Competing risk bias to explain the inverse relationship between smoking and malignant melanoma

Caroline A. Thompson, Zuo-Feng Zhang, Onyebuchi A. Arah

The relationship between smoking and melanoma remains unclear. Among the different results is the paradoxical finding that smoking was shown to be inversely associated with the risk of malignant melanoma in some large cohort and case-control studies, even after control for suspected confounding variables. Smoking is a known risk factor for many non-communicable diseases, including coronary heart disease, stroke, as well as other malignancies; it has been shown to be positively associated with other types of skin cancer, and there remains no clear biologic explanation for a possible protective effect on malignant melanoma. In this paper, we propose a plausible mechanism of bias from smoking-related competing risks that may explain or contribute to the inverse association between smoking and melanoma as spurious. Using directed acyclic graphs for formalization and visualization of assumptions, and Monte Carlo simulation techniques, we demonstrate how published inverse associations might be compatible with selection bias resulting from uncontrolled or unmeasured common causes of competing outcomes of smoking-related diseases and malignant melanoma. We present results from various scenarios assuming a true null as well as a true positive association between smoking and malignant melanoma. Under a true null assumption, we find inverse associations due to the biasing mechanism to be compatible with published results in the literature, especially after the addition of unmeasured confounding variables. This study could be seen as offering a cautionary note in the interpretation of published smoking-melanoma findings.