Longitudinal perspectives on event history analysis

Exchangeable Markov multi-state survival processes

We consider exchangeable Markov multi-state survival processes, which are temporal processes taking values over a state-space S , with at least one absorbing failure state b ∈ S that satisfy the natural invariance properties of exchangeability and consistency under subsampling. The set of processes contains many well-known examples from health and epidemiology including survival, illness-death, competing risk, and comorbidity processes. Here, an extension leads to recurrent event processes. We characterize exchangeable Markov multi-state survival processes in both discrete and continuous time. Statistical considerations impose natural constraints on the space of models appropriate for applied work. In particular, we describe constraints arising from the notion of composable systems. We end with an application to irregularly sampled and potentially censored multi-state survival data, developing a Markov chain Monte Carlo algorithm for inference.

Survival models and health sequences

Survival studies often generate not only a survival time for each patient but also a sequence of health measurements at annual or semi-annual check-ups while the patient remains alive. Such a sequence of random length accompanied by a survival time is called a survival process. Robust health is ordinarily associated with longer survival, so the two parts of a survival process cannot be assumed independent. This paper is concerned with a general technique-reverse alignment-for constructing statistical models for survival processes, here termed revival models. A revival model is a regression model in the sense that it incorporates covariate and treatment effects into both the distribution of survival times and the joint distribution of health outcomes. The revival model also determines a conditional survival distribution given the observed history, which describes how the subsequent survival distribution is determined by the observed progression of health outcomes.

Armitage lecture 2010: Understanding treatment effects: the value of integrating longitudinal data and survival analysis

There is a single-minded focus on events in survival analysis, and we often ignore longitudinal data that are collected together with the event data. This is due to a lack of methodology but also a result of the artificial distinction between survival and longitudinal data analyses. Understanding the dynamics of such processes is important but has been hampered by a lack of appreciation of the difference between confirmatory and exploratory causal inferences. The latter represents an attempt at elucidating mechanisms by applying mediation analysis to statistical data and will usually be of a more tentative character than a confirmatory analysis. The concept of local independence and the associated graphs are useful. This is related to Granger causality, an important method from econometrics that is generally undervalued by statisticians. This causality concept is different from the counterfactual one since it lacks lacks the intervention aspect. The notion that one can intervene at will in naturally occurring processes, which seems to underly much of modern causal inference, is problematic when studying mediation and mechanisms. It is natural to assume a stochastic process point of view when analyzing dynamic relationships. We present some examples to illustrate this. It is not clear how survival analysis must be developed to handle the complex life-history data that are increasingly being collected today. We give some suggestions.