New challenges and methods for the analysis of longitudinal and survival data

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Longitudinal studies are widely used in practice, especially in health related research. In a longitudinal *study, we collect data on a set of variables repeatedly over time, *and we are often interested in how the values of the variables change over time. *In addition, we may also observe certain events of interest, *such as dropouts and infection of a disease.*In many studies, the longitudinal trajectories and the times to *the events are associated, so some longitudinal variables may be used as *potential markers for the events of interest. For example, *in HIV/AIDS studies, CD4 and viral load data are usually collected over time, *and their longitudinal trajectories may be associated with times to AIDS or deaths. *In lung cancer studies, the histories and progressions of pre-invasive lesions may be associated *with occurrences of lung cancer. In these studies, it is important to detect the disease in early *stages, so a major goal is to identify markers or risk predictors for progression *to AIDS or cancer. For statistical analyses of these data, *joint models of longitudinal and survival data are required in order to obtain *unbiased results. ** There has been extensive research in the literature for *joint models of longitudinal and survival data in recent years. However, *new challenges in statistical analysis continue to arise in practice, due to*the complexity of longitudinal and survival data in many longitudinal studies. *In these cases, existing statistical models and methods cannot be used or undesirable. For example, (i)*the variables of interest may be discrete or continuous or other mixed types; (ii) the longitudinal data may be censored, e.g., viral load may drop below a limit of detection in AIDS*studies, or may be semi-continuous; (iii) the longitudinal data may contain measurement errors, missing data, and outliers;*(iv) the model parameters may be constrained by biological laws; (v) there may be spatial dependence as well as longitudinal dependence; and (vi)*the computation in statistical inference can be quite challenging. *Thus, new or better statistical models and methods need to be developed to address these issues. In this proposal, motivated by several*current HIV/AIDS datasets and cancer datasets, we propose to develop a series of new joint models and methods to *address the foregoing issues. Once developed, these new models and methods may have important*impacts in AIDS and cancer research, since they may lead to new insights and findings which are unavailable based on existing models and methods. ***