Re: Author's response to Professor Hemilä and Dr Holmes
I thank Professor Hemilä and Dr Holmes for taking the time to comment on our work.
Professor Hemilä implies that we have interpreted the odds ratio as an approximate relative risk – but this is not the case. I draw his attention to the methods section of our paper (1), where we highlight that absolute effect sizes were calculated from odds ratio data using the Visual Rx NNT calculator (www.nntonline.net/visualrx/). The resultant absolute risk reductions are presented in the Summary of Findings Table, and these were used to calculate NNTs presented in the manuscript. With respect to exploration of potential causes of heterogeneity: understanding these causes was the very reason why we felt it necessary to conduct an individual participant data meta-analysis as opposed to an aggregate data meta-analysis, and our pre-specified sub-group analyses were specifically conducted to address this issue (Tables 2 and 3). We identified two potential factors: baseline vitamin D status and dosing interval. Prof Hemilä’s rationale for wishing to exclude trials by Camargo et al (2) and Manaseki et al (3) is not clear to me: what is so ‘very special’ about Mongolian schoolchildren or 1-36 month old children in Afghanistan that justifies their post hoc exclusion from the meta-analysis? If the issue relates to ‘development’ of countries, why exclude a trial conducted in Mongolia (2) (which is ranked as a lower-middle income country by the World Bank), but retain another study conducted in Afghanistan (4) (ranked as Low Income)? The fact that many trials conducted in higher-income settings reported protective effects of vitamin D against ARI (5-9), while other trials conducted in lower-income settings reported no protective effects (4, 10), goes against the hypothesis that the degree of ‘development’ of a country influences vitamin D responsiveness. Furthermore, the biological explanation for such a phenomenon is not proposed: just like higher income countries, lower income countries are heterogeneous with respect to potential effect modifiers such as baseline vitamin D status and nutritional status.
In response to Dr Holmes: we pre-specified that we would use random effects modelling in the protocol of the meta-analysis, on the grounds that this is the most appropriate approach to take when results of trials are heterogeneous. The adjusted OR that Dr Holmes generates using fixed-effect modelling of data presented in Figure 2 (0.88, 95% CI 0.81 to 0.96) is in fact identical to the adjusted OR that we obtained in the one-step IPDMA using random effects modelling. The choice of modelling method does not therefore appear to have major effects on the estimate of effect size.
I acknowledge that there is a degree of asymmetry in the funnel plot, indicating that some small trials showing adverse effects of vitamin D might have escaped our attention. However, I reiterate the point made in the Discussion that if one or two small trials showing large adverse effects of vitamin D were to emerge, we do not anticipate that they would greatly alter the results of the one step IPD meta-analysis, since any negative signal from a modest number of additional participants would likely be diluted by the robust protective signal generated from analysis of data from nearly 11,000 participants. The rationale for excluding smaller trials post hoc is not clear to me, as there is no reason to suppose that bigger trials are necessarily more methodologically sound than smaller ones. Indeed, the largest RCT included in our meta-analysis (4) utilised an intermittent bolus dosing regimen, which sub-group analyses suggest may be less effective than daily or weekly supplementation regimens for reducing ARI risk (1).
1. Martineau AR, Jolliffe DA, Hooper RL, Greenberg L, Aloia JF, Bergman P, et al. Vitamin D supplementation to prevent acute respiratory tract infections: systematic review and meta-analysis of individual participant data. BMJ. 2017;356:i6583. Epub 2017/02/17.
2. Camargo CA, Jr., Ganmaa D, Frazier AL, Kirchberg FF, Stuart JJ, Kleinman K, et al. Randomized trial of vitamin D supplementation and risk of acute respiratory infection in Mongolia. Pediatrics. 2012;130(3):e561-7. Epub 2012/08/22.
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8. Goodall EC, Granados AC, Luinstra K, Pullenayegum E, Coleman BL, Loeb M, et al. Vitamin D3 and gargling for the prevention of upper respiratory tract infections: a randomized controlled trial. BMC infectious diseases. 2014;14:273. Epub 2014/06/03.
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10. Kumar GT, Sachdev HS, Chellani H, Rehman AM, Singh V, Arora H, et al. Effect of weekly vitamin D supplements on mortality, morbidity, and growth of low birthweight term infants in India up to age 6 months: randomised controlled trial. BMJ. 2011;342:d2975. Epub 2011/06/02.
Competing interests: I am the corresponding author of the article on which these authors have commented.