Analysis of time-to-event data with multi-state models and causal inference methods

Analyses of disease-free survival data for certain cancer types indicate that cohorts of patients treated for cancer consist of individuals who are susceptible to experience cancer related events and individuals who are cured. Cured individuals do not experience any cancer related event, and eventually die due to other causes. Individuals who are not cured may die after experiencing cancer recurrence or without experiencing any recurrence. Cure status is a partially latent variable and is only known if a disease related event, cancer recurrence or cancer death, is observed. Causes of some observed deaths may be masked. To model disease progression events, which are cancer recurrence and cancer death, we consider a multi-state model including partially latent cured and not cured states. We describe our modeling approach and discuss an inference method incorporating masked causes of deaths. Our method allows us to identify factors associated with the risk of experiencing a disease related event and with timing of disease events after the treatment of cancer. It is of interest to make inference on direct exposure effects on time-to-event outcomes in many studies. Traditional survival analysis methods may not reveal direct exposure effects on time-to-event outcomes when there are indirect exposure effects through intermediate variables which are confounded by some unmeasured factors. We propose a mediation analysis method to make inference about direct exposure effects on time-to-event outcomes under additive hazards model using estimating equations methodology. We examine properties of the proposed method and compare them with traditional survival analysis methods and the existing two-stage mediation analysis method which uses additive hazards model. The results show that our method provides valid inference about controlled direct exposure effects on time-to-event outcomes by successfully removing indirect effects through intermediate variables. It is robust against measured and unmeasured confounding of indirect effects.