OverviewReview of unstandardized coefficientsInterpretation of standardized coefficientsDescriptive statistics for multivariate models with standardized coefficientsThe Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
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.
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.
The availability of a free software MetaXL  that runs the IVhet model and all other models for comparison facilitates this for the research community.
Models incorporating additional information[ edit ] Quality effects model[ edit ] Doi and Thalib originally introduced the quality effects model.
The strength of the quality effects meta-analysis is that it allows available methodological evidence to be used over subjective random effects, and thereby helps to close the damaging gap which has opened up between methodology and statistics in clinical research.
To do this a synthetic bias variance is computed based on quality information to adjust inverse variance weights and the quality adjusted weight of the ith study is introduced.The Chicago Guide to Writing about Multivariate Analysis is the book researchers turn to when looking for guidance on how to clearly present statistical results and break through the jargon that often clouds writing about applications of statistical analysis.
The Chicago Guide to Writing about Multivariate Analysis, Second Edition (Chicago Guides to Writing, Editing, and Publishing) The Chicago Guide to Writing about Multivariate Analysis, Second Edition (Chicago Guides to Writing, Editing, and Publishing). The Chicago Guide to Writing about Multivariate Analysis is the book researchers turn to when looking for guidance on how to clearly present statistical results and break through the jargon that often clouds writing about applications of statistical analysis.
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