rma.mh(ai, bi, ci, di, n1i, n2i, data,
slab=NULL, subset=NULL, measure="OR",
add=c(1/2,0), to=c("only0","none"), level=95, digits=4)escalc function for more details.escalc function for more details.escalc function for more details.escalc function for more details.escalc function for more details.escalc function for more details."OR"), relative risk ("RR"), or risk difference ("RD").add should be added. When set to "all", the value of add is added to each cell of the 2x2 tables in all $k$ tables. When set to "only0"c("rma.mh","rma"). The object is a list containing the following components:measure="OR").measure="OR").measure="OR").measure="OR").print.rma.mh function. If you also want the fit statistics, use summary.rma (or use the fitstats.rma function to extract them).
The residuals.rma, rstandard.rma.mh, and rstudent.rma.mh functions extract raw and standardized residuals. Leave-one-out diagnostics can be obtained with leave1out.rma.mh.
Forest, funnel, and radial plots of the individual outcomes can be obtained with forest.rma, funnel.rma, and radial.rma. The qqnorm.rma.mh function provides a normal QQ plot of the standardized residuals. One can also just call plot.rma.mh on the fitted model object to obtain various plots at once.
A cumulative meta-analysis (i.e., adding one obervation at a time) can be obtained with cumul.rma.mh.
Other assessor functions include coef.rma, vcov.rma, logLik.rma, deviance.rma, AIC.rma, and BIC.rma.ai bi n1i
group 2 ci di n2i
}
where ai, bi, ci, and di denote the cell frequencies and n1i and n2i the row totals. For example, in a set of RCTs, group 1 and group 2 may refer to the treatment and placebo group, with outcome 1 denoting some event of interest and outcome 2 its complement. In a set of case-control studies, group 1 and group 2 may refer to the group of cases and the group of controls, with outcome 1 denoting, for example, exposure to some risk factor and outcome 2 non-exposure.
An approach for aggregating 2x2 table data of this type was suggested by Mantel and Haenszel (1959), which can be used in combination with the odds ratio, relative risk, or risk difference (measure="OR", "RR", or "RD"). The Mantel-Haenszel method provides a weighted estimate under a fixed-effects model. The method is particularly advantageous when aggregating a large number of tables with small sample sizes (the so-called sparse data or increasing strata case). When analyzing odds ratios, the Cochran-Mantel-Haenszel test and Tarone's test for heterogeneity are also provided. When analyzing odds ratios or relative risks, the printed results are given both in terms of the log and the raw units (for easier interpretation).
The Mantel-Haenszel method itself does not require the calculation of the individual outcome values and directly makes use of the 2x2 table counts. Zero cells are not a problem (except in extreme cases, such as when one of the two outcomes never occurs in any of the tables). Therefore, it is also unnecessary to add some constant to the cell counts when there are zero cells. However, for plotting and various other functions, it is necessary to calculate the individual outcome values for the $k$ tables. Here, zero cells can be problematic, so adding a constant value to the cell counts ensures that all $k$ values can be calculated. The add and to arguments are used to specify what value should be added to the 2x2 cell frequencies and under what circumstances when calculating the individual outcome values and when applying the Mantel-Haenszel method.### load BCG vaccine data
data(dat.bcg)
### meta-analysis of the (log) odds ratios using the Mantel-Haenszel method
rma.mh(ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg, measure="OR")
### meta-analysis of the (log) relative risks using the Mantel-Haenszel method
rma.mh(ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg, measure="RR")Run the code above in your browser using DataLab