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Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis.

Lunn D, Barrett J, Sweeting M, Thompson S - J R Stat Soc Ser C Appl Stat (2013)

Bottom Line: A Bayesian one-stage approach offers additional advantages, such as the acknowledgement of uncertainty in all parameters and greater flexibility.These are then used as proposal distributions in a computationally efficient second stage.The two-stage Bayesian approach closely reproduces a one-stage analysis when it can be undertaken, but can also be easily carried out when a one-stage approach is difficult or impossible.

View Article: PubMed Central - PubMed

Affiliation: Medical Research Council Biostatistics Unit Cambridge, UK.

ABSTRACT
Meta-analysis is often undertaken in two stages, with each study analysed separately in stage 1 and estimates combined across studies in stage 2. The study-specific estimates are assumed to arise from normal distributions with known variances equal to their corresponding estimates. In contrast, a one-stage analysis estimates all parameters simultaneously. A Bayesian one-stage approach offers additional advantages, such as the acknowledgement of uncertainty in all parameters and greater flexibility. However, there are situations when a two-stage strategy is compelling, e.g. when study-specific analyses are complex and/or time consuming. We present a novel method for fitting the full Bayesian model in two stages, hence benefiting from its advantages while retaining the convenience and flexibility of a two-stage approach. Using Markov chain Monte Carlo methods, posteriors for the parameters of interest are derived separately for each study. These are then used as proposal distributions in a computationally efficient second stage. We illustrate these ideas on a small binomial data set; we also analyse motivating data on the growth and rupture of abdominal aortic aneurysms. The two-stage Bayesian approach closely reproduces a one-stage analysis when it can be undertaken, but can also be easily carried out when a one-stage approach is difficult or impossible.

No MeSH data available.


Related in: MedlinePlus

Results of the two-stage and one-stage analyses of the pre-eclampsia data: estimates are posterior medians with 95% credible intervals; the medians are shown as squares with area inversely proportional to the posterior variance; the edges of the diamonds used to denote overall estimates correspond to the limits of the 95% credible interval, whereas the central vertices show the posterior median
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fig01: Results of the two-stage and one-stage analyses of the pre-eclampsia data: estimates are posterior medians with 95% credible intervals; the medians are shown as squares with area inversely proportional to the posterior variance; the edges of the diamonds used to denote overall estimates correspond to the limits of the 95% credible interval, whereas the central vertices show the posterior median

Mentions: Our results are summarized in the forest plot shown in Fig. 1. For each study we plot the posterior median value of τi and the corresponding 95% credible interval from each of the four analyses alluded to above:


Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis.

Lunn D, Barrett J, Sweeting M, Thompson S - J R Stat Soc Ser C Appl Stat (2013)

Results of the two-stage and one-stage analyses of the pre-eclampsia data: estimates are posterior medians with 95% credible intervals; the medians are shown as squares with area inversely proportional to the posterior variance; the edges of the diamonds used to denote overall estimates correspond to the limits of the 95% credible interval, whereas the central vertices show the posterior median
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3814003&req=5

fig01: Results of the two-stage and one-stage analyses of the pre-eclampsia data: estimates are posterior medians with 95% credible intervals; the medians are shown as squares with area inversely proportional to the posterior variance; the edges of the diamonds used to denote overall estimates correspond to the limits of the 95% credible interval, whereas the central vertices show the posterior median
Mentions: Our results are summarized in the forest plot shown in Fig. 1. For each study we plot the posterior median value of τi and the corresponding 95% credible interval from each of the four analyses alluded to above:

Bottom Line: A Bayesian one-stage approach offers additional advantages, such as the acknowledgement of uncertainty in all parameters and greater flexibility.These are then used as proposal distributions in a computationally efficient second stage.The two-stage Bayesian approach closely reproduces a one-stage analysis when it can be undertaken, but can also be easily carried out when a one-stage approach is difficult or impossible.

View Article: PubMed Central - PubMed

Affiliation: Medical Research Council Biostatistics Unit Cambridge, UK.

ABSTRACT
Meta-analysis is often undertaken in two stages, with each study analysed separately in stage 1 and estimates combined across studies in stage 2. The study-specific estimates are assumed to arise from normal distributions with known variances equal to their corresponding estimates. In contrast, a one-stage analysis estimates all parameters simultaneously. A Bayesian one-stage approach offers additional advantages, such as the acknowledgement of uncertainty in all parameters and greater flexibility. However, there are situations when a two-stage strategy is compelling, e.g. when study-specific analyses are complex and/or time consuming. We present a novel method for fitting the full Bayesian model in two stages, hence benefiting from its advantages while retaining the convenience and flexibility of a two-stage approach. Using Markov chain Monte Carlo methods, posteriors for the parameters of interest are derived separately for each study. These are then used as proposal distributions in a computationally efficient second stage. We illustrate these ideas on a small binomial data set; we also analyse motivating data on the growth and rupture of abdominal aortic aneurysms. The two-stage Bayesian approach closely reproduces a one-stage analysis when it can be undertaken, but can also be easily carried out when a one-stage approach is difficult or impossible.

No MeSH data available.


Related in: MedlinePlus