Meta-analysis Bayesian

There are now common practices in the analysis of safety data, though they are not necessarily the best. These are discussed in the remainder of this chapter, which seeks to review statistical methods on a use-by-use basis and to provide a foundation for the selection of alternatives in specific situations. Some of the newer available methodologies (meta-analysis and Bayesian approaches) should be kept in mind, however. 

Brophy JM, Joseph L, Rouleau JL. Beta-blockers in congestive heart failure a Bayesian meta-analysis. Ann Intern Med 2001 134(7) 550-60. 

K. Kinkel, Y. Lu, A. Mehdizade, M.-F. Pelte, FI. FlrRak, Indeterminate ovarian mass at US Incremental value of second imaging test for characterization Meta-analysis and Bayesian analysis, Radiol. 236 (2005) 85. 

Some of these difficulties could perhaps be overcome by Bayesian meta-analysis. In fact, any Bayesian analysis of clinical trials is, or ought to be, a meta-analysis. Yesterday s posterior becomes today s prior to which tomorrow s data are added. The result is a posterior which is available to serve as a prior for the day after tomorrow, and so on. This model can be represented schematically as P i P. With this model, there... 

However, Bayesians do commonly put a prior distribution on the treatment effect variance, that is the variance of the extent to which the true effect varies from trial to trial. The precision with which this is estimated depends largely on the number of trials in the meta-analysis. If this is large, then the Bayesian analysis is likely to produce similar results to the frequentist one. 

Bayesian Network Meta-Analysis for Safety Evaluation... 

Before presenting oin discussion, we present a brief and select overview of some relevant literature. Peto (1987) discusses some foimdational issues in systematic reviews of randomized trials for rare outcomes, in particular the need for such reviews and considerations of heterogeneity of the treatment effect. Hammad et al. (2011) present a thorough overview of the issues associated with the secondary use of randomized trials to evaluate safety. Bradbum et al. (2007) evaluate statistical meta-analysis methods for rare events. Kaizer et al. (2006) present an interesting example of a hierarchical Bayesian method for meta-analysis of safety. Crowe et al. (2009) provide recommendation for a premarket safety program. 

Kaizer E., Greenhouse J., Seltman H., Kelleher K. Do antidepressants cause suicidality in children A Bayesian meta-analysis. Clinical Trials, 2006 3 73-98. 

Application 2 Bayesian Survival Meta-Analysis Using... 

Bayesian piecewise exponential survival model can be utilized for Bayesian meta-analysis using IPD data [19,20]. 

A practical challenge of Bayesian meta-analysis for rare AE data is that noninformative priors may lead to convergence failure due to very sparse data. Weakly informative priors may be used to solve this issue. In the example of the previous Bayesian meta-analysis with piecewise exponential survival models, the following priors for log hazard ratio (HR) (see Table 14.1) were considered. Prior 1 assumes a nonzero treatment effect with a mean log(HR) of 0.7 and a standard deviation of 2. This roughly translates to that the 95% confidence interval (Cl) of HR is between 0.04 and 110, with an estimate of HR to be 2.0. Prior 2 assumes a 0 treatment effect, with a mean log(HR) of 0 and a standard deviation of 2. This roughly translates to the assumption that we are 95% sure that the HR for treatment effect is between 0.02 and 55, with an estimate of the mean hazard of 1.0. Prior 3 assumes a nonzero treatment effect that is more informative than that of Prior 1, with a mean log(HR) of 0.7 and a standard deviation of 0.7. This roughly translates to the assumption that we are 95% sure that the HR... 

Three Weakly Informative Prior Sp>ecifications for Bayesian Meta-Analysis... 

The use of Bayesian methods to conduct network meta-analysis is rapidly growing. For example, recent publications include the Evidence Synthesis Technical Support Documents series found on the website of the Decision Support Unit (DSU) of the National Institute for Health and Care Excellence [27]. The statistical methods used in these documents were primarily Bayesian, and WinBUGS was used as the main software platform for data analysis. The documents can be downloaded from the site http //www. nicedsu.org.uk/Evidence-Synthesis-TSD-series%282391675%29.htm. 

In general, the use of Bayesian network meta-analysis has broad applicability to evaluate AEs between related drugs. These methods can provide insight to prescribers and also assess cost-effectiveness. The direct probability statements that result from the Bayesian approach are helpful to decision makers evaluating a variety of medical products for a given therapeutic area/indication. Furthermore, the information obtained from the network meta-analysis can be utilized throughout the medical product development life cycle in simulations to design future clinical trials. 

Ohlssen D, Price KL, Xia HA, Hong H, Kerman J, Fu H, Quartey G, Heilmann CR, Ma H, and Carlin BP. 2014. Guidance on the implementation and reporting of a drug safety Bayesian network meta-analysis. Pharmaceutical Statistics 13(1) 55-70. 

Berry SM, Berry DA, Natarajan K, Hennekens CH, and Beider R. 2004. Bayesian survival analysis with nonproportional hazards Meta-analysis of combination pravastatin-aspirin. JASA 99 36-44. 

Covers several Bayesian approaches, including a meta-experimental design for evaluating cardiovascular risk, adaptive trials for drug safety, and network meta-analysis for safety evaluation... 

Frei KA, Kinkel K, Bonel HM, Lu Y, Zaloudek C, Hricak H (2000) Prediction of deep myometrial invasion in patients with endometrial cancer clinical utility of contrast-enhanced MR imaging - a meta-analysis and Bayesian analysis. Radiology 216 444-449... 

Death In a Bayesian meta-analysis of studies that had previously been included in meta-analyses of the relation between dose of vitamin E and all-cause mortality there was no evidence of an increases risk in those taking vitamin E [48 ]. The weaknesses of the Bayesian approach have been discussed [49 ], as have problems with other types of meta-analysis [50 ]. 

Berry D, Wathen JK, Newell M. Bayesian model averaging in meta-analysis vitamin E supplementation and mortality. Clin Trials 2009 6(1) 28-41. 

Evidence synthesis is a term used for synthesis of results from diverse sources and covers a wide range of analysis approaches (Sutton and Abrams, 2001). Bayesian Evidence Synthesis (here denoted as BES) is a statistical framework for exphcitly modeling several related and connected sources of data, in which uncertainty in model parameters are incorporated (Jackson et al., 2013). BES can be seen as a complex meta-analysis (Sutton and Abrams, 2001), where complex means to consider multiple effects from an intervention. Classical meta-analyses are usually based on studies that directly have observed the effect of an intervention. A broader view on meta-analyses allows for studies on effects on a lower level which are combined with quantitative modelling to assess the effect of an intervention on a higher level. In this view, a risk assessment can be seen as a meta-analysis (Linkov et al., 2009). Opening up for a quantitative assessment (or complex computer) model to measure effects, makes it possible to synthesize evidence for effects which are difficult, if at all, to empirically observe. In the PVA example, there is for example no possibility of... 

Sutton, A.J. Abrams, K.R. 2001. Bayesian methods in meta-analysis and evidence synthesis. Statistical Methods in Medical Research. 10, 277-303. 

Regardless of the method used, the basis of the final risk characterization must be explicit. All components and sources of evidence should be described. The explicit linkage between the analysis results and the assessment endpoints must be clearly but adequately stated. Tandem presentation of conventional methods (e.g., ad hoc weight of evidence) and formal methods (e.g., Bayesian, meta-anal-ysis) are recommended to enhance understanding. This is intended to facilitate acceptance of unfamiliar approaches, not to imply that the conventional methods are a touchstone. 

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