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Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

ABSTRACT: Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study variance by pseudo data and use meta-regression for estimation. To assist in this, we derive predictive inverse-gamma distributions for the between-study variance expected in future meta-analyses. These may serve as priors for heterogeneity in new meta-analyses. In a simulation study, we compare approximate Bayesian methods using meta-regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta-regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta-analysis is described. The proposed method facilitates Bayesian meta-analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

SUBMITTER: Rhodes KM

PROVIDER: S-EPMC5111594 | biostudies-literature | 2016 Dec

REPOSITORIES: biostudies-literature

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Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

Rhodes Kirsty M KM Turner Rebecca M RM White Ian R IR Jackson Dan D Spiegelhalter David J DJ Higgins Julian P T JP

Statistics in medicine 20160830 29

Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study v ...[more]

PMID: 27577523

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Project description:BackgroundTime-to-event data that is subject to interval censoring is common in the practice of medical research and versatile statistical methods for estimating associations in such settings have been limited. For right censored data, non-parametric pseudo-observations have been proposed as a basis for regression modeling with the possibility to use different association measures. In this article, we propose a method for calculating pseudo-observations for interval censored data.MethodsWe develop an extension of a recently developed set of parametric pseudo-observations based on a spline-based flexible parametric estimator. The inherent competing risk issue with an interval censored event of interest necessitates the use of an illness-death model, and we formulate our method within this framework. To evaluate the empirical properties of the proposed method, we perform a simulation study and calculate pseudo-observations based on our method as well as alternative approaches. We also present an analysis of a real dataset on patients with implantable cardioverter-defibrillators who are monitored for the occurrence of a particular type of device failures by routine follow-up examinations. In this dataset, we have information on exact event times as well as the interval censored data, so we can compare analyses of pseudo-observations based on the interval censored data to those obtained using the non-parametric pseudo-observations for right censored data.ResultsOur simulations show that the proposed method for calculating pseudo-observations provides unbiased estimates of the cumulative incidence function as well as associations with exposure variables with appropriate coverage probabilities. The analysis of the real dataset also suggests that our method provides estimates which are in agreement with estimates obtained from the right censored data.ConclusionsThe proposed method for calculating pseudo-observations based on the flexible parametric approach provides a versatile solution to the specific challenges that arise with interval censored data. This solution allows regression modeling using a range of different association measures.

Project description:BackgroundRandom effects modelling is routinely used in clustered data, but for prediction models, random effects are commonly substituted with the mean zero after model development. In this study, we proposed a novel approach of including prior knowledge through the random effects distribution and investigated to what extent this could improve the predictive performance.MethodsData were simulated on the basis of a random effects logistic regression model. Five prediction models were specified: a frequentist model that set the random effects to zero for all new clusters, a Bayesian model with weakly informative priors for the random effects of new clusters, Bayesian models with expert opinion incorporated into low informative, medium informative and highly informative priors for the random effects. Expert opinion at the cluster level was elicited in the form of a truncated area of the random effects distribution. The predictive performance of the five models was assessed. In addition, impact of suboptimal expert opinion that deviated from the true quantity as well as including expert opinion by means of a categorical variable in the frequentist approach were explored. The five models were further investigated in various sensitivity analyses.ResultsThe Bayesian prediction model using weakly informative priors for the random effects showed similar results to the frequentist model. Bayesian prediction models using expert opinion as informative priors showed smaller Brier scores, better overall discrimination and calibration, as well as better within cluster calibration. Results also indicated that incorporation of more precise expert opinion led to better predictions. Predictive performance from the frequentist models with expert opinion incorporated as categorical variable showed similar patterns as the Bayesian models with informative priors. When suboptimal expert opinion was used as prior information, results indicated that prediction still improved in certain settings.ConclusionsThe prediction models that incorporated cluster level information showed better performance than the models that did not. The Bayesian prediction models we proposed, with cluster specific expert opinion incorporated as priors for the random effects showed better predictive ability in new data, compared to the frequentist method that replaced random effects with zero after model development.

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Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

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Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

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