Estimating Associations Between Cumulative Exposure and Health via Generalized Distributed Lag Non-Linear Models using Penalized Splines

TL;DR

This paper introduces a generalized penalized spline-based ACE-DLNM framework for estimating associations between cumulative exposure and health outcomes, applicable to various response types and scalable to large datasets.

Contribution

It extends existing ACE-DLNM models by incorporating penalized splines and efficient estimation techniques, enabling analysis of diverse response types and large-scale data.

Findings

The proposed method provides more stable inferences than fixed-exposure models.

Simulation studies demonstrate improved performance and computational efficiency.

Application to Canadian pollution data shows practical advantages and interpretability.

Abstract

Quantifying associations between short-term exposure to ambient air pollution and health outcomes is an important public health priority. Many studies have investigated the association considering delayed effects within the past few days. Adaptive cumulative exposure distributed lag non-linear models (ACE-DLNMs) quantify associations between health outcomes and cumulative exposure that is specified in a data-adaptive way. While the ACE-DLNM framework is highly interpretable, it is limited to continuous outcomes and does not scale well to large datasets. Motivated by a large analysis of daily pollution and respiratory hospitalization counts in Canada between 2001 and 2018, we propose a generalized ACE-DLNM incorporating penalized splines, improving upon existing ACE-DLNM methods to accommodate general response types. We then develop a computationally efficient estimation strategy based on profile likelihood and Laplace approximate marginal likelihood with Newton-type methods. We demonstrate the performance and practical advantages of the proposed method through simulations. In application to the motivating analysis, the proposed method yields more stable inferences compared to generalized additive models with fixed exposures, while retaining interpretability.