Dealing with death when studying disease or physiological marker: the stochastic system approach to causality

TL;DR

This paper introduces a stochastic system approach to causality that explicitly accounts for death as a random horizon, enabling more accurate analysis of factors affecting health outcomes in the presence of mortality.

Contribution

It develops a framework unifying different types of processes and observation schemes to incorporate death into causal analysis using stochastic systems.

Findings

The approach accounts for death as a random horizon in causal models.

It unifies counting and quantitative processes under a common framework.

An application estimates blood pressure effects on cognitive ability in the elderly.

Abstract

The stochastic system approach to causality is applied to situations where the risk of death is not negligible. This approach grounds causality on physical laws, distinguishes system and observation and represents the system by multivariate stochastic processes. The particular role of death is highlighted, and it is shown that local influences must be defined on the random horizon of time of death. We particularly study the problem of estimating the effect of a factor $V$ on a process of interest $Y$, taking death into account. We unify the cases where $Y$ is a counting process (describing an event) and the case where $Y$ is quantitative; we examine the case of observations in continuous and discrete time and we give a typology of cases where the mechanism leading to incomplete data can be ignored. Finally, we give an example of a situation where we are interested in estimating the effect of a factor (blood pressure) on cognitive ability in elderly.