An Augmented Likelihood Approach for the Discrete Proportional Hazards Model Using Auxiliary and Validated Outcome Data -- with Application to the HCHS/SOL Study

TL;DR

This paper introduces an augmented likelihood method that combines error-prone and gold standard data to improve the analysis of disease risk in large epidemiologic studies, demonstrated through application to diabetes risk and dietary data.

Contribution

It develops a novel augmented likelihood approach for discrete proportional hazards models that efficiently incorporates auxiliary and validated outcome data, extending to complex survey designs.

Findings

Improved statistical efficiency over standard methods.

Effective application to the HCHS/SOL study data.

Demonstrated utility in addressing covariate measurement error.

Abstract

In large epidemiologic studies, it is typical for an inexpensive, non-invasive procedure to be used to record disease status during regular follow-up visits, with less frequent assessment by a gold standard test. Inexpensive outcome measures like self-reported disease status are practical to obtain, but can be error-prone. Association analysis reliant on error-prone outcomes may lead to biased results; however, restricting analyses to only data from the less frequently observed error-free outcome could be inefficient. We have developed an augmented likelihood that incorporates data from both error-prone outcomes and a gold standard assessment. We conduct a numerical study to show how we can improve statistical efficiency by using the proposed method over standard approaches for interval-censored survival data that do not leverage auxiliary data. We extend this method for the complex survey design setting so that it can be applied in our motivating data example. Our method is applied to data from the Hispanic Community Health Study/Study of Latinos to assess the association between energy and protein intake and the risk of incident diabetes. In our application, we demonstrate how our method can be used in combination with regression calibration to additionally address the covariate measurement error in self-reported diet.