Using threshold Cox models to estimate change points in exposure-response relationships in an occupational...

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 density-sampled 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 2 years and 5 years were identified as 4.038 mg/m³-years (95 CI: 3.109-4.967), and 0.264 mg/m³ (95 CI: 0.207-0.321), and 0.324 mg/m³ (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.