The two-stage time series design represents a powerful analytical tool in environmental epidemiology. Recently, models for both stages have been extended with the development of distributed lag non-linear models (DLNMs), a methodology for investigating simultaneously non-linear and lagged relationships, and multivariate meta-analysis, a methodology to pool estimates of multi-parameter associations. However, the application of both methods in two-stage analyses is prevented by the high-dimensional definition of DLNMs. In this contribution we propose a method to synthesize DLNMs to simpler summaries, expressed by a reduced set of parameters of one-dimensional functions, which are compatible with current multivariate meta-analytical techniques. The methodology and modelling framework are implemented in R through the packages dlnm and mvmeta. As an illustrative application, the method is adopted for the two-stage time series analysis of temperature-mortality associations using data from 10 regions in England and Wales. R code and data are available as supplementary online material. The methodology proposed here extends the use of DLNMs in two-stage analyses, obtaining meta-analytical estimates of easily interpretable summaries from complex non-linear and delayed associations. The approach relaxes the assumptions and avoids simplifications required by simpler modelling approaches.

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Reducing and meta-analysing estimates from distributed lag non-linear models.

https://pure.rug.nl/ws/files/146451450/Conducting_Indirect_Treatment_Comparison_and_Network_Meta_Analysis_Studies.pdf

Conducting indirect-treatment-comparison and network-meta-analysis studies: report of the ISPOR Task Force on Indirect Treatment Comparisons Good Research Practices: part 2.

Meta-analysis is an indispensable tool used to synthesize research findings in the social, educational, medical, management, and behavioral sciences. Most meta-analytic models assume independence among effect sizes. However, effect sizes can be dependent for various reasons. For example, studies might report multiple effect sizes on the same construct, and effect sizes reported by participants from the same cultural group are likely to be more similar than those reported by other cultural groups. This article reviews the problems and common methods to handle dependent effect sizes. The objective of this article is to demonstrate how 3-level meta-analyses can be used to model dependent effect sizes. The advantages of the structural equation modeling approach over the multilevel approach with regard to conducting a 3-level meta-analysis are discussed. This article also seeks to extend the key concepts of Q statistics, I2, and R2 from 2-level meta-analyses to 3-level meta-analyses. The proposed procedures are implemented using the open source metaSEM package for the R statistical environment. Two real data sets are used to illustrate these procedures. New research directions related to 3-level meta-analyses are discussed.

Modeling dependent effect sizes with three-level meta-analyses: a structural equation modeling approach.

This paper sets out a generalised linear model (GLM) framework for the synthesis of data from randomised controlled trials (RCTs). We describe a common model taking the form of a linear regression for both fixed and random effects synthesis, that can be implemented with Normal, Binomial, Poisson, and Multinomial data. The familiar logistic model for meta- analysis with Binomial data is a GLM with a logit link function, which is appropriate for probability outcomes. The same linear regression framework can be applied to continuous outcomes, rate models, competing risks, or ordered category outcomes, by using other link functions, such as identity, log, complementary log-log, and probit link functions. The common core model for the linear predictor can be applied to pair-wise meta-analysis, indirect comparisons, synthesis of multi-arm trials, and mixed treatment comparisons, also known as network meta-analysis, without distinction.We take a Bayesian approach to estimation and provide WinBUGS program code for a Bayesian analysis using Markov chain Monte Carlo (MCMC) simulation. An advantage of this approach is that it is straightforward to extend to shared parameter models where different RCTs report outcomes in different formats but from a common underlying model. Use of the GLM framework allows us to present a unified account of how models can be compared using the Deviance Information Criterion (DIC), and how goodness of fit can be assessed using the residual deviance. WinBUGS code for model critique is provided. Our approach is illustrated through a range of worked examples for the commonly encountered evidence formats, including shared parameter models.We give suggestions on computational issues that sometimes arise in MCMC evidence synthesis, and comment briefly on alternative software.

/pdf/nice-dsu-technical-support-document-2-a-generalised-linear-1shdbhlgms.pdf

NICE DSU Technical Support Document 2: A Generalised Linear Modelling Framework for Pairwise and Network Meta-Analysis of Randomised Controlled Trials

The art and science of meta-analysis, the combination of results from multiple independent studies, is now more than a century old. In the last 30 years, however, as the need for medical research and clinical practice to be based on the totality of relevant and sound evidence has been increasingly recognized, the impact of meta-analysis has grown enormously. In this paper, we review highlights of recent developments in meta-analysis in medical research. We outline in particular how emphasis has been placed on (i) heterogeneity and random-effects analyses; (ii) special consideration in different areas of application; (iii) assessing bias within and across studies; and (iv) extension of ideas to complex evidence synthesis. We conclude the paper with some remarks on ongoing challenges and possible directions for the future.

Recent developments in meta‐analysis

Meta-analysis is now a standard statistical tool for assessing the overall strength and interesting features of a relationship, on the basis of multiple independent studies. There is, however, recent acknowledgement of the fact that in many applications responses are rarely uniquely determined. Hence there has been some change of focus from a single response to the analysis of multiple outcomes. In this paper we propose and evaluate three Bayesian multivariate meta-analysis models: two multivariate analogues of the traditional univariate random effects models which make different assumptions about the relationships between studies and estimates, and a multivariate random effects model which is a Bayesian adaptation of the mixed model approach. Our preferred method is then illustrated through an analysis of a new data set on parental smoking and two health outcomes (asthma and lower respiratory disease) in children.

In-Sun Nam

Papers

Multivariate meta-analysis