  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 three different estimators, including a
doubly-robust estimator, for the SF-ACE. We implement our methodology for data
from two large cohorts to study the heterogeneity in the causal effect of
smoking on colorectal cancer with respect to MSI subtypes.
