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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

Population median probabilities of clinically significant events occurring within time periods of between 3 and 24 months, in 3-month intervals: (a) probability of rupture given a diameter of 50 mm; (b) probability of crossing the surgical intervention threshold given a diameter of 50 mm; estimates are posterior medians with 95% credible intervals
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fig05: Population median probabilities of clinically significant events occurring within time periods of between 3 and 24 months, in 3-month intervals: (a) probability of rupture given a diameter of 50 mm; (b) probability of crossing the surgical intervention threshold given a diameter of 50 mm; estimates are posterior medians with 95% credible intervals

Mentions: Fig. 5 shows the probabilities of rupture and of crossing the intervention threshold, given d=50, for various values of the monitoring interval u. These are obtained straightforwardly by adapting the procedure that was outlined above for u=0.25. We can see that monitoring intervals of 9 months or less and 6 months or less respectively are required to be confident that the population median probabilities of rupture and of crossing the intervention threshold are below 1% and 10%. However, given the degree of between-study variation, it would seem inappropriate to use this as a basis for justifying a longer monitoring interval.


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)

Population median probabilities of clinically significant events occurring within time periods of between 3 and 24 months, in 3-month intervals: (a) probability of rupture given a diameter of 50 mm; (b) probability of crossing the surgical intervention threshold given a diameter of 50 mm; estimates are posterior medians with 95% credible intervals
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig05: Population median probabilities of clinically significant events occurring within time periods of between 3 and 24 months, in 3-month intervals: (a) probability of rupture given a diameter of 50 mm; (b) probability of crossing the surgical intervention threshold given a diameter of 50 mm; estimates are posterior medians with 95% credible intervals
Mentions: Fig. 5 shows the probabilities of rupture and of crossing the intervention threshold, given d=50, for various values of the monitoring interval u. These are obtained straightforwardly by adapting the procedure that was outlined above for u=0.25. We can see that monitoring intervals of 9 months or less and 6 months or less respectively are required to be confident that the population median probabilities of rupture and of crossing the intervention threshold are below 1% and 10%. However, given the degree of between-study variation, it would seem inappropriate to use this as a basis for justifying a longer monitoring interval.

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