rma.peto(ai, bi, ci, di, n1i, n2i, data, slab, subset, add=1/2, to="only0", drop00=TRUE, level=95, digits=4, verbose=FALSE)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.escalc function for more details.add should be added (either "only0", "all", "if0all", or "none"). Can also be a character vector, where the first string again applies when calculating the observed outcomes and the second string when applying Peto's method. See below and the documentation of the escalc function for more details.NA). Can also be a vector of two logicals, where the first applies to the calculation of the observed outcomes and the second when applying Peto's method. See below and the documentation of the escalc function for more details.FALSE).c("rma.peto","rma"). The object is a list containing the following components:
print.rma.peto function. If fit statistics should also be given, use summary.rma (or use the fitstats.rma function to extract them).The residuals.rma, rstandard.rma.peto, and rstudent.rma.peto functions extract raw and standardized residuals. Leave-one-out diagnostics can be obtained with leave1out.rma.peto.Forest, funnel, radial, L'abbé, and Baujat plots can be obtained with forest.rma, funnel.rma, radial.rma, labbe.rma, and baujat.rma.peto. The qqnorm.rma.peto function provides normal QQ plots of the standardized residuals. One can also just call plot.rma.peto 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.peto.Other extractor functions include coef.rma, vcov.rma, logLik.rma, deviance.rma, AIC.rma, and BIC.rma.
Specifying the Data
The studies are assumed to provide data in terms of $2x2$ tables of the form:
| outcome 1 | outcome 2 | |
| total | group 1 | ai |
bi |
n1i |
ai, bi, ci, and di denote the cell frequencies and n1i and n2i the row totals. For example, in a set of randomized clinical trials (RCTs) or cohort studies, group 1 and group 2 may refer to the treatment (exposed) and placebo/control (not exposed) group, with outcome 1 denoting some event of interest (e.g., death) 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.Peto's Method
An approach for aggregating $2x2$ table data of this type was suggested by Peto (see Yusuf et al., 1985). The method provides a weighted estimate of the (log) odds ratio under a fixed-effects model. The method is particularly advantageous when the event of interest is rare, but it should only be used when the group sizes within the individual studies are not too dissimilar and effect sizes are generally small (Greenland & Salvan, 1990; Sweeting et al., 2004; Bradburn et al., 2007). Note that the printed results are given both in terms of the log and the raw units (for easier interpretation).
Observed Outcomes of the Individual Studies
Peto's method itself does not require the calculation of the observed (log) odds ratios of the individual studies 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 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 observed (log) odds ratios for the $k$ studies. 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 cell frequencies and under what circumstances when calculating the observed (log) odds ratios and when applying Peto's method. Similarly, the drop00 argument is used to specify how studies with no cases (or only cases) in both groups should be handled. The documentation of the escalc function explains how the add, to, and drop00 arguments work. If only a single value for these arguments is specified (as per default), then these values are used when calculating the observed (log) odds ratios and no adjustment to the cell counts is made when applying Peto's method. Alternatively, when specifying two values for these arguments, the first value applies when calculating the observed (log) odds ratios and the second value when applying Peto's method.
Note that drop00 is set to TRUE by default. Therefore, the observed (log) odds ratios for studies where ai=ci=0 or bi=di=0 are set to NA. When applying Peto's method, such studies are not explicitly dropped (unless the second value of drop00 argument is also set to TRUE), but this is practically not necessary, as they do not actually influence the results (assuming no adjustment to the cell/event counts are made when applying Peto's method).
Bradburn, M. J., Deeks, J. J., Berlin, J. A., & Localio, A. R. (2007). Much ado about nothing: A comparison of the performance of meta-analytical methods with rare events. Statistics in Medicine, 26, 53--77.
Greenland, S., & Salvan, A. (1990). Bias in the one-step method for pooling study results. Statistics in Medicine, 9, 247--252.
Sweeting, M. J., Sutton, A. J., & Lambert, P. C. (2004). What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data. Statistics in Medicine, 23, 1351--1375.
Yusuf, S., Peto, R., Lewis, J., Collins, R., & Sleight, P. (1985). Beta blockade during and after myocardial infarction: An overview of the randomized trials. Progress in Cardiovascular Disease, 27, 335--371.
Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. http://www.jstatsoft.org/v36/i03/.
rma.uni, rma.glmm, rma.mh, and rma.mv for other model fitting functions. dat.collins1985a, dat.collins1985b, and dat.yusuf1985 for further examples of the use of the rma.peto function.
### load data
data(dat.bcg)
### meta-analysis of the (log) odds ratios using Peto's method
rma.peto(ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
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