On Analysis of Changes in Rates and Averaged Correlated Rates

Changes in rates and averaged correlated rates are two common analyses for binary response data in longitudinal factorial studies. The traditional logistic regression for repeated measures can be used to obtain statistical inference for these two analyses, however, it has two potential deficiencies: first, the model may not converge, and second, the resulted statistical inference in terms of a linear contrast of odds ratios seems hard to be interpreted and understood by practitioners. The current article applies the methods in Fan and derives statistical inferential procedures for the analysis of changes in rates and averaged correlated rates in terms of the rate difference (RD), the odds ratio (OR), and the rate ratio (RR). Numerical assessments through simulation studies and examples were employed to demonstrate advantages of statistical inference in terms of the RD over the OR or the RR in different aspects including model convergence and interpretation of the results. The current article can be viewed as special case studies of the methods by Fan while it provides clearer and more direct comparisons of the methods when analyzing changes in rates and averaged correlated rates in longitudinal factorial studies.