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

该项目的目的是对来自前瞻性观察性研究的数据进行统计分析，在这些研究中，患者在较长的时间内撰写结构化日记，以检查对复发性病理状态的触发因素和影响。2007年，Zebenholzer等人， 2010年，Salhofer等人， 2010年，Salmal等人，2011），其中偏头痛患者每天写日记约3个月，包含潜在的偏头痛触发因素和其他影响的信息。这些数据可以通过经常性多状态模型来描述，其中必须使用非马尔可夫过程。PAMINA研究的目的是识别相关的触发因素，这显然与反复出现的病理状态有关（例如偏头痛）。这也包括医学干预，例如摄入急性药物，到目前为止，PAMINA数据仅用相对简单的统计方法进行分析，例如使用稳健方差估计的考克斯模型（Wöber et al，2007）.本研究项目的目的是研究如何用多状态模型的创新统计方法更好、更有效地回答这些问题。特别是转移和逗留概率以及转移风险的估计值。这里需要实施方法，必要时进行扩展，这些方法不依赖于常见但很强的马尔可夫假设，因为后者通常很难证明合理，特别是对于PAMINA数据。该策略考虑了事件历史上重复事件的依赖性。置信带应用于量化时间相关参数（例如转移概率或强度）估计中的不确定性。时间相关协变量（触发因子）的影响由特殊程序考虑，该程序考虑了观测值之间的相关性，并基于尚待开发的伪观测方法的扩展。

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.