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A random effects model was appropriately chosen (between study variation is allowed) as the analysis showed evidence of heterogeneity across studies that was of borderline significance (p = 0.049).
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Note that the random effect modelling between-study variation is described by a free variance parameter, τ.
The error term in a fixed effects model represents only within-study variation, and between-study variation is ignored.
The ignorance of this between-study variation is also the main difference from a random effect model.
When there is heterogeneity between a few studies for the same diagnostic test, one solution to absorb the extra between-study variation is to use a random/mixed effects model.
The estimate of the between-study variation is incorporated into both the SE of the estimate of the common effect and the weight of individual studies, which was calculated as the inverse sum of the within and between study variance.
There are no clear guidelines on how much heterogeneity is allowable, but as a rough guide, we would suggest only using a random-effects model if the standard deviation of the between-study variation is less than 25% of the pooled effect size for instance, a log odds ratio.
The majority of between-study variation was attributed to studies that defined cases on serology.
Reasons based upon heterogeneity (or between-study variation) were the most commonly cited (46/69; 66.7%).
Between-study variation was also lower within subgroups of tumor grade and tumor size.
The overall estimate for this effect was 0.77 (95% CI, 0.66 0.88) and significant between-study variation was found.
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