Abstract
Studies have shown that the effect an exposure may have on a disease can vary for different subtypes of the same disease. However, existing approaches to estimate and compare these effects largely overlook causality. In this paper, we study the effect smoking may have on having colorectal cancer subtypes defined by a trait known as microsatellite instability (MSI). We use principal stratification to propose an alternative causal estimand, the Subtype-Free Average Causal Effect (SF-ACE). The SF-ACE is the causal effect of the exposure among those who would be free from other disease subtypes under any exposure level. We study non-parametric identification of the SF-ACE and discuss different monotonicity assumptions, which are more nuanced than in the standard setting. As is often the case with principal stratum effects, the assumptions underlying the identification of the SF-ACE from the data are untestable and can be too strong. Therefore, we also develop sensitivity analysis methods that relax these assumptions. We present 3 different estimators, including a doubly robust estimator, for the SF-ACE. We implement our methodology for data from 2 large cohorts to study the heterogeneity in the causal effect of smoking on colorectal cancer with respect to MSI subtypes.