Cumulative Meta-Analysis for 'rma' Objects

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.

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.

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).

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

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/.

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 
#>