Statistical modelling for complex longitudinal multi-state data

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The primary objective of the proposed research program is the refinement and development of methodologies in event history analysis for the analysis of longitudinal data from complex surveys. ******Event history analysis and the field of complex surveys are two areas in statistics which have developed independently of one another. The origins of event history analysis lies in survival analysis models used to estimate survival times; whereas the origins of complex survey data lie in sampling designs which allow one to lower costs by over sampling and under sampling particular sub-populations. Although there are many benefits to complex multistage sampling, the main disadvantage is that is complicates the analysis of survey data. Models in event history analysis, as the name suggests, account for the covariate histories of individuals and are specifically developed for the analysis of longitudinal data. These models also address types of incomplete data such as right censoring which can occur either from the attrition of individuals as people are lost to follow up in the survey or by the end of a survey panel. A bias which occurs in complex longitudinal data known as left truncation can also be addressed. Left truncation occurs when for example an unemployment spell is cut off by the start of a panel and is therefore incomplete.******Limited methods from event history analysis have already been used to analyze unemployment spells for example. Typically incomplete data, such as left truncated spells, are discarded and the remaining spells are analyzed by introducing a dependency between spells on the same individual using a shared frailty model. Multi-state models offer a superior parametrization. For unemployment durations, the simplest multi-state model will allow one to jump between two states: employed and unemployed. An unemployment spell is also known as a sojourn time in the unemployment state.******My proposal is to develop multi-state models to account for common features of panel survey data, such as, incomplete sojourn time information for many individuals. A primary advantage of this approach is that the parametrization captures may essential elements of a dynamic process in a population. Furthermore, addressing features such as missing sojourn time information by developing likelihoods to include people with missing data and methods to optimize them will significantly improve inference from these complex longitudinal surveys.