Article type
Year
Abstract
Background: Meta-epidemiological studies aim to identify and quantify biases in estimates of intervention effectiveness by contrasting estimates from trials with different characteristics within meta-analyses, e.g. using the ratio of odds ratios (ROR). Several frequentist approaches to meta-epidemiological estimation have been proposed [1,2,3,4], but they do not take into account all sources of uncertainty and variability, and limitations of existing software preclude flexible modeling. Bayesian approaches offer an appealing alternative.
Objectives: To develop Bayesian approaches to meta-epidemiology and assess their flexibility and performance relative to existing approaches.
Methods: Six models were developed by extending existing meta-epidemiological models. Three meta-epidemiological datasets[3,4,5], were used to explore the performance of the models fitted using both frequentist and Bayesian paradigms. Attempts were made to fit models in a frequentist framework using SAS procedures GENMOD, MIXED, and NLMIXED, and GLMMIX macro and using R functions glm, clogit, lme, and nlme. With additional specification of priors and hyperpriors for unknown parameters, BUGS software was used to fit the models, test Markov Chain Monte Carlo (MCMC) convergence, and explore sensitivity to specification of priors. Posterior modes and their standard deviations were compared across models and with estimates from frequentist approaches.
Results: Due to computational difficulties and software limitations, little success was obtained fitting more complex models in the frequentist framework. MCMC convergence proved delicate, however with careful choice of prior distributions, convergence was achieved for most models. Results from the Schulz model[1] were closely replicated using a Bayesian analogue, except that the posterior standard deviation of the ROR was always larger than the Schulz standard error. Some model parameters were found to be relatively insensitive to changes in prior distributions, while changes in priors for other parameters had drastic effects.
Conclusions: Choice of prior can have a substantial impact on point estimates and measures of uncertainty. The Bayesian paradigm permits flexible modeling, allowing for models with diverse fixed and random effects structures, which cannot presently be handled by frequentist software. Especially for more complex models, Bayesian approaches to meta-epidemiology are indispensable.
Acknowledgements: This research was supported by a grant from the Canadian Institutes of Health Research.
References: 1. Schulz KF, Chalmers I, Hayes RJ, Altman DG. Empirical evidence of bias: dimensions of methodological quality associated with estimates of treatment effects in controlled trials. JAMA. 1995; 273:408-412. 2. Sterne JA, Juni P, Schulz KF, Altman DG, Bartlett C, Egger M. Statistical methods for assessing the influence of study characteristics on treatment effects in meta-epidemiological research. Stat Med. 2002; 21(11):1513-1524. 3. Sampson M, Barrowman NJ, Moher D, Klassen TP, Pham B, Platt R et al. Should meta-analysts search Embase in addition to Medline? J Clin Epidemiol. 2003; 56:943-955. 4. Moher D, Pham B, Klassen TP, Schulz KF, Berlin JA, Jadad AR et al. What contributions do languages other than English make on the results of meta-analyses? J Clin Epidemiol. 2000; 53(9):964-972. 5. McAuley L, Pham B, Tugwell P, Moher D. Does the inclusion of grey literature influence estimates of intervention effectiveness reported in meta-analyses? Lancet. 2000; 356(9237):1228-1231.
Objectives: To develop Bayesian approaches to meta-epidemiology and assess their flexibility and performance relative to existing approaches.
Methods: Six models were developed by extending existing meta-epidemiological models. Three meta-epidemiological datasets[3,4,5], were used to explore the performance of the models fitted using both frequentist and Bayesian paradigms. Attempts were made to fit models in a frequentist framework using SAS procedures GENMOD, MIXED, and NLMIXED, and GLMMIX macro and using R functions glm, clogit, lme, and nlme. With additional specification of priors and hyperpriors for unknown parameters, BUGS software was used to fit the models, test Markov Chain Monte Carlo (MCMC) convergence, and explore sensitivity to specification of priors. Posterior modes and their standard deviations were compared across models and with estimates from frequentist approaches.
Results: Due to computational difficulties and software limitations, little success was obtained fitting more complex models in the frequentist framework. MCMC convergence proved delicate, however with careful choice of prior distributions, convergence was achieved for most models. Results from the Schulz model[1] were closely replicated using a Bayesian analogue, except that the posterior standard deviation of the ROR was always larger than the Schulz standard error. Some model parameters were found to be relatively insensitive to changes in prior distributions, while changes in priors for other parameters had drastic effects.
Conclusions: Choice of prior can have a substantial impact on point estimates and measures of uncertainty. The Bayesian paradigm permits flexible modeling, allowing for models with diverse fixed and random effects structures, which cannot presently be handled by frequentist software. Especially for more complex models, Bayesian approaches to meta-epidemiology are indispensable.
Acknowledgements: This research was supported by a grant from the Canadian Institutes of Health Research.
References: 1. Schulz KF, Chalmers I, Hayes RJ, Altman DG. Empirical evidence of bias: dimensions of methodological quality associated with estimates of treatment effects in controlled trials. JAMA. 1995; 273:408-412. 2. Sterne JA, Juni P, Schulz KF, Altman DG, Bartlett C, Egger M. Statistical methods for assessing the influence of study characteristics on treatment effects in meta-epidemiological research. Stat Med. 2002; 21(11):1513-1524. 3. Sampson M, Barrowman NJ, Moher D, Klassen TP, Pham B, Platt R et al. Should meta-analysts search Embase in addition to Medline? J Clin Epidemiol. 2003; 56:943-955. 4. Moher D, Pham B, Klassen TP, Schulz KF, Berlin JA, Jadad AR et al. What contributions do languages other than English make on the results of meta-analyses? J Clin Epidemiol. 2000; 53(9):964-972. 5. McAuley L, Pham B, Tugwell P, Moher D. Does the inclusion of grey literature influence estimates of intervention effectiveness reported in meta-analyses? Lancet. 2000; 356(9237):1228-1231.