On the global identifiability of logistic regression models with misclassified outcomes

TL;DR

This paper establishes necessary and sufficient conditions for the global identifiability of logistic regression models with misclassified outcomes, providing practical tools for biomedical research involving electronic health records.

Contribution

It introduces a novel submodel analysis approach and applies differential equation techniques to determine global identifiability in misclassified logistic models, especially with discrete covariates.

Findings

Derived clear conditions for model identifiability

Proposed hypothesis testing methods for non-identifiable models

Applicable to common biomedical data scenarios

Abstract

In the last decade, the secondary use of large data from health systems, such as electronic health records, has demonstrated great promise in advancing biomedical discoveries and improving clinical decision making. However, there is an increasing concern about biases in association studies caused by misclassification in the binary outcomes derived from electronic health records. We revisit the classical logistic regression model with misclassified outcomes. Despite that local identification conditions in some related settings have been previously established, the global identification of such models remains largely unknown and is an important question yet to be answered. We derive necessary and sufficient conditions for global identifiability of logistic regression models with misclassified outcomes, using a novel approach termed as the submodel analysis, and a technique adapted from the Picard-Lindel\"{o}f existence theorem in ordinary differential equations. In particular, our results are applicable to logistic models with discrete covariates, which is a common situation in biomedical studies, The conditions are easy to verify in practice. In addition to model identifiability, we propose a hypothesis testing procedure for regression coefficients in the misclassified logistic regression model when the model is not identifiable under the null.