Studies On Several Issues For Recurrent Events With Their Longitudinal Measurements

Recurrent events and their longitudinal measurements frequently arise in medical follow-up and observational studies,and they have become one of the research hotspots in the field of biostatistics.Many methods have been developed to deal with recurrent events and their longitudinal measurements in the literature.Some included marginal modeling of recurrent events and longitudinal measurements respectively,and shared frailty modeling for both recurrent events and longitudinal measurements.Others involved joint modeling between recurrent events,terminal events,and longitudinal measurements.This dissertation investigates recurrent events and their longitudinal measurements in terms of missing data issues and quantile regression modeling.Chapter 1 mainly introduces the research status of the statistical model and reviews the latest research results about the missing data issues and the quantile regression modeling related to the recurrent events,longitudinal measurements and terminal events in the recurrent process,and outlines the research contents and innovational points of this dissertation.In practice,event times are always observed,but the event categories may be missing at random.In Chapter 2,we propose parametric and nonparametric estimators for both the propensity score of missing probability and the conditional expectation of missing categories respectively,and then construct two double robust counting processes,namely parametrically augmented inverse probability weighting counting process and nonparametrically augmented inverse probability weighting counting process,to impute the missing counting process.By modeling the multivariate recurrent events with semiparametric proportional rate models,we derive estimators for unknown parameters and baseline mean functions and prove that they are consistent and asymptotically normal.Furthermore,a formal lack-of-fit test is proposed to assess the adequacy of the models.Simulation studies show that the proposed methods outperform that in Schaubel and Cai(2006b)and Lin at el(2021),and finally the proposed methods are applied to a real data.In Chapter 3,we consider semiparametric additive rate models to model the multivariate recurrent events with event categories missing at random.We propose three estimatable counting processes,namely inverse probability weighting counting process,augmented inverse probability weighting counting process,and estimating equation projection counting process,to impute the missing counting processes,we obtain estimators for both the unknown parameters and the baseline mean functions in the additive rate models,and prove the consistency and asymptotical normality of the proposed estimators.A large set of simulation studies demonstrate the proposed methods are robust.We apply the proposed methods to a real data and derive better conclusions than that in Ye at al(2015)and Lin at el(2021).When longitudinal measurement response variable depends on the observation time which is related to a counting process,and furthermore is associated with a terminal event.In Chapter 4,we propose a marginal conditional quantile regression method to model longitudinal data.By constructing a non-smooth estimation equation weighted by inverse probability,the estimation is obtained by the iterative algorithm.Using the empirical process theory,namely the uniform law of large number and the stochastic equicontinuity,it is proved that the estimation has consistency and asymptotic normality.Simulation studies show that the proposed method performs well.The conclusions and some outlook of the dissertation are placed in Chapter 5.