Estimation for Non-Markov Multi-states Models

Multi-state models are powerful tools to understand and describe complex disease. Patients can move among a certain number of states defined by specific conditions of disease level often including death. Typically in these studies, the issues of interest include overall survival, effects of prognostic factors on disease progress and estimation of transition probabilities. Often multi-state models are employed under the Markov assumption, or it is assumed that the multi-state model can be described by a Markov renewal process. These assumptions are mainly made for mathematical convenience, since it is easier to estimate transition intensities and covariate effects. Moreover the transition probabilities can be computed. Obviously these assumptions could be rather unrealistic or too restrictive. The Markov assumption might not hold because there is association between transition times. In case a positive association is present, later transition will show higher rate if earlier...Show moreMulti-state models are powerful tools to understand and describe complex disease. Patients can move among a certain number of states defined by specific conditions of disease level often including death. Typically in these studies, the issues of interest include overall survival, effects of prognostic factors on disease progress and estimation of transition probabilities. Often multi-state models are employed under the Markov assumption, or it is assumed that the multi-state model can be described by a Markov renewal process. These assumptions are mainly made for mathematical convenience, since it is easier to estimate transition intensities and covariate effects. Moreover the transition probabilities can be computed. Obviously these assumptions could be rather unrealistic or too restrictive. The Markov assumption might not hold because there is association between transition times. In case a positive association is present, later transition will show higher rate if earlier transitions had taken place earlier. This implies a violation of the Markov assumption because the future depends not only on the present status but also on the past. In this thesis the Markov Renewal assumption is relaxed and two methods are proposed to deal with a violation of this assumption. The first method focus on the illness-death model, which is a 3-states model where only an intermediate event can occur before the main event of interest takes place. By relaxing the Markov renewal assumption, the proposed method models the correlation between transition times in the framework of Cox model. To obtain predictions for patients with a given history, formulas for prediction of transition probabilities are developed. For application purpose, some general functions for prediction are also developed in R and their use is illustrated through a set of data coming from a breast cancer trial. Relying on the frailty theory, the second approach proposed in this thesis models a forward-going sequential process in a framework of hidden Markov model. By extending the two-point mixture frailty model, frailties are modeled as hidden states which can have an impact on the transition rates and eventually be observed by the sojourn times and occurrence of events. Based on the likelihood construction an Expectation-Maximization algorithm was proposed.Show less

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Estimation for Non-Markov Multi-states Models