Analysis of Multi-State Models with Mismeasured Covariates or Misclassified States
Multi-state models provide a useful framework for estimating the rate of transitions between defined disease states and understanding the influence of covariates on transitions in studies of the disease progression. Statistical analysis of data from studies of disease progression often involves a number of challenges. A particular challenge is that the classification of the disease state may be subject to error. Another common problem is that there are many sources of heterogeneity in the data in which situation the assumption of time-homogeneous for common Markov models is not valid. In addition, it is common for discrete covariates subject to misclassification and the panel data collected from disease progression studies is time-dependence in the covariates. In Chapter 2, the progressive multi-state model with misclassification is developed to simultaneously estimate transition rates and account for potential misclassification. The performance of the maximum likelihood and pairwise likelihood estimators is evaluated by simulation studies. The proposed progressive model is illustrated on coronary allograft vasculopathy data, in which the diagnosis based on the coronary angiography is subject to error. In Chapter 3, hidden mover-stayer models are proposed to provide a solution to a type of heterogeneity where the population consists of both movers and stayers in the presence of misclassification. The likelihood inference procedure based on the EM algorithm is developed for the proposed model. The performance of the likelihood method is investigated through simulation studies. The proposed method is applied to the Waterloo Smoking Prevention Project. In Chapter 4, we propose estimation procedures for Markov models with binary covariates subject to misclassification. We show that the model is not identifiable under covariate misclassification. Consequently, we develop likelihood inference methods based on known reclassification probabilities and the main/validation study design. Simulation studies are conducted to investigate the performance of proposed methods and the consequence of the naive analysis which ignores the misclassification. In Chapter 5, we consider two-state Markov models where time-dependent surrogate covariates are available. We exploit both functional and structural inference methods to reduce or remove bias effects induced from covariate measurement error. The performance of proposed methods is investigated based on simulation studies.