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，患者在很长一段时间内写下结构化的日记，以检查反复出现的病理状态的触发因素和影响。一个例子是PAMINA研究（Wöber等人，2007，Zebenholzer等人，2010，Salhofer等人，2010，Salmal等人，2011），偏头痛患者写了大约3个月的每日日记，其中包含偏头痛潜在触发因素和其他影响因素的信息。这样的数据可以用循环多状态模型来描述，其中必须使用非马尔可夫过程。PAMINA研究的目的是确定与复发性病理状态（如偏头痛）明显相关的相关触发因素。这也包括医疗干预，如服用急性药物，其效果也应加以检查。到目前为止，PAMINA数据只使用相对简单的统计方法进行了分析，例如使用稳健方差估计的Cox模型（Wöber et al ., 2007）。本研究项目的目的是研究如何用创新的多状态模型统计方法更好、更有效地回答这些问题。特别是过渡概率和逗留概率的估计，以及过渡风险的估计。这里的方法需要实现，如有必要，扩展，不依赖于常见但强马尔可夫假设，因为后者很难证明一般，特别是对于PAMINA数据。该策略考虑了循环事件对事件历史的依赖性。置信带应使用用于量化估计时变参数（如转移概率或强度）的不确定性。时间相关协变量（触发因素）的影响是通过特殊程序来考虑的，这些程序考虑了观测值之间的依赖性，并基于仍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.