Extension of Logic regression to Longitudinal data: Transition Logic Regression

Logic regression is a generalized regression and classification method that is able to make Boolean combinations as new predictive variables from the original binary variables. Logic regression was introduced for case control or cohort study with independent observations. Although in various studies, correlated observations occur due to different reasons, logic regression have not been studied in theory and application to analyze of correlated observations and longitudinal data. Due to the importance of identifying and considering the interactions between variables in longitudinal studies, in this paper we propose Transition Logic Regression as an extension of Logic Regression to binary longitudinal data. AIC of the models are used as score function of Annealing algorithm. In order to assess the performance of the method, simulation study is done in various conditions of sample size, first order dependency and interaction effect. According to results of simulation study, by increasing the sample size, percentage of identification of true interactions and MSE of estimations get better. As an application, we assess interaction effect of some SNPs on HDL level over time in TLGS study using our proposed model.