A Semiparametric Bayesian Method for Instrumental Variable Analysis with Partly Interval-Censored Time-to-Event Outcome

TL;DR

This work tackles causal effect estimation with an endogenous covariate when unobserved confounding and measurement error are present for partly interval-censored time-to-event outcomes. It introduces DPMIV, a semiparametric Bayesian instrumental variable method that uses a two-stage Dirichlet process mixture to flexibly model error distributions in both the exposure and the survival outcome, extending prior work to handle interval censoring. A tailored MCMC algorithm (Neal's algorithm 8) accommodates non-conjugate DP priors and censored data, enabling data-driven clustering and robust inference for the causal parameter $\\beta_1$. Simulations demonstrate robustness to non-normal errors and superior performance over parametric PBIV, and a UK Biobank analysis shows negative causal effects of systolic blood pressure on time-to-CVD from DM onset, with evidence of heterogeneity in the error structure. The work provides practical tools (R package) and highlights the importance of accounting for censoring and error heterogeneity in causal IV analyses.

Abstract

This paper develops a semiparametric Bayesian instrumental variable analysis method for estimating the causal effect of an endogenous variable when dealing with unobserved confounders and measurement errors with partly interval-censored time-to-event data, where event times are observed exactly for some subjects but left-censored, right-censored, or interval-censored for others. Our method is based on a two-stage Dirichlet process mixture instrumental variable (DPMIV) model which simultaneously models the first-stage random error term for the exposure variable and the second-stage random error term for the time-to-event outcome using a bivariate Gaussian mixture of the Dirichlet process (DPM) model. The DPM model can be broadly understood as a mixture model with an unspecified number of Gaussian components, which relaxes the normal error assumptions and allows the number of mixture components to be determined by the data. We develop an MCMC algorithm for the DPMIV model tailored for partly interval-censored data and conduct extensive simulations to assess the performance of our DPMIV method in comparison with some competing methods. Our simulations revealed that our proposed method is robust under different error distributions and can have superior performance over its parametric counterpart under various scenarios. We further demonstrate the effectiveness of our approach on an UK Biobank data to investigate the causal effect of systolic blood pressure on time-to-development of cardiovascular disease from the onset of diabetes mellitus.

Figures (3)

• Figure 1: Directed acyclic graph of instrumental variable analysis. $Y$ is the outcome, $W$ the unobserved endogenous covariate, $X$ the noisy surrogate, $G$ is the instrument, $Z$ the observed confounders, and $U$ the unobserved confounders. $\beta_1$ represents the causal effect of $W$ on $Y$. A line with no arrow indicates association and an arrow indicates a causal relationship in a specific direction.
• Figure 2: True and estimated error distributions of the DPMIV method for simulation studies under different sample sizes.
• Figure 3: Log-density contour plots of random errors ($\xi_1$, $\xi_2$) and trace plots of causal effect $\beta_1$ of the Dirichlet process mixture model for the UKB data.