Kenward‐Roger–type corrections for inference methods of network meta‐analysis and meta‐regression

Abstract

Network meta‐analysis has been an essential methodology of systematic reviews for comparative effectiveness research. The restricted maximum likelihood (REML) method is one of the current standard inference methods for multivariate, contrast‐based meta‐analysis models, but recent studies have revealed the resultant confidence intervals of average treatment effect parameters in random‐effects models can seriously underestimate statistical errors; that is, the actual coverage probability of a true parameter cannot retain the nominal level (e.g., 95%). In this article, we provided improved inference methods for the network meta‐analysis and meta‐regression models using higher‐order asymptotic approximations based on the approach of Kenward and Roger (Biometrics 1997;53:983–997). We provided two corrected covariance matrix estimators for the REML estimator and improved approximations for its sample distribution using a t‐distribution with adequate degrees of freedom. All of the proposed procedures can be implemented using only simple matrix calculations. In simulation studies under various settings, the REML‐based Wald‐type confidence intervals seriously underestimated the statistical errors, especially in cases of small numbers of trials meta‐analyzed. By contrast, the proposed Kenward‐Roger–type inference methods consistently showed accurate coverage properties under all the settings considered in our experiments. We also illustrated the effectiveness of the proposed methods through applications to two real network meta‐analysis datasets.

Improved methods to construct prediction intervals for network meta‐analysis

“…For inferences of μ in the random-effects model (*), the ordinary Wald-type approximation of the REML estimator is not good, especially under small N settings. Noma et al 19 developed improved inference methods using the Kenward-Roger-type approximations. 18 The higher-order approximation methods were not originally considered to apply to the construction of prediction intervals, but Partlett and Riley 9 proposed applying the same approximation to construct a prediction interval of pairwise meta-analysis.…”

“…First, Noma et al 19 derived improved covariance estimators of the REML estimator b μ. They were motivated by the tendency of the ordinary asymptotic covariance estimator b Φ to generally underestimate the true variability of b μ, mainly because it does not consider the variability of the heterogeneity variance estimator b τ 2 : 19 The variance estimator of b τ 2 based on the expected information is given as…”

“…, Noma et al 19 proposed using the t-distribution with an adjusted degree of freedom derived by the higher-order asymptotics considered by Kenward and Roger. 18 The adjusted degree of freedom is…”

“…The Kenward-Roger methods were originally developed as inference methods, not as prediction tools; however, Partlett and Riley 9 showed that they can be effectively applied to the prediction issues in conventional pairwise meta-analysis. Recently, Noma et al 19 developed Kenward-Roger-type approximation methods for network meta-analysis. In the present work, we propose a new method that applies the improved approximation method 19 to the prediction problem.…”

“…Recently, Noma et al 19 developed Kenward-Roger-type approximation methods for network meta-analysis. In the present work, we propose a new method that applies the improved approximation method 19 to the prediction problem. We also developed an R package, PINMA (https://cran.r-project.org/web/packages/PINMA/), for implementing these new methods.…”