Model Selection Approach Suggests Causal Association between 25-Hydroxyvitamin D and Colorectal Cancer

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Abstract
Vitamin D deficiency has been associated with increased risk of colorectal cancer (CRC), but causal relationship has not yet been confirmed. We investigate the direction of causation between vitamin D and CRC by extending the conventional approaches to allow pleiotropic relationships and by explicitly modelling unmeasured confounders. Plasma 25-hydroxyvitamin D (25-OHD), genetic variants associated with 25-OHD and CRC, and other relevant information was available for 2645 individuals (1057 CRC cases and 1588 controls) and included in the model. We investigate whether 25-OHD is likely to be causally associated with CRC, or vice versa, by selecting the best modelling hypothesis according to Bayesian predictive scores. We examine consistency for a range of prior assumptions. Model comparison showed preference for the causal association between low 25-OHD and CRC over the reverse causal hypothesis. This was confirmed for posterior mean deviances obtained for both models (11.5 natural log units in favour of the causal model), and also for deviance information criteria (DIC) computed for a range of prior distributions. Overall, models ignoring hidden confounding or pleiotropy had significantly poorer DIC scores. Results suggest causal association between 25-OHD and colorectal cancer, and support the need for randomised clinical trials for further confirmations.

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