We read with interest the meta-analysis by Wang et al  regarding the efficacy of fruit and vegetable consumption on mortality. We were however concerned that the random effects model applied underestimated the statistical error and has thereby produced overconfident results.
This is a major problem when authors’ use the conventional random effects (RE) model for pooling as its coverage (of the confidence interval) is known to be well below the nominal level (of 95%) [2,3]. We thus ran a re-analysis using the inverse variance heterogeneity  (IVhet), and the quality effects [5-7] (QE) models. Both are implemented in MetaXL (www.epigear.com). The IVhet model is our replacement for the RE model that has coverage of the confidence interval at the nominal level of 95%.
With this model (Figure 1) we had a HR for fruits of 0.98 (0.91 – 1.05), for vegetables of 0.97 (0.93 – 1.01) and for combined (fruits & vegetables) of 0.99 (0.93 – 1.04). None of these results demonstrate a statistically significant effect on mortality.
Finally, the QE model, by adding quality information to the IVhet model, tries to reduce variance in the estimator further (assessments done by Wang et al  used) and thus may result in more precise estimates. However, this did not help (Figure 2) and HR results for fruits was 0.98 (0.91 – 1.05) for vegetables was 0.97 (0.92 – 1.01) and for fruits & vegetables was 0.98 (0.93 – 1.03). The difference between the RE model and these models is that the RE model always transfers weights one-way : from larger to smaller studies and has a confidence interval that significantly underestimates the statistical error as demonstrated here. The QE model uses information about the studies based on quality assessments and indeed only defaults to the IVhet model when quality assessments are absent in which cases studies are assumed to be at the same risk of bias. Our conclusion is that there is no evidence based on this analysis for the effect of fruits and/or vegetables on all cause mortality and whatever effect the authors’ demonstrate is probably a result of an underestimation of the statistical error.
Suhail A. R. Doi
Jan J Barendregt
School of Population Health
University of Queensland
Herston Road, Herston
QLD 4006, Australia
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Competing interests: No competing interests