal study of health effects of air pollution, the cluster is a person, and the repeated measures are the responses at the different times. Repeated measures studies present some quite unique problems, especially when the response is categorical, and it is these problems on which this proposal is focused. The longterm research objectives to develop new methods for analyzing repeated categorical responses as well as to make the old and new methods more accessible to the non-statistician. The proposed methods address a variety of issues that are relevant to repeated measures studies in epidemiology, clinical trials, and environmental science. Since small samples can invalidate the asymptotic approximations that have been proposed for analyzing repeated measures data, methods appropriate for small samples will be explored. Because the jackknife has been shown to provide consistent estimates of the variance of regression parameter estimates in longitudinal studies, we propose to use the jackknife in a wider range of problems, including providing an estimate of the variance of the estimated correlation parameters. In the simplest kind of repeated measures study with no covariates, investigators are often interested in measuring agreement among a set of repeated binary (or polychotomous) measurements on individuals; the third goal is to develop simple methods for estimating measures of agreement. A fourth goal is to extend the methods for analyzing repeated binary responses to analyze also repeated polychotomous responses, and in particular, repeated ordinal responses. A final goal is to develop methods for calculating the sample size (of clusters and subjects within clusters) necessary to obtain a given level of precision.
