Semi-parametric modelling of longitudinal data when the observation process is neither completely random nor completely deterministic

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Many studies in healthcare research follow patients over time. This allows researchers to evaluate how, for example, treatment impacts a patient's health over a number of months or years, rather than looking at just the initial response to treatment. Most research involving patients who are followed over time involves some unpredictability in the times when patients are seen by their physicians, or in the information that is gathered at each visit. Even if the researcher lays out a timeline specifying when visits should occur, patients my miss a scheduled visit, see their doctor more often when unwell, ask that a test or measurement not be taken at a particular visit, or withdraw from the study altogether. These variations in visit times and information collected at each visit are rarely completely random, and are often associated with the patient's health. If this is ignored when analysing the data, the results of the analysis can be very misleading. Work outlined in this proposal will develop methods to analyse this type of irregular data, with a focus on providing precise, unbiased answers to important healthcare questions.