Print and Summary Methods for 'escalc' Objects

Function to print objects of class "escalc" (and to obtain inferences for the individual studies/rows in such an object).

# S3 method for escalc
print(x, digits=attr(x,"digits"), ...)

# S3 method for escalc
summary(object, out.names=c("sei","zi","pval","ci.lb","ci.ub"), var.names,
        H0=0, append=TRUE, replace=TRUE, level=95, olim, digits, transf, ...)

Arguments

x: an object of class "escalc" obtained with escalc.
object: an object of class "escalc" obtained with escalc.
digits: integer to specify the number of decimal places to which the printed results should be rounded (the default is to take the value from the object).
out.names: character string with four elements to specify the variable names for the standard errors, test statistics, and lower/upper confidence interval bounds.
var.names: character string with two elements to specify the variable names for the observed effect sizes or outcomes and the sampling variances (the default is to take the value from the object if possible).
H0: numeric value to specify the value of the effect size or outcome under the null hypothesis (the default is 0).
append: logical to specify whether the data frame specified via the object argument should be returned together with the additional variables that are calculated by the summary function (the default is TRUE).
replace: logical to specify whether existing values for sei, zi, ci.lb, and ci.ub in the data frame should be replaced. Only relevant when the data frame already contains these variables. If replace=TRUE (the default), all of the existing values will be overwritten. If replace=FALSE, only NA values will be replaced.
level: numeric value between 0 and 100 to specify the confidence interval level (the default is 95; see here for details).
olim: optional argument to specify observation/outcome limits. If unspecified, no limits are used.
transf: optional argument to specify a function to transform the observed effect sizes or outcomes and interval bounds (e.g., transf=exp; see also transf). If unspecified, no transformation is used. Any additional arguments needed for the function specified here can be passed via ....
...: other arguments.

Value

The print.escalc function formats and prints the data frame, so that the observed effect sizes or outcomes and sampling variances are rounded (to the number of digits specified).

The summary.escalc function creates an object that is a data frame containing the original data (if append=TRUE) and the following components:

yi: observed effect sizes or outcomes (transformed if transf is specified).
vi: corresponding sampling variances.
sei: corresponding standard errors.
zi: test statistics for testing \(\mbox{H}_0{:}\; \theta_i = \mbox{H0}\) (i.e., (yi-H0)/sei).
pval: corresponding p-values.
ci.lb: lower confidence interval bounds (transformed if transf is specified).
ci.ub: upper confidence interval bounds (transformed if transf is specified).

When the transf argument is specified, elements vi, sei, zi, and pval are not included (since these only apply to the untransformed effect sizes or outcomes).

Note that the actual variable names above depend on the out.names (and var.names) arguments. If the data frame already contains variables with names as specified by the out.names argument, the values for these variables will be overwritten when replace=TRUE (which is the default). By setting replace=FALSE, only values that are NA will be replaced.

The print.escalc function again formats and prints the data frame, rounding the added variables to the number of digits specified.

Note

If some transformation function has been specified for the transf argument, then yi, ci.lb, and ci.ub will be transformed accordingly. However, vi and sei then still reflect the sampling variances and standard errors of the untransformed values.

The summary.escalc function computes level% Wald-type confidence intervals, which may or may not be the most accurate method for computing confidence intervals for the chosen effect size or outcome measure.

If the outcome measure used is bounded (e.g., correlations are bounded between -1 and +1, proportions are bounded between 0 and 1), one can use the olim argument to enforce those observation/outcome limits (the observed outcomes and confidence intervals cannot exceed those bounds then).

Author

Wolfgang Viechtbauer wvb@metafor-project.org https://www.metafor-project.org

References

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. https://doi.org/10.18637/jss.v036.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)
dat
#> 
#>    trial               author year tpos  tneg cpos  cneg ablat      alloc      yi     vi 
#> 1      1              Aronson 1948    4   119   11   128    44     random -0.8893 0.3256 
#> 2      2     Ferguson & Simes 1949    6   300   29   274    55     random -1.5854 0.1946 
#> 3      3      Rosenthal et al 1960    3   228   11   209    42     random -1.3481 0.4154 
#> 4      4    Hart & Sutherland 1977   62 13536  248 12619    52     random -1.4416 0.0200 
#> 5      5 Frimodt-Moller et al 1973   33  5036   47  5761    13  alternate -0.2175 0.0512 
#> 6      6      Stein & Aronson 1953  180  1361  372  1079    44  alternate -0.7861 0.0069 
#> 7      7     Vandiviere et al 1973    8  2537   10   619    19     random -1.6209 0.2230 
#> 8      8           TPT Madras 1980  505 87886  499 87892    13     random  0.0120 0.0040 
#> 9      9     Coetzee & Berjak 1968   29  7470   45  7232    27     random -0.4694 0.0564 
#> 10    10      Rosenthal et al 1961   17  1699   65  1600    42 systematic -1.3713 0.0730 
#> 11    11       Comstock et al 1974  186 50448  141 27197    18 systematic -0.3394 0.0124 
#> 12    12   Comstock & Webster 1969    5  2493    3  2338    33 systematic  0.4459 0.5325 
#> 13    13       Comstock et al 1976   27 16886   29 17825    33 systematic -0.0173 0.0714 
#> 

### apply summary function
summary(dat)
#> 
#>    trial               author year tpos  tneg cpos  cneg ablat      alloc      yi     vi    sei 
#> 1      1              Aronson 1948    4   119   11   128    44     random -0.8893 0.3256 0.5706 
#> 2      2     Ferguson & Simes 1949    6   300   29   274    55     random -1.5854 0.1946 0.4411 
#> 3      3      Rosenthal et al 1960    3   228   11   209    42     random -1.3481 0.4154 0.6445 
#> 4      4    Hart & Sutherland 1977   62 13536  248 12619    52     random -1.4416 0.0200 0.1415 
#> 5      5 Frimodt-Moller et al 1973   33  5036   47  5761    13  alternate -0.2175 0.0512 0.2263 
#> 6      6      Stein & Aronson 1953  180  1361  372  1079    44  alternate -0.7861 0.0069 0.0831 
#> 7      7     Vandiviere et al 1973    8  2537   10   619    19     random -1.6209 0.2230 0.4722 
#> 8      8           TPT Madras 1980  505 87886  499 87892    13     random  0.0120 0.0040 0.0629 
#> 9      9     Coetzee & Berjak 1968   29  7470   45  7232    27     random -0.4694 0.0564 0.2376 
#> 10    10      Rosenthal et al 1961   17  1699   65  1600    42 systematic -1.3713 0.0730 0.2702 
#> 11    11       Comstock et al 1974  186 50448  141 27197    18 systematic -0.3394 0.0124 0.1114 
#> 12    12   Comstock & Webster 1969    5  2493    3  2338    33 systematic  0.4459 0.5325 0.7297 
#> 13    13       Comstock et al 1976   27 16886   29 17825    33 systematic -0.0173 0.0714 0.2672 
#>          zi   pval   ci.lb   ci.ub 
#> 1   -1.5586 0.1191 -2.0077  0.2290 
#> 2   -3.5941 0.0003 -2.4500 -0.7208 
#> 3   -2.0917 0.0365 -2.6113 -0.0849 
#> 4  -10.1908 <.0001 -1.7188 -1.1643 
#> 5   -0.9613 0.3364 -0.6611  0.2260 
#> 6   -9.4599 <.0001 -0.9490 -0.6232 
#> 7   -3.4323 0.0006 -2.5465 -0.6953 
#> 8    0.1899 0.8494 -0.1114  0.1353 
#> 9   -1.9760 0.0482 -0.9350 -0.0038 
#> 10  -5.0747 <.0001 -1.9010 -0.8417 
#> 11  -3.0460 0.0023 -0.5577 -0.1210 
#> 12   0.6111 0.5412 -0.9843  1.8762 
#> 13  -0.0648 0.9483 -0.5410  0.5064 
#> 
summary(dat, transf=exp)
#> 
#>    trial               author year tpos  tneg cpos  cneg ablat      alloc     yi  ci.lb  ci.ub 
#> 1      1              Aronson 1948    4   119   11   128    44     random 0.4109 0.1343 1.2574 
#> 2      2     Ferguson & Simes 1949    6   300   29   274    55     random 0.2049 0.0863 0.4864 
#> 3      3      Rosenthal et al 1960    3   228   11   209    42     random 0.2597 0.0734 0.9186 
#> 4      4    Hart & Sutherland 1977   62 13536  248 12619    52     random 0.2366 0.1793 0.3121 
#> 5      5 Frimodt-Moller et al 1973   33  5036   47  5761    13  alternate 0.8045 0.5163 1.2536 
#> 6      6      Stein & Aronson 1953  180  1361  372  1079    44  alternate 0.4556 0.3871 0.5362 
#> 7      7     Vandiviere et al 1973    8  2537   10   619    19     random 0.1977 0.0784 0.4989 
#> 8      8           TPT Madras 1980  505 87886  499 87892    13     random 1.0120 0.8946 1.1449 
#> 9      9     Coetzee & Berjak 1968   29  7470   45  7232    27     random 0.6254 0.3926 0.9962 
#> 10    10      Rosenthal et al 1961   17  1699   65  1600    42 systematic 0.2538 0.1494 0.4310 
#> 11    11       Comstock et al 1974  186 50448  141 27197    18 systematic 0.7122 0.5725 0.8860 
#> 12    12   Comstock & Webster 1969    5  2493    3  2338    33 systematic 1.5619 0.3737 6.5284 
#> 13    13       Comstock et al 1976   27 16886   29 17825    33 systematic 0.9828 0.5821 1.6593 
#>