Nonparametric Methods For Analyzing Incomplete Nondecreasing Repeated Measurements.

In comparing the effectiveness of two treatments, suppose that nondecreasing repeated measurements of the same characteristic are scheduled to be taken over a common set of time points for each study subject. In this case, if there is a missing observation at a particualr time u, then the observations at times s and t, where s $<$ u $<$ t, provide a lower and an upper bound for the observation missed at time u. We propose several classes of nonparametric tests for testing for differences between two treatments over the entire study: (1) tests which exclude missing values (but are valid even when the patterns of missing observations in the two groups are different); (2) tests based on the assumption that the missing value patterns are the same in the two groups; (3) tests which are valid when the patterns of missing observations in the two groups are different. All of these methods take advantage of the nondecreasing property of the repeated measurements from each subject. The large-sample distributions are derived and the small-sample properties are compared in a simulation study. In particular, the effects of the amount and pattern of missing data on the distributions of the test criteria under the null and alternative hypotheses are investigated. The proposed test of type (3) are shown to be more powerful than existing nonparametric method. Based on these tests, consistent point estimators and test-based nonparametric confidence intervals for the overall treatment effect are derived. Next, statistical inference procedures are developed to examine the changes of treatment effect over time. For example, one may like to know if a particular treatment is beneficial only in the early stages of a study. Nonparametric tests based on the increments of the repeated measurements are proposed for this situation and a simultaneous inference procedure for evaluating the time trend for treatment effect is described. In addition, consistent point estimators and test-based nonparametric simultaneous confidence regions for the treatment effects are derived. Finally, the above methods are extended to the case of more than two groups of subjects.Ph.D.Biological SciencesBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128049/2/8720255.pd