Inference for ranking data

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Consider a situation where patients are being monitored with respect to their responses to a particular treatment. Patients are supposed to report at a clinic at regular times in order that measurements be taken reflecting their health status. It is conjectured that there should be an improvement over a period of time and that this improvement is not constant but that it is only noticeable at certain times. Unfortunately not every patient reports to the clinic at the required times, so there are  missing observations. The object of the analysis is to show, in spite of the missing data, that there has been an improvement over the monitored times, and to identify those times at which improvement is marked and significant. Consider also the situation where patients are required to take medications over a period of time for a particular ailment. Not all patients are careful in following the required schedules for the taking of medications particularly if there are combinations of different  medications that must be taken at different times, nor do all patients comply with the prescribed activities that may be part of the regime. In order to determine the success of different  methods (such as written material, one-on-one instruction, etc.) for educating patients as to their condition, their medication requirements and related activities, patients are divided into several groups in which different methods were used to impart information and conduct training. After a certain period of time has elapsed, patients in these groups are given questionnaires relating to their level of understanding. It is desired to compare the level of comprehension between the groups, in the light of the fact that not all patients answer all questions. These scenarios are examples of direct applications of the anticipated results of my proposed research in Inference for Ranking Data.