Joint mixture quantile regressions and time-to-event analysis

. Growth curve mixture models for longitudinal data are often developed on the conditional mean of a response, focusing only on the central section of the distribution. There is, however, an increasing desire to provide holistic information on different parts of the distribution of the response such as lower and higher quantiles. This article presents quantile regression analysis within the framework of growth curve models by jointly analyzing time to an event and longitudinal data with multiphasic features. The multiphasic patterns are accounted for at different quantiles by modeling heterogeneous growth trajectories which show gradual changes from a declining trend to an increasing trend over time within latent classes. Thus, we assess these important features of longitudinal data using bent-cable models along with a joint modeling of time to event process and response process. The proposed methods are illustrated using a real data set from an AIDS clinical study. model for assessing conditional quantiles of a response process with latent classes of growth trajectories and a time to event process. These processes were assessed by measuring the association between HIV viral load dynamics and time to first