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研究的数据进行统计分析，在前瞻性观察研究中，患者在较长时间内写结构化日记，以检查触发因素和对复发病理状态的影响。例如Pamina研究(Wöber等人，2007，Zebenholzer等人，2010，Salhofer等人，2010，Salmal等人，2011)，其中偏头痛患者每天写日记约3个月，其中包含关于潜在偏头痛触发因素和其他影响的信息。这样的数据可以用循环多状态模型来描述，Pamina研究的目的是确定相关的触发因素，这些因素明显与复发的病理状态(例如偏头痛)相关。这也包括医疗干预，如急性药物的摄入，其有效性也应该被检查。到目前为止，Pamina的数据只用相对简单的统计方法进行分析，例如使用使用稳健方差估计的Cox模型(Wöber等人，2007)。本研究项目的目的是检查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。尤其需要使用转移概率和逗留概率的估计器，以及转移风险的估计器。这些方法需要实施，如果必要的话，还需要扩展，这些方法不依赖于常见的但强的马尔可夫假设，因为后者在一般情况下几乎是不合理的，特别是对于Pamina数据。该策略考虑了重复事件对事件历史的依赖性。应使用置信带来量化与时间相关的参数(例如转移概率或强度)的估计的不确定性。特殊程序考虑了与时间相关的协变量(触发因素)的影响，该程序考虑了观测之间的相关性，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.