To the Editor:
In our recently proposed quality effects model for meta-analysis, we made use of ˆτi as a quality adjustor for the i th study. Given that N is the number of studies in the analysis, w i is the inverse variance weight and Q i is the probability (0–1) that study i is credible, then ˆτi 1
where
This adjustor redistributed the weight removed from each study equally to the remaining studies. However, we could also redistribute the weight removed to the other studies proportionate to their quality. In this case, the total value of the redistributed weight is the same, but the individual studies receive a slightly different amount based on their quality as follows:
The final summary estimate is then given by the same methodology we had previously outlined.1
What are the implications of this update? It will not grossly alter the overall estimate in the majority of meta-analyses carried out using this model, so there is a fine line between this and the original adjustor. Nevertheless, using this update might result in less bias due to a quality-effect size discordance when there is extreme heterogeneity of both quality and effect size across the studies included in the meta-analysis. To take an example, we use the meta-analysis example studied by Verhagen et al and apply the quality effects model (QEM) to the 17 studies that report on intravenous thrombolysis.2 Figure 1 depicts the adjusted individual effect sizes using the original (QEM) and the updated adjustor (QEM2). The pooled effect size was 0.73 (0.6–0.88) and 0.72 (0.59–0.89) using the original and updated adjustor respectively. It is clear, however, that only the Lasierra and Schreiber studies, which had the highest individual (unadjusted) effect sizes and extremes of quality (0.22 and 0.78, respectively) are handled differently by each adjustor. However, as this sort of discordance only affects low precision studies, the pooled effect size remains stable.
FIGURE 1.:
Estimation of adjusted individual effect sizes (IEM) using the QEM and QEM2 models with weight-adjusted effect sizes. The 2 discordant studies under QEM2 are those by Lasierra and Schreiber.
Suhail A. R. Doi
Lukman Thalib
Department of Medicine and Community Medicine (Biostatistics)
Kuwait University
Kuwait
[email protected]
REFERENCES
1. Doi SA, Thalib L. A quality-effects model for meta-analysis.
Epidemiology . 2008;19:94–100.
2. Verhagen AP, de Vet HC, Vermeer F, et al. The influence of methodologic quality on the conclusion of a landmark meta-analysis on thrombolytic therapy.
Int J Technol Assess Health Care . 2002;18:11–23.
