| In randomized clinical trials, more powerful and precise statistical inferences are possible once the between groups comparisons have been adjusted for baseline values. However, adjusting for baseline values is not an easy task and there is no unique way of doing it. One method is to treat the problem as longitudinal data and fit a cumulative logistics regression model. But this comes with the common burden of parametric assumptions which may not have any relevance to the data generating process. The other popular option is to resort to nonparametric techniques such as the Mann-Whitney-Wilcoxon test or Smirnov tests. Each of these procedures invokes an artificial order in the ordinal data. This is a major drawback of such procedures yielding false significance between categories which otherwise are not comparable. Also the tests are dependent on the particular pseudo-ordering chosen to construct the test statistic, thus being highly sensitive to the order of the categories.; In this dissertation, we seek to overcome the aforementioned drawbacks of nonparametric baseline adjustment procedures. We propose a new method which adjusts for baseline without relying on any specific assumptions on the data generating process. In the context of two-armed clinical trials in which an ordinal response is observed on entry and at a follow-up, data are composed of counts of patients who have improved from one category to other, stayed the same or deteriorated. Not every pair of patterns of change in patients condition during the study are comparable. Thus the results can only be compared through a partial ordering. We define several partial orderings, some rich and some sparse. Different Smirnov-like tests based on this idea are developed. These tests do not suffer from the deficiencies (mentioned earlier) of the classical Smirnov tests for baseline adjustment. The conditional exact power of these Smirnov-like tests are calculated under different alternative hypotheses in order to compare them among themselves as well as with the traditional tests. Asymptotic null distribution of our test is derived, and consistency of test is shown. |
