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EDITORIAL COMMENTARY 



Year : 2019  Volume
: 65
 Issue : 2  Page : 7071 
Interpreting the metaanalysis of efficacy of vitamin D supplementation in major depression
L Jeyaseelan
Department of Biostatistics, Christian Medical College, Vellore  632 002, Tamil Nadu, India
Date of Web Publication  26Apr2019 
Correspondence Address: L Jeyaseelan Department of Biostatistics, Christian Medical College, Vellore  632 002, Tamil Nadu India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jpgm.JPGM_267_18
How to cite this article: Jeyaseelan L. Interpreting the metaanalysis of efficacy of vitamin D supplementation in major depression. J Postgrad Med 2019;65:701 
Vellekkatt and Menon ^{[1]} have performed an interesting metaanalysis to summarize the efficacy of vitamin D supplementation in the treatment of major depression. This wellwritten article has included 43 clinical trial articles for systematic review, of which 4 finally qualified for further analysis. The conclusion from the metaanalysis (MA) was that the difference in depression symptom score was 0.58 units in vitamin D groups when compared with the control group. Of the four studies, one study dealt with 746 subjects out of the total 948 subjects, while the other studies dealt with roughly 200 subjects in total. Thus, one study result had dominated the results of the other studies. However, they all showed favorable result of vitamin D group over the control group.
The analysis of the effect sizes of those selected studies considered two models: fixed effect and random effects models. Under the fixed effects model, we assume that there is one true effect size and that all differences in observed effects between studies are due to sampling error. For example, multisite studies by pharmaceutical industry might like to find an average effect of few sites as they are using the same protocol. Therefore, they like to use fixed effects model. Thus, fixed effect implies that there is no sampling and the interest is restricted to selected studies only. On the other hand, random effects model allows the true effect to vary from study to study. For example, the effect size might be higher (or lower) in studies where the participants are older and so on.^{[2]} Thus, random effects model is valid when the studies are random sample. In the present metaanalysis ^{[1]}, the studies are not randomly selected, but they are a sample, and this so happens with almost any MA. So long as the intention is to extrapolate the results to the other similar studies, random effect model is considered better representation Schmidt et al.^{[3]}
The heterogeneity of the effect size is an important statistic that quantifies if these studies can be pooled together. The heterogeneity statistics determines whether the studies in hand are of similar kind or not. The result of the pooled analysis may be sceptical if these studies are very much different from each other. The statistic that assesses the variability across studies is Q statistic. However, the I^{2} index, derived out of Q statistic quantifies the amount of variance on a relative scale. For example, if we are planning to speculate about reasons for variation, we should first use I^{2} to determine what proportion of the observed variance is real. If I^{2} is close to zero, then almost all the observed variance is spurious, which means that there is nothing to explain.^{[4]}
In the present MA ^{[1]}, there are three studies that look similar in terms of variability; however, the study by Wang et al.^{[5]} has a narrow confidence interval (CI) as compared to other studies. Higgins et al.^{[6]} has provided some tentative benchmarks for I^{2}. The present MA has provided I^{2} as zero which suggests that there is no considerable between study variability.
A MA is expected to provide accurate summary of the studies included in the analysis. However, if these studies are a biased sample of all relevant studies, then MA would provide a biased result. It is a known fact that studies that report relatively high effect sizes are more likely to be published than studies that report lower or insignificant effect sizes. Thus, any bias in the literature is likely to be reflected in the MA. This is generally known as publication bias. It is important to recognize that publication bias, if any, is present. The Funnel plot is a simple graphical method to assess publication bias. The Xaxis of the Funnel plot has the effect size, whereas the Yaxis represents the standard errors (SEs). The smaller SE implies large sample size, whereas larger SE implies small sample size studies. Smallscale studies are expected to be scattered around the bottom of the Funnel plot, whereas largescale studies are expected to be placed at the top of the Funnel plot. Usually, there are two vertical lines displayed. One is at the null value (relative risk and odds ratio = 1, average effect size = 0) and another is at the average effect size. An asymmetric scatter plot of studies from the null value suggests publication bias. In other words, smallscale studies or insignificant studies would not have been included. Thus, in such as example there will be a hallow space below (lefthand side) the null value of 0.
The Funnel plot in the present MA needs a careful interpretation. The study by Wang et al.^{[5]} had a large sample size and therefore had a smaller SE, and a narrower confidence interval (CI) (refer to Figure 2).^{[1]} However, the Funnel plot showed great asymmetry suggesting a bias. Thus there are two view points to this Funnel plot. One is that the present MA dealt with publication bias or in reality there is no smallscale insignificant study at all. In the present MA, the presentation of Funnel plot is appreciated despite there being only four studies in toto.^{[3]} From the flowchart, it is obvious that the authors have made considerable effort to search for published and unpublished studies.
:: References   
1.  Vellekkatt F, Menon V. Efficacy of vitamin D supplementation in major depression: A metaanalysis of randomized controlled trials. J Postgrad Med 2019;65:7480. [ PUBMED] [Full text] 
2.  Borenstein M, Hedges LV, Higgins JPT, Rothstein, HR. Introduction to meta analyses. West Sussex: John Wiley & Sons; 2009. 
3.  Schmidt FL, Oh LS, Hayes TL. Fixed versus randomeffects models in metaanalysis: Model properties and an empirical comparison of differences in results. Br J Math Stat Psychol 2009;62:97128. 
4.  Sterne JA, Egger M, Smith GD. Systematic reviews in healthcare: Investigating and dealing with publication and other biases in metaanalysis. BMJ 2001;323:1015. 
5.  Wang Y, Liu Y, Lian Y, Li N, Liu H, Li G. Efficay of highdose supplementation with oral vitamin D3 on depressive symptoms in dialysis patients with vitamin D3 insufficiency. A prospective, Randomized, doubleblind study. J Clin Psychopharmacol 2016;39: 22935. 
6.  Higgins J, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in metaanalyses. BMJ 2003;327:55760. 





