- tuan nguyen

# Vitamin D and calcium supplements and cancer risk: another interpretation

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The relationship between vitamin D and cancer is controversial.While there are data showing a beneficial effect of vitamin D on cancer risk reduction, there are also data showing no association. The only way to resolve the controversy is a randomized controlled trial (RCT). Well, Lappe and colleagues have conducted such a trial (1), but their results -- or their interpretation of results -- is, well, controversial. Here, I would like to offer another interpretation of data.

Lappe and colleagues did a 4-year RCT, in which 2303 postmenopausal women were randomly assigned into a treatment group (CaD; n = 1156) and a control group (n = 1147). The treatment was vitamin D3 (2000 IU/d) plus calcium (1500 mg/d). After 4 years of followup, they found that CaD reduced the risk of cancer by ~30% in a group who were already vitamin D replete. But they note concluded that in older women, a 4-year supplementation of vitamin D and calcium (CaD) did not significantly reduce the risk of all-type cancer! This conclusion appears to be based on the *P*-value of 0.06. Presumably, if *P* = 0.049, they would conclude that there was a significant effect.

It is well known that *P*-value is not an ideal metric of evidence, because being sensitive to sample size, it is subject to high sampling variation (2). In the current study, if the incidence of cancers *were* reduced by just 1 case in the CaD group or increased by just 1 case in the control group, the effect size would have achieved a statistical significance (i.e., *P *< 0.05)! I note that the authors' subgroup analysis revealed a statistically significant reduction in cancer risk induced by CaD supplementation. Thus, inference based on *P*-value, particularly at the threshold of 0.05, is not always consistent.

Let us consider that a more sensible question to ask is: given the data at hand, what is the chance that CaD supplementation reduces cancer incidence? This question can be addressed by a Bayesian analysis (3), which takes into account prior knowledge of the effect size and existing data. Under the assumption that all effect sizes (i.e., relative risks) are equally probable, then given the authors' data, our analysis shows that there is a 97% probability that CaD supplementation reduces cancer risk. Moreover, if a relative reduction of at least 5% is considered clinically relevant, then there is a 95% chance that the effect of CaD supplements on cancer risk is clinically relevant.

In a previous meta-analysis (4), CaD supplementation was associated with a relative risk of 0.97 (95% CI, 0.91 to 1.04). Combining this relative risk as a prior information with the existing data (1) yields a posterior relative risk of 0.96 (95% CI, 0.90 to 1.03). There is a 88% probability that CaD supplementation reduces cancer risk. These results are also consistent with the fact that serum levels of 25(OH)D were significantly inversely associated with cancer risk (1).

So, my interpretation of Lappe et al's data is that there is a high likelihood that CaD supplements have beneficial effect on cancer risk reduction, but the effect size is likely to be modest.

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(1) Lappe J, Watson P, Travers-Gustafson D, Recker R, Garland C, Gorham E, Baggerly K, McDonnell SL. Effect of vitamin D and calcium supplementation on cancer incidence in older women: a randomized clinical trial. JAMA 2017.

(2) Halsey LG, Curran-Everett D, Vowler SL, Drummond GB. The fickle P value generates irreproducible results. Nat Methods 2015; 12:179-85.

(3) Greenland S. Bayesian perspectives for epidemiological research: I. Foundations and basic methods. International Journal of Epidemiology 2006;35:765–775.

(4) Bjelakovic G, Gluud LL, Nikolova D, Whitfield K, Krstic G, Wetterslev J, Gluud C. Vitamin D supplementation for prevention of cancer in adults. Cochrane Database Syst Rev. 2014 Jun 23;(6):CD007469.