Abstract
Meta-analysis of clinical trials targeting rare events face particular challenges when the data lack adequate number of events and are susceptible to high levels of heterogeneity. The standard meta-analysis methods (DerSimonian Laird (DL) and Mantel–Haenszel (MH)) often lead to serious distortions because of such data sparsity. Applications of the methods suited to specific incidence and heterogeneity characteristics are lacking, thus we compared nine available methods in a simulation study. We generated 360 meta-analysis scenarios where each considered different incidences, sample sizes, between-study variance (heterogeneity) and treatment allocation. We include globally recommended methods such as inverse-variance fixed/random-effect (IV-FE/RE), classical-MH, MH-FE, MH-DL, Peto, Peto-DL and the two extensions for MH bootstrapped-DL (bDL) and Peto-bDL. Performance was assessed on mean bias, mean error, coverage and power. In the absence of heterogeneity, the coverage and power when combined revealed small differences in meta-analysis involving rare and very rare events. The Peto-bDL method performed best, but only in smaller sample sizes involving rare events. For medium-to-larger sample sizes, MH-bDL was preferred. For meta-analysis involving very rare events, Peto-bDL was the best performing method which was sustained across all sample sizes. However, in meta-analysis with 20% or more heterogeneity, the coverage and power were insufficient. Performance based on mean bias and mean error was almost identical across methods. To conclude, in meta-analysis of rare binary outcomes, our results suggest that Peto-bDL is better in both rare and very rare event settings in meta-analysis with limited sample sizes. However, when heterogeneity is large, the coverage and power to detect rare events are insufficient. Whilst this study shows that some of the less studied methods appear to have good properties under sparse data scenarios, further work is needed to assess them against the more complex distributional-based methods to understand their overall performances.
Highlights
Meta-analysis (MAs) of binary data encounter problems when proportions of events are few.[1]
We present the results on the five performance measures separately, and in the final part, we provide a summary for application of the methods for practitioners
For MAs involving ‘rare events’ with imbalanced patient randomisation to each treatment group (r 1⁄4 0.1), the results show that when there is no heterogeneity, the pattern of mean bias is consistently low across all of the methods (Figure 1)
Summary
Statistical Methods in MedicalResearch 30(7)from each trial. We concentrate here on MAs of study-level summaries, which is far more common in the assessment of adverse events, though patient-level analysis is to be preferred when data are available.[3]The methods used when performing MAs of binary data are frequently done using the standard inversevariance fixed-effects model which is based on large-sample normal approximation, or fixed-effects methods based on exact distributional theory such as the Mantel–Haenszel (MH)[4] or Peto model,[5] or the standard random-effects DerSimonian–Laird (DL) model.[6]. The following methods described were used in our simulation study because they met our criteria: (i) simple to implement (i.e. a lay trained person with basic MAs training could apply them), (ii) are mentioned in the Cochrane handbook with the exception of the Peto/MH bootstrap methods and (iii) because of their accessibility in free and/or mainstream statistical software such as RevMan, Stata or R.25–27. When analysing rare events and binary data in particular, the most commonly encountered effect measure used in clinical trials is the OR. True values for the design factors were gathered where possible, from empirical data on performed MAs. the largest study to date includes 14,886 Cochrane reviews.[38] Other meta-analyses[39,40,41] of rare events were used to help inform on the design
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