Non-parametric and semi-parametric inference for a longitudinal multi-state model with an application to migraine research

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Aim of the project is the statistical analysis of data from prospective observational studies, in which patients write structured diaries over an extended amount of time, in order to examine triggers and influences on recurring pathological states.An example is the PAMINA study (Wöber et al., 2007, Zebenholzer et al., 2010, Salhofer et al., 2010, Salmal et al., 2011) where migraine patients wrote a daily diary for about 3 months containing information on potential migraine trigger factors and other influences.Such data can be described by recurrent multi-state models, where one has to use non-Markov processes.Aim of the PAMINA study was to identify relevant trigger factors, which are clearly associated with recurring pathological states (e.g. migraine headache).This includes also medical interventions, such as intake of acute medication, whose efficacy should also be examined.So far the PAMINA data have only been analyzed with relatively simple statistical methods, e.g. with Cox models using robust variance estimators (Wöber et al, 2007).The aim of this research project is to examine, how these questions can be answered better and more effectively with innovative statistical methods for multi-state models. Especially estimators of transition and sojourn probabilities as well as transition hazards shall be used.Here methods need to be implemented and, if necessary, extended, which do not rely on the common but strong Markov assumption, since the latter is hardly justified in general and especially for the PAMINA data.This strategy takes into account the dependency of the recurrent events on the event history. Confidence bands shall be used to quantify the uncertainty in the estimation of the time-dependent parameters (such as e.g. transition probabilities or intensities).The influence of time-dependent covariates (trigger factors) is considered by special procedures, which take into account the dependency between the observations and which are based on extensions of pseudo observations approaches still to be developed.