Estimating the variance for heterogeneity in arm-based network meta-analysis

A REML method for the evidence-splitting model in network meta-analysis

Checking for possible inconsistency between direct and indirect evidence is an important task in network meta-analysis. Recently, an evidence-splitting (ES) model has been proposed, that allows separating direct and indirect evidence in a network and hence assessing inconsistency. A salient feature of this model is that the variance for heterogeneity appears in both the mean and the variance structure. Thus, full maximum likelihood (ML) has been proposed for estimating the parameters of this model. Maximum likelihood is known to yield biased variance component estimates in linear mixed models, and this problem is expected to also affect the ES model. The purpose of the present paper, therefore, is to propose a method based on residual (or restricted) maximum likelihood (REML). Our simulation shows that this new method is quite competitive to methods based on full ML in terms of bias and mean squared error. In addition, some limitations of the ES model are discussed. While this model splits direct and indirect evidence, it is not a plausible model for the cause of inconsistency.

Model selection for component network meta-analysis in connected and disconnected networks: a simulation study

BACKGROUND

Network meta-analysis (NMA) allows estimating and ranking the effects of several interventions for a clinical condition. Component network meta-analysis (CNMA) is an extension of NMA which considers the individual components of multicomponent interventions. CNMA allows to "reconnect" a disconnected network with common components in subnetworks. An additive CNMA assumes that component effects are additive. This assumption can be relaxed by including interaction terms in the CNMA.

METHODS

We evaluate a forward model selection strategy for component network meta-analysis to relax the additivity assumption that can be used in connected or disconnected networks. In addition, we describe a procedure to create disconnected networks in order to evaluate the properties of the model selection in connected and disconnected networks. We apply the methods to simulated data and a Cochrane review on interventions for postoperative nausea and vomiting in adults after general anaesthesia. Model performance is compared using average mean squared errors and coverage probabilities.

RESULTS

CNMA models provide good performance for connected networks and can be an alternative to standard NMA if additivity holds. For disconnected networks, we recommend to use additive CNMA only if strong clinical arguments for additivity exist.

CONCLUSIONS

CNMA methods are feasible for connected networks but questionable for disconnected networks.

How to observe the principle of concurrent control in an arm-based meta-analysis using SAS procedures GLIMMIX and BGLIMM

Network meta-analysis is a popular method to synthesize the information obtained in a systematic review of studies (e.g. randomized clinical trials) involving subsets of multiple treatments of interest. The dominant method of analysis employs within-study information on treatment contrasts and integrates this over a network of studies. One advantage of this approach is that all inference is protected by within-study randomization. By contrast, arm-based analyses have been criticized in the past because they may also recover inter-study information when studies are modelled as random, which is the dominant practice, hence violating the principle of concurrent control, requiring treated individuals to only be compared directly with randomized controls. This issue arises regardless of whether analysis is implemented within a frequentist or a Bayesian framework. Here, we argue that recovery of inter-study information can be prevented in an arm-based analysis by adding a fixed study main effect. This simple device means that it is possible to honour the principle of concurrent control in a two-way analysis-of-variance approach that is very easy to implement using generalized linear mixed model procedures and hence may be particularly welcome to those not well versed in the more intricate coding required for a contrast-based analysis. This article is protected by copyright. All rights reserved.

Software to Conduct a Meta-Analysis and Network Meta-Analysis

Statistical software for meta-analysis (MA) and network meta-analysis (NMA) have become indispensable for researchers. The aim of this chapter is to introduce key features of MA and NMA software to compare the effectiveness of interventions. Commonly used or routinely maintained statistical software are reviewed, including commercial and open-sourced programs such as Stata, R and Excel plug-ins. It does not provide a comprehensive overview of all features available in the software covered. Rather, it focuses on the essential features required to carry out an MA or NMA . This chapter begins with a review of key considerations when implementing an MA or NMA , then presents a summary of the software. Key features of each software option are discussed.

Effect of mannose-binding lectin gene polymorphisms on the risk of rheumatoid arthritis: Evidence from a meta-analysis

BACKGROUND

The effect of mannose-binding lectin (MBL) gene polymorphisms on susceptibility of rheumatoid arthritis (RA) were evaluated in ethnically different populations, whereas the results were always inconsistent.

MATERIALS AND METHODS

Fourteen articles involving 36 datasets were recruited to evaluate the association between MBL gene polymorphisms and rheumatoid arthritis in a meta-analysis. The random or fixed effect models were used to evaluate the pooled odds ratios (ORs) and their corresponding 95% confidence intervals (CIs).

RESULTS

Stratified analysis by ethnicities was conducted and the result revealed that rs1800450 (T vs C, OR = 1.32, 95% CI: 1.04-1.67, P < .05) and MBL-A/O (T vs C, OR = 1.20, 95% CI: 1.08-1.34, P < .001) were strongly associated with RA in Brazilian populations. In addition, the significant relationship between rs11003125 (T vs C, OR = 1.16, 95% CI: 1.06-1.26, P < .05) with RA were also observed in East Asian populations. Meanwhile, the inverse associations between rs5030737 with RA in East Asians and rs1800450 with RA in Indians were acquired. However, no association between any MBL polymorphism with RA susceptibility was confirmed in Caucasians.

CONCLUSIONS

The structural polymorphisms in exon 1 of MBL gene may significantly contribute to susceptibility and development of RA in Brazilian and Indian populations, whereas the functional polymorphisms in the promoter region were more likely to associate with RA in East Asians.

Nonproportional Hazards in Network Meta-Analysis: Efficient Strategies for Model Building and Analysis

OBJECTIVES

To develop efficient approaches for fitting network meta-analysis (NMA) models with time-varying hazard ratios (such as fractional polynomials and piecewise constant models) to allow practitioners to investigate a broad range of models rapidly and to achieve a more robust and comprehensive model selection strategy.

METHODS

We reformulated the fractional polynomial and piecewise constant NMA models using analysis of variance-like parameterization. With this approach, both models are expressed as generalized linear models (GLMs) with time-varying covariates. Such models can be fitted efficiently with standard frequentist techniques. We applied our approach to the example data from the study by Jansen et al, in which fractional polynomial NMA models were introduced.

RESULTS

Fitting frequentist fixed-effect NMAs for a large initial set of candidate models took less than 1 second with standard GLM routines. This allowed for model selection from a large range of hazard ratio structures by comparing a set of criteria including Akaike information criterion/Bayesian information criterion, visual inspection of goodness-of-fit, and long-term extrapolations. The "best" models were then refitted in a Bayesian framework. Estimates agreed very closely.

CONCLUSIONS

NMA models with time-varying hazard ratios can be explored efficiently with a stepwise approach. A frequentist fixed-effect framework enables rapid exploration of different models. The best model can then be assessed further in a Bayesian framework to capture and propagate uncertainty for decision-making.

Component network meta-analysis compared to a matching method in a disconnected network: A case study

Network meta-analysis is a method to combine evidence from randomized controlled trials (RCTs) that compare a number of different interventions for a given clinical condition. Usually, this requires a connected network. A possible approach to link a disconnected network is to add evidence from nonrandomized comparisons, using propensity score or matching-adjusted indirect comparisons methods. However, nonrandomized comparisons may be associated with an unclear risk of bias. Schmitz et al. used single-arm observational studies for bridging the gap between two disconnected networks of treatments for multiple myeloma. We present a reanalysis of these data using component network meta-analysis (CNMA) models entirely based on RCTs, utilizing the fact that many of the treatments consisted of common treatment components occurring in both networks. We discuss forward and backward strategies for selecting appropriate CNMA models and compare the results to those obtained by Schmitz et al. using their matching method. CNMA models provided a good fit to the data and led to treatment rankings that were similar, though not fully equal to that obtained by Schmitz et al. We conclude that researchers encountering a disconnected network with treatments in different subnets having common components should consider a CNMA model. Such models, exclusively based on evidence from RCTs, are a promising alternative to matching approaches that require additional evidence from observational studies. CNMA models are implemented in the R package netmeta.

One-stage individual participant data meta-analysis models for continuous and binary outcomes: Comparison of treatment coding options and estimation methods

A one-stage individual participant data (IPD) meta-analysis synthesizes IPD from multiple studies using a general or generalized linear mixed model. This produces summary results (eg, about treatment effect) in a single step, whilst accounting for clustering of participants within studies (via a stratified study intercept, or random study intercepts) and between-study heterogeneity (via random treatment effects). We use simulation to evaluate the performance of restricted maximum likelihood (REML) and maximum likelihood (ML) estimation of one-stage IPD meta-analysis models for synthesizing randomized trials with continuous or binary outcomes. Three key findings are identified. First, for ML or REML estimation of stratified intercept or random intercepts models, a t-distribution based approach generally improves coverage of confidence intervals for the summary treatment effect, compared with a z-based approach. Second, when using ML estimation of a one-stage model with a stratified intercept, the treatment variable should be coded using "study-specific centering" (ie, 1/0 minus the study-specific proportion of participants in the treatment group), as this reduces the bias in the between-study variance estimate (compared with 1/0 and other coding options). Third, REML estimation reduces downward bias in between-study variance estimates compared with ML estimation, and does not depend on the treatment variable coding; for binary outcomes, this requires REML estimation of the pseudo-likelihood, although this may not be stable in some situations (eg, when data are sparse). Two applied examples are used to illustrate the findings.

A comparison of arm-based and contrast-based models for network meta-analysis

Differences between arm-based (AB) and contrast-based (CB) models for network meta-analysis (NMA) are controversial. We compare the CB model of Lu and Ades (2006), the AB model of Hong et al(2016), and two intermediate models, using hypothetical data and a selected real data set. Differences between models arise primarily from study intercepts being fixed effects in the Lu-Ades model but random effects in the Hong model, and we identify four key difference. (1) If study intercepts are fixed effects then only within-study information is used, but if they are random effects then between-study information is also used and can cause important bias. (2) Models with random study intercepts are suitable for deriving a wider range of estimands, eg, the marginal risk difference, when underlying risk is derived from the NMA data; but underlying risk is usually best derived from external data, and then models with fixed intercepts are equally good. (3) The Hong model allows treatment effects to be related to study intercepts, but the Lu-Ades model does not. (4) The Hong model is valid under a more relaxed missing data assumption, that arms (rather than contrasts) are missing at random, but this does not appear to reduce bias. We also describe an AB model with fixed study intercepts and a CB model with random study intercepts. We conclude that both AB and CB models are suitable for the analysis of NMA data, but using random study intercepts requires a strong rationale such as relating treatment effects to study intercepts.

A coefficient of determination (R2 ) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R² ) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance-covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.