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Publication bias in meta-analysis. In Publication bias in meta-analysis: Prevention, assessment and adjustments pp.
Schwarzer, G. Meta: Meta-analysis with R. R package version 3. The purpose of meta-analysis is to combine individual estimates of treatment effect or effect sizes ESs across studies.
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If estimates of the treatment effect or effect size are not provided for the individual studies but the number of patients who respond to treatment are provided as in this example , it is possible to calculate the effect size for each study and to subsequently pool the estimated effect sizes across all of the studies in a meta-analysis. For binomial outcome measures, such as response to treatment versus non-response to treatment, the most commonly use estimator of effect size is the risk-ratio.
The risk-ratios for the studies included in the MA of the effectiveness of lamotrigine are defined as:. The method of estimating the variance of this risk ratio is based on the normal distribution approximation; the RR is transformed using the natural logarithm and the variance of the natural log of RR is estimated using the delta method:.
Subsequently, the point estimate for ln RR and the corresponding confidence intervals are transformed back to RR and the confidence interval for RR. When conducting the MA using R, data from column 1 to 5 in Figure 1 would first be loaded into R as:. The printout for this coding would be as follows:.
The first four trials are not statistically significant i. The last part of the summary first quantifies the level of heterogeneity of the included studies and then tests whether or not there is statistically significant heterogeneity. The Q statistic only assesses the presence or absence of heterogeneity.
For any MA, a forest plot is typically produced for summary and publication purposes. The risk-ratio is probably the most commonly used measure of ES in MA for binomial data, but other measures of ES include the risk-difference and oddsratio. The statistical inference for RD is to test whether this RD is statistically significant different from zero. The odds-ratio OR , which is familiar because of its use in logistic regression, is intuitively less appealing than the RR or RD. The odds-ratio OR associated with an event is defined as the ratio of the odds of the event in one study group to the odds of the event in another study group.
The odds of the event is defined as:. Thus the odds-ratio OR of the treatment group such as, lamotrigine to the control group for kth study can be formulated as follows:.
The statistical inference for the OR in meta-analysis is usually conducted by converting the odds-ratio to the log scale and estimating the log odds-ratio and its standard error based on an approximate normal distribution. The implementation of these alternative methods for estimated ES in R is very straightforward. Ding-Geng Din Chen received his Ph. Professor Chen was a professor in biostatistics at the University of Rochester from to and the Karl E. Professor Chen is also a senior biostatistics consultant for biopharmaceuticals and government agencies with extensive expertise in clinical trials and bioinformatics.
Conflict of interest: The author declares that he has no conflicts of interest.
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National Center for Biotechnology Information , U. Journal List Shanghai Arch Psychiatry v. Shanghai Arch Psychiatry. Author information Article notes Copyright and License information Disclaimer. Received May 29; Accepted Jun This article has been cited by other articles in PMC.
Abstract Summary This paper provides a brief overview of meta-analysis MA with emphasis on classical fixedeffects and random-effects MA models. Keywords: meta-analysis, fixed-effects model, random-effects model, bipolar disorder, lamotrigine.