Multiple imputation (MI) is a commonly used approach to impute missing data. This thesis studies missing covariates in recurrent event data, and discusses ways to include the survival outcomes in the imputation model. Some MI methods under consideration are the event indicator D combined with, respectively, the right-censored event times T, the logarithm of T and the cumulative baseline hazard H0(T). After imputation, we can then proceed to the complete data analysis. The Cox proportional hazards (PH) model and the PWP model are chosen as the analysis models, and the coefficient estimates are of substantive interest. A Monte Carlo simulation study is conducted to compare different MI methods, the relative bias and mean square error will be used in the evaluation process. Furthermore, an empirical study based on cardiovascular disease event data which contains missing values will be conducted. Overall, the results show that MI based on the Nelson-Aalen estimate of H0(T) is preferred in most circumstances.

V této práci se zabýváme metodami pro regresní analýzu výskytu opako- vaných událostí, při které je třeba se vypořádat se závislostí čas· do události v rámci jednoho subjektu. V první části práce se zabýváme možným rozšířením Coxova modelu proporcionálního rizika, který se využívá při analýze cenzoro- vaných dat, pro analýzu výskytu opakovaných událostí. Hlavní část práce je věnována odhadu parametr· v marginálních modelech a jejich asymptotickým vlastnostem. Následně se zabýváme i odhadem parametr· v marginálních mo- delech pro mnohorozměrná cenzorovaná data. Vhodnost použití marginálních model· je zkoumána pomocí simulací. 1

Incomplete data often arise in the study of life history processes. Examples include missing responses, missing covariates, and unobservable latent processes in addition to right censoring. This thesis is on the development of statistical models and methods to address these problems as they arise in oncology and chronic disease. Methods of estimation and inference in parametric, weakly parametric and semiparametric settings are investigated. Studies of chronic diseases routinely sample individuals subject to conditions on an event time of interest. In epidemiology, for example, prevalent cohort studies aiming to evaluate risk factors for survival following onset of dementia require subjects to have survived to the point of screening. In clinical trials designed to assess the effect of experimental cancer treatments on survival, patients are required to survive from the time of cancer diagnosis to recruitment. Such conditions yield samples featuring left-truncated event time distributions. Incomplete covariate data often arise in such settings, but standard methods do not deal with the fact that the covariate distribution is also affected by left truncation. We develop a likelihood and algorithm for estimation for dealing with incomplete covariate data in such settings. An expectation-maximization algorithm deals with the left truncation by using the covariate distribution conditional on the selection criterion. An extension to deal with sub-group analyses in clinical trials is described for the case in which the stratification variable is incompletely observed. In studies of affective disorder, individuals are often observed to experience recurrent symptomatic exacerbations of symptoms warranting hospitalization. Interest lies in modeling the occurrence of such exacerbations over time and identifying associated risk factors to better understand the disease process. In some patients, recurrent exacerbations are temporally clustered following disease onset, but cease to occur after a period of time. We develop a dynamic mover-stayer model in which a canonical binary variable associated with each event indicates whether the underlying disease has resolved. An individual whose disease process has not resolved will experience events following a standard point process model governed by a latent intensity. If and when the disease process resolves, the complete data intensity becomes zero and no further events will arise. An expectation-maximization algorithm is developed for parametric and semiparametric model fitting based on a discrete time dynamic mover-stayer model and a latent intensity-based model of the underlying point process. The method is applied to a motivating dataset from a cohort of individuals with affective disorder experiencing recurrent hospitalization for their mental health disorder. Interval-censored recurrent event data arise when the event of interest is not readily observed but the cumulative event count can be recorded at periodic assessment times. Extensions on model fitting techniques for the dynamic mover-stayer model are discussed and incorporate interval censoring. The likelihood and algorithm for estimation are developed for piecewise constant baseline rate functions and are shown to yield estimators with small empirical bias in simulation studies. Data on the cumulative number of damaged joints in patients with psoriatic arthritis are analysed to provide an illustrative application.