On 2017 Apr 07, Harri Hemila commented:

Statistical problems in the vitamin D review by Martineau et al.

In their abstract, Martineau et al. state that "Vitamin D supplementation reduced the risk of acute respiratory tract infection among all participants (adjusted odds ratio 0.88 ...".

The odds ratio [OR] is often used as an approximation for the risk ratio [RR]. Martineau's abstract suggests that vitamin D might reduce the risk of respiratory infections by 12%. However, when the incidence of events is high, then OR can be highly misleading as it exaggerates the size of the effect, see eg. Viera AJ, 2008, Knol MJ, 2012, Katz KA, 2006, and Holcomb WL Jr, 2001 .

Acute respiratory infections are not rare. In Figure 2 of the Martineau et al. meta-analysis, only 2 of the 24 trials had event rates less than 20% in both groups. I reproduced their Figure 2 using the random effects Mantel-Haenszel approach and calculated OR=0.82 (95% CI 0.72 to 0.95) for the 24 trials. The minor discrepancy with their published OR (i.e. OR=0.80) in Figure 2 is explained by adjustments. The Figure 2 data gives RR=0.92 (95% CI 0.87 to 0.98). Thus, the OR suggests that the incidence of respiratory infections might be reduced by 18%, but the RR shows that 8% reduction is the valid estimate. Thus, OR exaggerates the effect of vitamin D by over two times.

Further statistical problems are described at the BMJ pages: http://www.bmj.com/content/356/bmj.i6583/rr-3 and http://www.bmj.com/content/356/bmj.i6583/rr-8 and in some other BMJ rapid responses.

On 2017 Apr 07, Harri Hemila commented:

Statistical problems in the vitamin D review by Martineau et al.

In their abstract, Martineau et al. state that "Vitamin D supplementation reduced the risk of acute respiratory tract infection among all participants (adjusted odds ratio 0.88 ...".

The odds ratio [OR] is often used as an approximation for the risk ratio [RR]. Martineau's abstract suggests that vitamin D might reduce the risk of respiratory infections by 12%. However, when the incidence of events is high, then OR can be highly misleading as it exaggerates the size of the effect, see eg. Viera AJ, 2008, Knol MJ, 2012, Katz KA, 2006, and Holcomb WL Jr, 2001 .

Acute respiratory infections are not rare. In Figure 2 of the Martineau et al. meta-analysis, only 2 of the 24 trials had event rates less than 20% in both groups. I reproduced their Figure 2 using the random effects Mantel-Haenszel approach and calculated OR=0.82 (95% CI 0.72 to 0.95) for the 24 trials. The minor discrepancy with their published OR (i.e. OR=0.80) in Figure 2 is explained by adjustments. The Figure 2 data gives RR=0.92 (95% CI 0.87 to 0.98). Thus, the OR suggests that the incidence of respiratory infections might be reduced by 18%, but the RR shows that 8% reduction is the valid estimate. Thus, OR exaggerates the effect of vitamin D by over two times.

Further statistical problems are described at the BMJ pages: http://www.bmj.com/content/356/bmj.i6583/rr-3 and http://www.bmj.com/content/356/bmj.i6583/rr-8 and in some other BMJ rapid responses.