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Approaches[ edit ] In general, two types of evidence can be distinguished when performing a meta-analysis: The aggregate data can be direct or indirect. AD is more commonly available e. This can be directly synthesized across conceptually similar studies using several approaches see below.
On the other hand, indirect aggregate data measures the effect of two treatments that were each compared against a similar control group in a meta-analysis. For example, if treatment A and treatment B were directly compared vs placebo in separate meta-analyses, we can use these two pooled results to get an estimate of the effects of A vs B in an indirect comparison as effect A vs Placebo minus effect B vs Placebo.
IPD evidence represents raw data as collected by the study centers. This distinction has raised the need for different meta-analytic methods when evidence synthesis is desired, and has led to the development of one-stage and two-stage methods. Two-stage methods first compute summary statistics for AD from each study and then calculate overall statistics as a weighted average of the study statistics.
By reducing IPD to AD, two-stage methods can also be applied when IPD is available; this makes them an appealing choice when performing a meta-analysis. Although it is conventionally believed that one-stage and two-stage methods yield similar results, recent studies have shown that they may occasionally lead to different conclusions.
Models incorporating study effects only[ edit ] Fixed effects model[ edit ] The fixed effect model provides a weighted average of a series of study estimates.
The inverse of the estimates' variance is commonly used as study weight, so that larger studies tend to contribute more than smaller studies to the weighted average.
Consequently, when studies within a meta-analysis are dominated by a very large study, the findings from smaller studies are practically ignored. This assumption is typically unrealistic as research is often prone to several sources of heterogeneity; e. Random effects model[ edit ] A common model used to synthesize heterogeneous research is the random effects model of meta-analysis.
This is simply the weighted average of the effect sizes of a group of studies. The weight that is applied in this process of weighted averaging with a random effects meta-analysis is achieved in two steps: Inverse variance weighting Step 2: Un-weighting of this inverse variance weighting by applying a random effects variance component REVC that is simply derived from the extent of variability of the effect sizes of the underlying studies.
This means that the greater this variability in effect sizes otherwise known as heterogeneitythe greater the un-weighting and this can reach a point when the random effects meta-analysis result becomes simply the un-weighted average effect size across the studies.
At the other extreme, when all effect sizes are similar or variability does not exceed sampling errorno REVC is applied and the random effects meta-analysis defaults to simply a fixed effect meta-analysis only inverse variance weighting.
The extent of this reversal is solely dependent on two factors: Indeed, it has been demonstrated that redistribution of weights is simply in one direction from larger to smaller studies as heterogeneity increases until eventually all studies have equal weight and no more redistribution is possible.
One interpretational fix that has been suggested is to create a prediction interval around the random effects estimate to portray the range of possible effects in practice. These advanced methods have also been implemented in a free and easy to use Microsoft Excel add-on, MetaEasy.
Thus it appears that in small meta-analyses, an incorrect zero between study variance estimate is obtained, leading to a false homogeneity assumption. Overall, it appears that heterogeneity is being consistently underestimated in meta-analyses and sensitivity analyses in which high heterogeneity levels are assumed could be informative.
The authors state that a clear advantage of this model is that it resolves the two main problems of the random effects model. When heterogeneity becomes large, the individual study weights under the RE model become equal and thus the RE model returns an arithmetic mean rather than a weighted average.
This side-effect of the RE model does not occur with the IVhet model which thus differs from the RE model estimate in two perspectives: The latter study also reports that the IVhet model resolves the problems related to underestimation of the statistical error, poor coverage of the confidence interval and increased MSE seen with the random effects model and the authors conclude that researchers should henceforth abandon use of the random effects model in meta-analysis.
While their data is compelling, the ramifications in terms of the magnitude of spuriously positive results within the Cochrane database are huge and thus accepting this conclusion requires careful independent confirmation.USDA Super Tracker website was shut down June 30, For current users of Super Tracker, My Food Record would be an excellent alternative website .
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