Bayesian statistics meta analysis

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. 

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. 

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. 

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. 

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. 

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