Non-linearity in cancer dose-response: The role of exposure duration

Abstract

Context

An apparent deviation from nonlinearity in cancer dose-response was reported for various carcinogens. In particular, some studies hypothesized that in mesothelioma, the exposure-response relationship can be modelled as a power function with exponent from 0.6 to 1. However, various factors can affect the shape of the dose-response, producing the apparent supralinear trend.

Objective

To develop a mathematical model that would demonstrate a relationship of mesothelioma lifetime risk and exposure duration, with various assumptions about a hazard rate function.

Methods

Two different hazard rate functions – the Peto model and the two-stage clonal expansion (TSCE) model – were considered. The analytical formulas for lifetime risk were developed, with and without a lifetable correction. Standard calculus methods were applied to test the shape of the lifetime risk curve.

Results

For both Peto and TSCE models, it was shown that mesothelioma lifetime risk changes supralinearly with duration; the exponent of the power function was ranging from 0.68 to 0.89. However, the dose-response curve by cumulative exposure is close to linearity and is linear if the exposure duration would be constant. The model has been tested for chrysotile asbestos cohorts, with a good agreement demonstrated with published mesothelioma excess mortality (R=0.88, p<0.0041).

Conclusion

For mesothelioma, the observed deviation from linearity in the dose-response relationship can be potentially explained by the impact of a change in the duration of exposure. In a meta-analysis, this deviation can be eliminated by standardizing the mortality data for various cohorts by duration of exposure.

Short Abstract

An apparent deviation from nonlinearity in cancer dose-response was reported for various carcinogens. We applied two different hazard rate equations – the Peto model and the two-stage clonal expansion (TSCE) model – to pleural mesothelioma mortality. The analytical formulas for lifetime risk were developed. For both the Peto and TSCE models, it was shown that mesothelioma lifetime risk changes supralinearly with duration. However, the dose-response curve for cumulative exposure is close to linearity.