The functions repeatedly fit the specified model, adding one observation/study at a time to the model.

cumul(x, ...)

# S3 method for rma.uni
cumul(x, order, digits, transf, targs, progbar=FALSE, ...)
# S3 method for rma.mh
cumul(x, order, digits, transf, targs, progbar=FALSE, ...)
# S3 method for rma.peto
cumul(x, order, digits, transf, targs, progbar=FALSE, ...)

Arguments

x

an object of class "rma.mh", "rma.peto", "rma.uni".

order

optional vector with indices giving the desired order for the cumulative meta-analysis.

digits

integer specifying the number of decimal places to which the printed results should be rounded (if unspecified, the default is to take the value from the object).

transf

optional argument specifying the name of a function that should be used to transform the model coefficients and interval bounds (e.g., transf=exp; see also transf). If unspecified, no transformation is used.

targs

optional arguments needed by the function specified under transf.

progbar

logical indicating whether a progress bar should be shown (the default is FALSE).

...

other arguments.

Details

For "rma.uni" objects, the model specified by x must be a model without moderators (i.e., either a fixed- or a random-effects model).

Value

An object of class c("list.rma","cumul.rma"). The object is a list containing the following components:

estimate

estimated coefficients of the model.

se

standard errors of the coefficients.

zval

test statistics of the coefficients.

pval

p-values for the test statistics.

ci.lb

lower bounds of the confidence intervals for the coefficients.

ci.ub

upper bounds of the confidence intervals for the coefficients.

QE

test statistics for the tests of heterogeneity.

QEp

p-values for the tests of heterogeneity.

tau2

estimated amounts of (residual) heterogeneity (only for random-effects models).

I2

values of \(I^2\) (only for random-effects models).

H2

values of \(H^2\) (only for random-effects models).

The object is formatted and printed with print.list.rma. A forest plot showing the results from the cumulative meta-analysis can be obtained with forest.cumul.rma. For random-effects models, plot.cumul.rma can also be used to visualize the results.

Note

When using the transf option, the transformation is applied to the estimated coefficients and the corresponding interval bounds. The standard errors are then set equal to NA and are omitted from the printed output.

References

Chalmers, T. C., & Lau, J. (1993). Meta-analytic stimulus for changes in clinical trials. Statistical Methods in Medical Research, 2, 161--172.

Lau, J., Schmid, C. H., & Chalmers, T. C. (1995). Cumulative meta-analysis of clinical trials builds evidence for exemplary medical care. Journal of Clinical Epidemiology, 48, 45--57.

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/.

See also

Examples

### calculate log risk ratios and corresponding sampling variances dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg) ### random-effects model res <- rma(yi, vi, data=dat) ### cumulative meta-analysis (in the order of publication year) cumul(res, transf=exp, order=order(dat$year))
#> #> estimate zval pvals ci.lb ci.ub QE QEp tau2 I2 H2 #> 1 0.4109 -1.5586 0.1191 0.1343 1.2574 0.0000 1.0000 0.0000 0.0000 1.0000 #> 2 0.2658 -3.7967 0.0001 0.1341 0.5268 0.9315 0.3345 0.0000 0.0000 1.0000 #> 6 0.3783 -3.9602 0.0001 0.2338 0.6120 3.1879 0.2031 0.0872 40.7090 1.6866 #> 3 0.3675 -4.5037 0.0000 0.2377 0.5681 3.8614 0.2768 0.0763 33.9750 1.5146 #> 10 0.3324 -5.5164 0.0000 0.2248 0.4916 7.6415 0.1056 0.0858 48.4120 1.9384 #> 9 0.3778 -5.1875 0.0000 0.2615 0.5457 10.1854 0.0702 0.1046 60.0008 2.5000 #> 12 0.4061 -4.7250 0.0000 0.2794 0.5901 13.2116 0.0398 0.1205 59.9982 2.4999 #> 5 0.4545 -4.0039 0.0001 0.3089 0.6686 19.5749 0.0066 0.1780 72.3904 3.6219 #> 7 0.4208 -4.4107 0.0000 0.2864 0.6182 22.8208 0.0036 0.2023 73.5065 3.7745 #> 11 0.4560 -4.3588 0.0000 0.3204 0.6491 34.1203 0.0001 0.2005 81.4029 5.3772 #> 13 0.4925 -3.9701 0.0001 0.3472 0.6987 39.6122 0.0000 0.2281 83.0110 5.8862 #> 4 0.4517 -4.4184 0.0000 0.3175 0.6426 67.9858 0.0000 0.2732 87.0314 7.7109 #> 8 0.4894 -3.9744 0.0001 0.3441 0.6962 152.2330 0.0000 0.3132 92.2214 12.8558 #>
### meta-analysis of the (log) risk ratios using the Mantel-Haenszel method res <- rma.mh(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg) ### cumulative meta-analysis cumul(res, order=order(dat.bcg$year))
#> #> estimate se zval pval ci.lb ci.ub QE QEp #> 1 -0.8893 0.5706 -1.5586 0.1191 -2.0077 0.2290 0.0000 1.0000 #> 2 -1.3517 0.3455 -3.9124 0.0001 -2.0289 -0.6746 0.9373 0.3330 #> 6 -0.8273 0.0808 -10.2371 0.0000 -0.9857 -0.6689 3.2109 0.2008 #> 3 -0.8379 0.0802 -10.4490 0.0000 -0.9951 -0.6807 3.8945 0.2731 #> 10 -0.8940 0.0769 -11.6254 0.0000 -1.0447 -0.7433 7.7589 0.1008 #> 9 -0.8507 0.0730 -11.6480 0.0000 -0.9938 -0.7075 10.2660 0.0680 #> 12 -0.8358 0.0725 -11.5275 0.0000 -0.9779 -0.6937 13.2768 0.0388 #> 5 -0.7744 0.0688 -11.2623 0.0000 -0.9092 -0.6397 19.6127 0.0065 #> 7 -0.7896 0.0680 -11.6188 0.0000 -0.9228 -0.6564 22.8443 0.0036 #> 11 -0.6660 0.0577 -11.5373 0.0000 -0.7792 -0.5529 34.1377 0.0001 #> 13 -0.6351 0.0563 -11.2811 0.0000 -0.7454 -0.5247 39.6232 0.0000 #> 4 -0.7758 0.0520 -14.9267 0.0000 -0.8777 -0.6739 68.3763 0.0000 #> 8 -0.4537 0.0393 -11.5338 0.0000 -0.5308 -0.3766 152.5676 0.0000 #>
cumul(res, order=order(dat.bcg$year), transf=TRUE)
#> #> estimate zval pval ci.lb ci.ub QE QEp #> 1 0.4109 -1.5586 0.1191 0.1343 1.2574 0.0000 1.0000 #> 2 0.2588 -3.9124 0.0001 0.1315 0.5094 0.9373 0.3330 #> 6 0.4372 -10.2371 0.0000 0.3732 0.5123 3.2109 0.2008 #> 3 0.4326 -10.4490 0.0000 0.3697 0.5062 3.8945 0.2731 #> 10 0.4090 -11.6254 0.0000 0.3518 0.4756 7.7589 0.1008 #> 9 0.4271 -11.6480 0.0000 0.3702 0.4929 10.2660 0.0680 #> 12 0.4335 -11.5275 0.0000 0.3761 0.4997 13.2768 0.0388 #> 5 0.4610 -11.2623 0.0000 0.4028 0.5275 19.6127 0.0065 #> 7 0.4540 -11.6188 0.0000 0.3974 0.5187 22.8443 0.0036 #> 11 0.5138 -11.5373 0.0000 0.4588 0.5753 34.1377 0.0001 #> 13 0.5299 -11.2811 0.0000 0.4745 0.5917 39.6232 0.0000 #> 4 0.4603 -14.9267 0.0000 0.4158 0.5097 68.3763 0.0000 #> 8 0.6353 -11.5338 0.0000 0.5881 0.6862 152.5676 0.0000 #>
### meta-analysis of the (log) odds ratios using Peto's method res <- rma.mh(ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg) ### cumulative meta-analysis cumul(res, order=order(dat.bcg$year))
#> #> estimate se zval pval ci.lb ci.ub QE QEp #> 1 -0.9387 0.5976 -1.5708 0.1162 -2.1100 0.2326 0.0000 1.0000 #> 2 -1.4215 0.3595 -3.9539 0.0001 -2.1261 -0.7169 0.9404 0.3322 #> 6 -0.9968 0.0957 -10.4137 0.0000 -1.1844 -0.8092 2.3134 0.3145 #> 3 -1.0061 0.0947 -10.6259 0.0000 -1.1917 -0.8205 2.6721 0.4450 #> 10 -1.0542 0.0893 -11.8020 0.0000 -1.2293 -0.8792 4.6200 0.3286 #> 9 -0.9846 0.0835 -11.7978 0.0000 -1.1482 -0.8211 9.5987 0.0874 #> 12 -0.9652 0.0827 -11.6734 0.0000 -1.1273 -0.8032 13.3029 0.0385 #> 5 -0.8805 0.0775 -11.3644 0.0000 -1.0323 -0.7286 22.4178 0.0022 #> 7 -0.8957 0.0766 -11.6965 0.0000 -1.0457 -0.7456 24.9324 0.0016 #> 11 -0.7286 0.0624 -11.6815 0.0000 -0.8508 -0.6063 41.0143 0.0000 #> 13 -0.6914 0.0607 -11.3982 0.0000 -0.8103 -0.5725 47.3437 0.0000 #> 4 -0.8333 0.0552 -15.0934 0.0000 -0.9415 -0.7251 73.1329 0.0000 #> 8 -0.4734 0.0410 -11.5444 0.0000 -0.5538 -0.3930 163.9426 0.0000 #>
cumul(res, order=order(dat.bcg$year), transf=TRUE)
#> #> estimate zval pval ci.lb ci.ub QE QEp #> 1 0.3911 -1.5708 0.1162 0.1212 1.2619 0.0000 1.0000 #> 2 0.2414 -3.9539 0.0001 0.1193 0.4883 0.9404 0.3322 #> 6 0.3691 -10.4137 0.0000 0.3059 0.4452 2.3134 0.3145 #> 3 0.3656 -10.6259 0.0000 0.3037 0.4402 2.6721 0.4450 #> 10 0.3485 -11.8020 0.0000 0.2925 0.4151 4.6200 0.3286 #> 9 0.3736 -11.7978 0.0000 0.3172 0.4400 9.5987 0.0874 #> 12 0.3809 -11.6734 0.0000 0.3239 0.4479 13.3029 0.0385 #> 5 0.4146 -11.3644 0.0000 0.3562 0.4826 22.4178 0.0022 #> 7 0.4083 -11.6965 0.0000 0.3514 0.4745 24.9324 0.0016 #> 11 0.4826 -11.6815 0.0000 0.4271 0.5454 41.0143 0.0000 #> 13 0.5009 -11.3982 0.0000 0.4447 0.5641 47.3437 0.0000 #> 4 0.4346 -15.0934 0.0000 0.3901 0.4843 73.1329 0.0000 #> 8 0.6229 -11.5444 0.0000 0.5748 0.6750 163.9426 0.0000 #>