On analysis of binary response data in longitudinal factorial studies

Binary data are commonly used as responses to assess the effects of independent variables in longitudinal factorial studies. Such effects can be assessed in terms of the rate difference (RD), the odds ratio (OR), or the rate ratio (RR). Traditionally, the logistic regression seems always a recommended method with statistical comparisons made in terms of the OR. Statistical inference in terms of the RD and RR can then be derived using the delta method. However, this approach is hard to realize when repeated measures occur. To obtain statistical inference in longitudinal factorial studies, the current article shows that the mixed-effects model for repeated measures, the logistic regression for repeated measures, the log-transformed regression for repeated measures, and the rank-based methods are all valid methods that lead to inference in terms of the RD, OR, and RR, respectively. Asymptotic linear relationships between the estimators of the regression coefficients of these models are derived when the weight (working covariance) matrix is an identity matrix. Conditions for the Wald-type tests to be asymptotically equivalent in these models are provided and powers were compared using simulation studies. A phase III clinical trial is used to illustrate the investigated methods with corresponding SAS (R) code supplied.