Exploring consequences of simulation design for apparent performance of methods of meta-analysis

Relative likelihood ratios for neutral comparisons of statistical tests in simulation studies

When comparing the performance of two or more competing tests, simulation studies commonly focus on statistical power. However, if the size of the tests being compared are either different from one another or from the nominal size, comparing tests based on power alone may be misleading. By analogy with diagnostic accuracy studies, we introduce relative positive and negative likelihood ratios to factor in both power and size in the comparison of multiple tests. We derive sample size formulas for a comparative simulation study. As an example, we compared the performance of six statistical tests for small-study effects in meta-analyses of randomized controlled trials: Begg's rank correlation, Egger's regression, Schwarzer's method for sparse data, the trim-and-fill method, the arcsine-Thompson test, and Lin and Chu's combined test. We illustrate that comparing power alone, or power adjusted or penalized for size, can be misleading, and how the proposed likelihood ratio approach enables accurate comparison of the trade-off between power and size between competing tests.

The impact of correction methods on rare-event meta-analysis

Meta-analyses have become the gold standard for synthesizing evidence from multiple clinical trials, and they are especially useful when outcomes are rare or adverse since individual trials often lack sufficient power to detect a treatment effect. However, when zero events are observed in one or both treatment arms in a trial, commonly used meta-analysis methods can perform poorly. Continuity corrections (CCs), and numerical adjustments to the data to make computations feasible, have been proposed to ameliorate this issue. While the impact of various CCs on meta-analyses with rare events has been explored, how this impact varies based on the choice of pooling method and heterogeneity variance estimator is not widely understood. We compare several correction methods via a simulation study with a variety of commonly used meta-analysis methods. We consider how these method combinations impact important meta-analysis results, such as the estimated overall treatment effect, 95% confidence interval coverage, and Type I error rate. We also provide a website application of these results to aid researchers in selecting meta-analysis methods for rare-event data sets. Overall, no one-method combination can be consistently recommended, but some general trends are evident. For example, when there is no heterogeneity variance, we find that all pooling methods can perform well when paired with a specific correction method. Additionally, removing studies with zero events can work very well when there is no heterogeneity variance, while excluding single-zero studies results in poorer method performance when there is non-negligible heterogeneity variance and is not recommended.

Rare events meta-analysis using the Bayesian beta-binomial model

In meta-analyses of rare events, it can be challenging to obtain a reliable estimate of the pooled effect, in particular when the meta-analysis is based on a small number of studies. Recent simulation studies have shown that the beta-binomial model is a promising candidate in this situation, but have thus far only investigated its performance in a frequentist framework. In this study, we aim to make the beta-binomial model for meta-analysis of rare events amenable to Bayesian inference by proposing prior distributions for the effect parameter and investigating the models' robustness to different specifications of priors for the scale parameter. To evaluate the performance of Bayesian beta-binomial models with different priors, we conducted a simulation study with two different data generating models in which we varied the size of the pooled effect, the degree of heterogeneity, the baseline probability, and the sample size. Our results show that while some caution must be exercised when using the Bayesian beta-binomial in meta-analyses with extremely sparse data, the use of a weakly informative prior for the effect parameter is beneficial in terms of mean bias, mean squared error, and coverage. For the scale parameter, half-normal and exponential distributions are identified as candidate priors in meta-analysis of rare events using the Bayesian beta-binomial model.

Estimation of heterogeneity variance based on a generalized Q statistic in meta-analysis of log-odds-ratio

For estimation of heterogeneity varianceτ 2 in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized Q statistic,Q F , in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators based on the inverse-variance-weights version of Q ,Q IV . In an extensive simulation, we studied the bias (including median bias) of the point estimators and the coverage (including left and right coverage error) of the confidence intervals. Most estimators add 0.5 to each cell of the 2 × 2 table when one cell contains a zero count; we include a version that always adds 0.5 . The results show that: two of the new point estimators and two of the familiar point estimators are almost unbiased when the total sample size n ≥ 250 and the probability in the Control arm (p iC ) is 0.1, and when n ≥ 100 andp iC is 0.2 or 0.5; for 0.1 ≤ τ 2 ≤ 1 , all estimators have negative bias for small to medium sample sizes, but for larger sample sizes some of the new median-unbiased estimators are almost median-unbiased; choices of interval estimators depend on values of parameters, but one of the new estimators is reasonable whenp iC = 0.1 and another, whenp iC = 0.2 orp iC = 0.5 ; and lack of balance between left and right coverage errors for small n and/orp iC implies that the available approximations for the distributions ofQ IV andQ F are accurate only for larger sample sizes.

On the Q statistic with constant weights in meta-analysis of binary outcomes

BACKGROUND

Cochran's Q statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value (under an incorrect null distribution) is part of several popular estimators of the between-study variance, [Formula: see text]. Those applications generally do not account for use of the studies' estimated variances in the inverse-variance weights that define Q (more explicitly, [Formula: see text]). Importantly, those weights make approximating the distribution of [Formula: see text] rather complicated.

METHODS

As an alternative, we are investigating a Q statistic, [Formula: see text], whose constant weights use only the studies' arm-level sample sizes. For log-odds-ratio (LOR), log-relative-risk (LRR), and risk difference (RD) as the measures of effect, we study, by simulation, approximations to distributions of [Formula: see text] and [Formula: see text], as the basis for tests of heterogeneity.

RESULTS

The results show that: for LOR and LRR, a two-moment gamma approximation to the distribution of [Formula: see text] works well for small sample sizes, and an approximation based on an algorithm of Farebrother is recommended for larger sample sizes. For RD, the Farebrother approximation works very well, even for small sample sizes. For [Formula: see text], the standard chi-square approximation provides levels that are much too low for LOR and LRR and too high for RD. The Kulinskaya et al. (Res Synth Methods 2:254-70, 2011) approximation for RD and the Kulinskaya and Dollinger (BMC Med Res Methodol 15:49, 2015) approximation for LOR work well for [Formula: see text] but have some convergence issues for very small sample sizes combined with small probabilities.

CONCLUSIONS

The performance of the standard [Formula: see text] approximation is inadequate for all three binary effect measures. Instead, we recommend a test of heterogeneity based on [Formula: see text] and provide practical guidelines for choosing an appropriate test at the .05 level for all three effect measures.

Random-effects meta-analysis models for the odds ratio in the case of rare events under different data-generating models: A simulation study

Meta-analysis of binary data is challenging when the event under investigation is rare, and standard models for random-effects meta-analysis perform poorly in such settings. In this simulation study, we investigate the performance of different random-effects meta-analysis models in terms of point and interval estimation of the pooled log odds ratio in rare events meta-analysis. First and foremost, we evaluate the performance of a hypergeometric-normal model from the family of generalized linear mixed models (GLMMs), which has been recommended, but has not yet been thoroughly investigated for rare events meta-analysis. Performance of this model is compared to performance of the beta-binomial model, which yielded favorable results in previous simulation studies, and to the performance of models that are frequently used in rare events meta-analysis, such as the inverse variance model and the Mantel-Haenszel method. In addition to considering a large number of simulation parameters inspired by real-world data settings, we study the comparative performance of the meta-analytic models under two different data-generating models (DGMs) that have been used in past simulation studies. The results of this study show that the hypergeometric-normal GLMM is useful for meta-analysis of rare events when moderate to large heterogeneity is present. In addition, our study reveals important insights with regard to the performance of the beta-binomial model under different DGMs from the binomial-normal family. In particular, we demonstrate that although misalignment of the beta-binomial model with the DGM affects its performance, it shows more robustness to the DGM than its competitors.

A comparison of confidence distribution approaches for rare event meta-analysis

Meta-analysis of rare event data has recently received increasing attention due to the challenging issues rare events pose to traditional meta-analytic methods. One specific way to combine information and analyze rare event meta-analysis data utilizes confidence distributions (CDs). While several CD methods exist, no comparisons have been made to determine which method is best suited for homogeneous or heterogeneous meta-analyses with rare events. In this article, we review several CD methods: Fisher's classic P-value combination method, one that combines P-value functions, another that combines confidence intervals, and one that combines confidence log-likelihood functions. We compare these CD approaches, and we propose and compare variations of these methods to determine which method produces reliable results for homogeneous or heterogeneous rare event meta-analyses. We find that for homogeneous rare event data, most CD methods perform very well. On the other hand, for heterogeneous rare event data, there is a clear split in performance between some CD methods, with some performing very poorly and others performing reasonably well.