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.