Abstract
BackgroundConfidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates. Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Whilst, under the random effects model, these new methods furnish confidence intervals with the correct coverage, the resulting intervals are usually very wide, making them uninformative.MethodsWe discuss a simple strategy for obtaining 95 % confidence intervals for the between-study variance with a markedly reduced width, whilst retaining the nominal coverage probability. Specifically, we consider the possibility of using methods based on generalised heterogeneity statistics with unequal tail probabilities, where the tail probability used to compute the upper bound is greater than 2.5 %. This idea is assessed using four real examples and a variety of simulation studies. Supporting analytical results are also obtained.ResultsOur results provide evidence that using unequal tail probabilities can result in shorter 95 % confidence intervals for the between-study variance. We also show some further results for a real example that illustrates how shorter confidence intervals for the between-study variance can be useful when performing sensitivity analyses for the average effect, which is usually the parameter of primary interest.ConclusionsWe conclude that using unequal tail probabilities when computing 95 % confidence intervals for the between-study variance, when using methods based on generalised heterogeneity statistics, can result in shorter confidence intervals. We suggest that those who find the case for using unequal tail probabilities convincing should use the ‘1–4 % split’, where greater tail probability is allocated to the upper confidence bound. The ‘width-optimal’ interval that we present deserves further investigation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0219-y) contains supplementary material, which is available to authorized users.
Highlights
Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates
In order to investigate the full potential of using α2 > α1, we will focus on the α-split that post hoc, minimises the resulting Q profile confidence intervals’ width
As we explain in the discussion, we suggest that further investigation is needed before we can safely recommend presenting the W -optimal interval as a confidence interval
Summary
Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Our main reason for investigating the use of Jackson and Bowden BMC Medical Research Methodology (2016) 16:118 these particular methods is because, under the assumptions of the random-effects model, they are exact This means that we can explore the use of confidence intervals with unequal tail probabilities whilst retaining the nominal coverage probability; if we instead explored the use of alternative, and approximate, methods we would have the added complication that using unequal tail probabilities would have implications for the actual coverage probability. The use of unequal tails when calculating confidence intervals using the methods we use here is not methodologically novel, but to our knowledge this paper is the first to investigate this particular issue in detail
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