Meta-analysis statistical method

Fleiss JF (1993) The statistical basis of meta-analysis Statistical Methods in Medical Research, 2, 121-145... 

The article that follows is a controversial one. It reaches a controversial conclusion - that much of the therapeutic benefit of antidepressant medications actually derives from placebo responding. The article reaches this conclusion by utilizing a controversial statistical approach - meta-analysis. And it employs meta-analysis controversially - by meta-analysing studies that are very heterogeneous in subject selection criteria, treatments employed, and statistical methods used. Nonetheless, we have chosen to publish the article. We have done so because a number of the colleagues who originally reviewed the manuscript believed it had considerable merit, even while they recognized the clearly contentious conclusions it... 

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. 

Meta-analysis aims to increase the statistical power of the available evidence by combining the results of smaller trials together using specific statistical methods. The validity of the meta-analysis will depend on the quality of the evidence on which it is based and how homogeneous or comparable the samples are. Combining very heterogeneous study populations can lead to bias. 

In simple terms, meta-analysis is the practice of using statistical methods to combine and quantify the outcomes of a series of studies in a single, pooled analysis. What is crucial in this definition is the emphasis on the use of statistical methods. In most biomedical research, the scientific review has a lengthy history and is still widely used. However, insofar that it does not utilise statistical methods for pooling results, and tends to summarise more in qualitative rather than quantitative terms it cannot be regarded as meta-analysis. 

Methods of statistical meta-analysis may be useful for combining information across studies. There are 2 principal varieties of meta-analytic estimation (Normand 1995). In a hxed-effects analysis the observed variation among estimates is attributable to the statistical error associated with the individual estimates. An important step is to compute a weighted average of unbiased estimates, where the weight for an estimate is computed by means of its standard error estimate. In a random-effects analysis one allows for additional variation, beyond statistical error, making use of a htted random-effects model. 

The correct statistical methods for combining data in meta-analysis -the summary statistics that are combined must come from independent data sets... 

Meta-analysis is a statistical method that combines data from individual drug studies to obtain a quantitative summary of their results. This statistical approach includes the following ... 

The results of the seven studies were analyzed using the statistical method of meta-analysis. Homogeneity of the studies was checked with an appropriate statistical test, while combined Pearson correlation coefficients were estimated with four different methods. The main findings were ... 

More innovative methods for examining relationships between individual LOE for the SQT include quantitative estimation of probability derived from odds ratio (Smith et al., 2002) and meta-analysis resulting in pooled, empirically derived P-values (Bailer et al., 2002). Comparison of odds ratio and meta-analysis with PCA for clustering sites into groups of similar impact (Reynoldson et al., 2002a) revealed similarities and differences. The differences between the three methods (PCA, odds ratio and meta-analysis) were ascribed to three factors, which almost certainly apply to all integrations the variables selected the manner in which information is combined within a LOE and, the statistical methodology employed. 

The collecting together of a number of trials with the same objective in a systematic revieuF and analysing the accumulated results using appropriate statistical methods is termed meta-analysis. The principles of a meta-analysis are that... 

Hedges, L.V., and I. Olkin. 1985. Statistical Methods for Meta-Analysis. Orlando, FL Academic Press. 

Hedges L, Olkin I (1985) Statistical Method for Meta-analysis. Academic Press, Orlando. 

Thompson SG (1993) Controversies in meta-analysis the case of the trials of serum cholesterol reduction. Statistical Methods in Medical Research 2 173-192. 

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. 

There are important statistical considerations in meta-analyses for the evaluation of safety. In particular, statistical methods must be valid in the presence of sparse data. As discussed previously, safety outcomes may be infrequent. Some trials may not have any relevant events. We refer to these trials as zero-event trials. The statistical methods should provide estimates with good bias properties and with valid standard errors and confidence intervals in the presence of low event coimts and zero-event trials. In any meta-analysis, the overall estimator and associated standard errors and confidence intervals should be stratified by the trials. Simple pooling of data across the trials can result in misleading results because of Simspon s paradox. With stratification, the randomize comparisons within trials are maintained. 

The meta-analysis employed a prespecified analysis plan, which specified trial inclusion criteria, hypotheses, outcome definitions, analysis methods, sensitivity analyses, and subgroups. The trial inclusion criteria and the outcome definitions have already been discussed. The primary analysis method stratified by trial and accounted for the sparse nature of the outcome events by using exact statistical methods. The sensitivity analysis examined the possibility and consequences of the following differential exposure time between the randomized treatment arms, heterogeneity of the effect measure across the trials, and trials with no events (FDA 2006). The patient-level data allowed for the examination of important subgroups, including patient age, and for the examination of changing risk over time. 

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. 

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