Alcohol and drug uses are common in today’s society and it swell-known that they can lead to serious consequences. Studies have been conducted in order, for example, to understand short- or long-term teem-poral processes of alcohol and drug uses., there are many deaths indirectly related to their uses such as motor vehicle accidents and suicide. Among the alcohol and drug users, some suffer from alcohol or drug use disorder, abuse or dependence, but many simply misuse alcohol or drug. A number of studies have been conducted to investigate various aspects of alcohol and drug uses. These approaches will then be applied to the data from the AHB study with the focus on the assessment of temporal processes of alcohol and drug uses and the effects of covariates such as gender and personality on the processes. Note that for alcohol and drug use studies, response variables are often given in the form of counts such as the number of alcohol or drug uses and the number of negative consequences due to alcohol or drug use within a week or month. Also note that many methods have been developed specifically for the analysis of alcohol and drug use-related studies based on the Poisson distribution or process assumption for the count response variables representing alcohol and drug uses. In this paper, we present some alternatives to these Poisson-based methods. In addition to avoid the Poisson assumption, the proposed approaches also allow time-varying covariates, missing responses and covariates, and correlated response variables, which present in the data from the AHB study and the longitudinal data from many other studies or fields.