Chronic Disease Prevention Research Methods and Their Reliability, With Illustrations From the Women’s Health Initiative

How to control for unmeasured confounding in an observational time-to-event study with exposure incidence information: the treatment choice Cox model

In an observational study of the effect of a treatment on a time-to-event outcome, a major problem is accounting for confounding because of unknown or unmeasured factors. We propose including covariates in a Cox model that can partially account for an unknown time-independent frailty that is related to starting or stopping treatment as well as the outcome of interest. These covariates capture the times at which treatment is started or stopped and so are called treatment choice (TC) covariates. Three such models are developed: first, an interval TC model that assumes a very general form for the respective hazard functions of starting treatment, stopping treatment, and the outcome of interest and second, a parametric TC model that assumes that the log hazard functions for starting treatment, stopping treatment, and the outcome event include frailty as an additive term. Finally, a hybrid TC model that combines attributes from the parametric and interval TC models. As compared with an ordinary Cox model, the TC models are shown to substantially reduce the bias of the estimated hazard ratio for treatment when data are simulated from a realistic Cox model with residual confounding due to the unobserved frailty. The simulations also indicate that the bias decreases or levels off as the sample size increases. A TC model is illustrated by analyzing the Women's Health Initiative Observational Study of hormone replacement for post-menopausal women. Published 2017. This article has been contributed to by US Government employees and their work is in the public domain in the USA.

Measurement error in two-stage analyses, with application to air pollution epidemiology

Public health researchers often estimate health effects of exposures (e.g., pollution, diet, lifestyle) that cannot be directly measured for study subjects. A common strategy in environmental epidemiology is to use a first-stage (exposure) model to estimate the exposure based on covariates and/or spatio-temporal proximity and to use predictions from the exposure model as the covariate of interest in the second-stage (health) model. This induces a complex form of measurement error. We propose an analytical framework and methodology that is robust to misspecification of the first-stage model and provides valid inference for the second-stage model parameter of interest. We decompose the measurement error into components analogous to classical and Berkson error and characterize properties of the estimator in the second-stage model if the first-stage model predictions are plugged in without correction. Specifically, we derive conditions for compatibility between the first- and second-stage models that guarantee consistency (and have direct and important real-world design implications), and we derive an asymptotic estimate of finite-sample bias when the compatibility conditions are satisfied. We propose a methodology that (1) corrects for finite-sample bias and (2) correctly estimates standard errors. We demonstrate the utility of our methodology in simulations and an example from air pollution epidemiology.