ORIGINAL RESEARCH article
Front. Public Health
Sec. Occupational Health and Safety
Volume 13 - 2025 | doi: 10.3389/fpubh.2025.1628965
This article is part of the Research TopicMineral Particles and Fibers and Human Health Risks: State-of-the-Art in Characterization, Analysis, Tissue Analytics, Exposure Thresholds for Risk, Epidemiology, and Risk Assessment for Science-Based Regulation and Disease Prevention and Implications for Occupational Health and SafetyView all 20 articles
Using Threshold Cox Models to Estimate Change Points in Exposure-Response Relationships in an Occupational Epidemiological Study of Respirable Crystalline Silica and Silicosis Risk
Provisionally accepted
- University of Massachusetts Amherst, Amherst, United States
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In occupational epidemiology, accurately quantifying exposure-response relationships is crucial.We introduce a threshold Cox model that includes a change point term to identify the optimal threshold. To address bias associated with maximum likelihood estimation under monotone likelihood, we employ Firth's penalized likelihood approach. The methodology was validated using simulation studies that evaluated model performance under various censoring rates and sample sizes. We applied our threshold Cox model to data from an occupational epidemiological study of respirable crystalline silica (RCS) exposure and risk of silicosis (defined as ILO category 1/0 or higher). To improve the condition of the data for analysis using Cox regression, which is sensitive to small proportions of events, we included all silicosis cases, and for each case we densitysampled four non-cases from workers in the same production areas (mostly materials preparation).Thresholds for (a) cumulative RCS exposure and (b) average RCS exposure intensity over 2yr and 5yr silicosis risk were identified as 4.038 mg/m 3 -years (95 CI: 3.109 -4.967), and 0.264 mg/m 3 (95 CI: 0.207 -0.321), and 0.324 mg/m 3 (95 CI: 0.263 -0.385), respectively. These quantified exposure thresholds may be useful in verifying that occupational exposure limits are protective against silicosis and for quantitative risk assessment. This methodology also could be applied to other exposure-disease relationships to identify and quantify possible exposure thresholds.
Keywords: Change point, Exposure-response relationship, Firth's penalized likelihood, Heavy censoring, occupational epidemiology, Respirable crystalline silica, Silicosis, threshold Cox model
Received: 15 May 2025; Accepted: 13 Aug 2025.
Copyright: © 2025 Wu, Mundt and Qian. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Jing Qian, University of Massachusetts Amherst, Amherst, United States
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