<b><i>Objective:</i></b> Drugs take effect at different times in different individuals. Consequently, researchers seek to examine how the timing of the biological response to drugs may be affected by factors such as gender, genotypes, age, or baseline symptom scores. <b><i>Methods:</i></b> Typically, studies measure symptoms immediately after the initiation of drug treatment and then at a sequence of later time points. In this study, we develop a statistical mixture model for analyzing such longitudinal data. Our method estimates the onset of drug effect and assesses the association between the probability distribution of the onset times and possible contributing factors. Our mixture model treats the timing of onset as missing for each individual but restricts it, for simplicity, to two possible onset points, early or late. To estimate the model, we use an expectation-maximization-based approach and provide the general formulas of the variance and covariance matrix for the estimated parameters. <b><i>Results:</i></b> We evaluate the model's overall utility and performance via simulation studies. In addition, we illustrate its use by application to longitudinal data from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study. The algorithm identified age and anxiety status as significant factors in affecting the onset distribution of citalopram (Celexa).