Some new models and methods for complex longitudinal and survival data

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Longitudinal studies are widely used in practice. They allow researchers to investigate how the values of key variables change over time and if these changes may be associated with events of interest such as infection of a disease. For example, researchers may be interested in studying if the declines in CD4 counts may be associated with the risk of HIV infection, or if the increases of Covid-19 daily counts in different countries may be associated with increases in the risk of death. Here, the repeated measurements of CD4 or Covid-19 daily counts over time are longitudinal data, while the time-to-infection or time-to-death are survival data. Statistical analyses of complex longitudinal data and survival data can be highly challenging, since i) longitudinal trajectories of key variables may vary substantially across individuals and these variations may be individual-specific and change over time; ii) there may be outliers, measurement errors, censoring, and missing values in the data so that existing statistical methods may be unreliable; iii) two-phase studies may be necessary where the second phase may involve unequal probability sampling and more frequent repeated measurements; and iv) computations associated with statistical inference for complex models can be highly challenging. Although there has been extensive research in the analyses of longitudinal data and survival data, many issues remain to be addressed and new challenging issues emerge, due to the complexities of many new longitudinal studies and datasets.         We propose to develop some innovative statistical models and methods to address some of the foregoing issues. These proposed new models and methods are expected to make significant contributions in many fields, such as HIV/AIDS research and Covid-19 research, because they may lead to new findings which may be unavailable based on existing models and methods. For example, the proposed new methods may allow us to better evaluate anti-HIV treatments than existing ones. The proposed new models and methods are quite general in the sense that they can be used to analyse a wide variety of longitudinal data or clustered data, and thus they are expected to make important impacts in many fields.