Nonparametric estimation of the random effects distribution for the risk or rate ratio in rare events meta-analysis with the arm-based and contrast-based approaches.

Rare events are events which occur with low frequencies. These often arise in clinical trials or cohort studies where the data are arranged in binary contingency tables. In this article, we investigate the estimation of effect heterogeneity for the risk-ratio parameter in meta-analysis of rare events studies through two likelihood-based nonparametric mixture approaches: an arm-based and a contrast-based model. Maximum likelihood estimation is achieved using the EM algorithm. Special attention is given to the choice of initial values. Inspired by the classification likelihood, a strategy is implemented which repeatably uses random allocation of the studies to the mixture components as choice of initial values. The likelihoods under the contrast-based and arm-based approaches are compared and differences are highlighted. We use simulations to assess the performance of these two methods. Under the design of sampling studies with nested treatment groups, the results show that the nonparametric mixture model based on the contrast-based approach is more appropriate in terms of model selection criteria such as AIC and BIC. Under the arm-based design the results from the arm-based model performs well although in some cases it is also outperformed by the contrast-based model. Comparisons of the estimators are provided in terms of bias and mean squared error. Also included in the comparison is the mixed Poisson regression model as well as the classical DerSimonian-Laird model (using the Mantel-Haenszel estimator for the common effect). Using simulation, estimating effect heterogeneity in the case of the contrast-based method appears to behave better than the compared methods although differences become negligible for large within-study sample sizes. We illustrate the methodologies using several meta-analytic data sets in medicine.

Comparing various Bayesian random-effects models for pooling randomized controlled trials with rare events.

The meta-analysis of rare events presents unique methodological challenges owing to the small number of events. Bayesian methods are often used to combine rare events data to inform decision-making, as they can incorporate prior information and handle studies with zero events without the need for continuity corrections. However, the comparative performances of different Bayesian models in pooling rare events data are not well understood. We conducted a simulation to compare the statistical properties of four parameterizations based on the binomial-normal hierarchical model, using two different priors for the treatment effect: weakly informative prior (WIP) and non-informative prior (NIP), pooling randomized controlled trials with rare events using the odds ratio metric. We also considered the beta-binomial model proposed by Kuss and the random intercept and slope generalized linear mixed models. The simulation scenarios varied based on the treatment effect, sample size ratio between the treatment and control arms, and level of heterogeneity. Performance was evaluated using median bias, root mean square error, median width of 95% credible or confidence intervals, coverage, Type I error, and empirical power. Two reviews are used to illustrate these methods. The results demonstrate that the WIP outperforms the NIP within the same model structure. Among the compared models, the model that included the treatment effect parameter in the risk model for the control arm did not perform well. Our findings confirm that rare events meta-analysis faces the challenge of being underpowered, highlighting the importance of reporting the power of results in empirical studies.

Bias propagation in network meta-analysis models.

Network meta-analysis combines direct and indirect evidence to compare multiple treatments. As direct evidence for one treatment contrast may be indirect evidence for other treatment contrasts, biases in the direct evidence for one treatment contrast may affect not only the estimate for this particular treatment contrast but also estimates of other treatment contrasts. Because network structure determines how direct and indirect evidence are combined and weighted, the impact of biased evidence will be determined by the network geometry. Thus, this study's aim was to investigate how the impact of biased evidence spreads across the whole network and how the propagation of bias is influenced by the network structure. In addition to the popular Lu & Ades model, we also investigate bias propagation in the baseline model and arm-based model to compare the effects of bias in the different models. We undertook extensive simulations under different scenarios to explore how the impact of bias may be affected by the location of the bias, network geometry and the statistical model. Our results showed that the structure of a network has an important impact on how the bias spreads across the network, and this is especially true for the Lu & Ades model. The impact of bias is more likely to be diluted by other unbiased evidence in a well-connected network. We also used a real network meta-analysis to demonstrate how to use the new knowledge about bias propagation to explain questionable results from the original analysis.

Outlier detection and influence diagnostics in network meta-analysis.

Network meta-analysis has been gaining prominence as an evidence synthesis method that enables the comprehensive synthesis and simultaneous comparison of multiple treatments. In many network meta-analyses, some of the constituent studies may have markedly different characteristics from the others, and may be influential enough to change the overall results. The inclusion of these "outlying" studies might lead to biases, yielding misleading results. In this article, we propose effective methods for detecting outlying and influential studies in a frequentist framework. In particular, we propose suitable influence measures for network meta-analysis models that involve missing outcomes and adjust the degree of freedoms appropriately. We propose three influential measures by a leave-one-trial-out cross-validation scheme: (1) comparison-specific studentized residual, (2) relative change measure for covariance matrix of the comparative effectiveness parameters, (3) relative change measure for heterogeneity covariance matrix. We also propose (4) a model-based approach using a likelihood ratio statistic by a mean-shifted outlier detection model. We illustrate the effectiveness of the proposed methods via applications to a network meta-analysis of antihypertensive drugs. Using the four proposed methods, we could detect three potential influential trials involving an obvious outlier that was retracted because of data falsifications. We also demonstrate that the overall results of comparative efficacy estimates and the ranking of drugs were altered by omitting these three influential studies.

Statistical approaches to adjusting weights for dependent arms in network meta-analysis.

Network meta-analysis compares multiple treatments in terms of their efficacy and harm by including evidence from randomized controlled trials. Most clinical trials use parallel design, where patients are randomly allocated to different treatments and receive only 1 treatment. However, some trials use within person designs such as split-body, split-mouth, and crossover designs, where each patient may receive more than one treatment. Data from treatment arms within these trials are no longer independent, so the correlations between dependent arms need to be accounted for within the statistical analyses. Ignoring these correlations may result in incorrect conclusions. The main objective of this study is to develop statistical approaches to adjusting weights for dependent arms within special design trials. In this study, we demonstrate the following 3 approaches: the data augmentation approach, the adjusting variance approach, and the reducing weight approach. These 3 methods could be perfectly applied in current statistical tools such as R and STATA. An example of periodontal regeneration was used to demonstrate how these approaches could be undertaken and implemented within statistical software packages and to compare results from different approaches. The adjusting variance approach can be implemented within the network package in STATA, while reducing weight approach requires computer software programming to set up the within-study variance-covariance matrix.