Severity of publication bias needed to "explain away" resultsSource:
Estimates the S-value, defined as the severity of publication bias (i.e., the
ratio by which affirmative studies are more likely to be published than
nonaffirmative studies) that would be required to shift the pooled point
estimate or its confidence interval limit to the value
pubbias_svalue( yi, vi, sei, cluster = 1:length(yi), q = 0, model_type = "robust", favor_positive = TRUE, alpha_select = 0.05, ci_level = 0.95, small = TRUE, selection_ratio_max = 200, return_worst_meta = FALSE ) svalue( yi, vi, q, clustervar = 1:length(yi), model, alpha.select = 0.05, eta.grid.hi = 200, favor.positive, CI.level = 0.95, small = TRUE, return.worst.meta = FALSE )
A vector of point estimates to be meta-analyzed.
A vector of estimated variances (i.e., squared standard errors) for the point estimates.
A vector of estimated standard errors for the point estimates. (Only one of
seineeds to be specified).
Vector of the same length as the number of rows in the data, indicating which cluster each study should be considered part of (defaults to treating studies as independent; i.e., each study is in its own cluster).
The attenuated value to which to shift the point estimate or CI. Should be specified on the same scale as
yiis on the log-RR scale, then
qshould be as well).
"fixed" for fixed-effects (a.k.a. "common-effect") or "robust" for robust random-effects.
TRUEif publication bias are assumed to favor significant positive estimates;
FALSEif assumed to favor significant negative estimates.
Alpha level at which an estimate's probability of being favored by publication bias is assumed to change (i.e., the threshold at which study investigators, journal editors, etc., consider an estimate to be significant).
Confidence interval level (as proportion) for the corrected point estimate. (The alpha level for inference on the corrected point estimate will be calculated from
Should inference allow for a small meta-analysis? We recommend always using
The largest value of
selection_ratiothat should be included in the grid search. This argument is only needed when
model_type = "robust".
Should the worst-case meta-analysis of only the nonaffirmative studies be returned?
(deprecated) see cluster
(deprecated) see model_type
(deprecated) see alpha_select
(deprecated) see selection_ratio_max
(deprecated) see favor_positive
(deprecated) see ci_level
(deprecated) see return_worst_meta
An object of class
metabias::metabias(), a list containing:
A tibble with one row per study and the columns
A list with the elements
A tibble with the columns
sval_estrepresents the amount of publication bias required to attenuate the pooled point estimate to
sval_cirepresents the amount of publication bias required to attenuate the confidence interval limit of the pooled point estimate to
A list of fitted models, if any.
To illustrate interpretation of the S-value, if the S-value for the
point estimate is 30 with
q=0, this indicates that affirmative studies
(i.e., those with a "statistically significant" and positive estimate)
would need to be 30-fold more likely to be published than nonaffirmative
studies (i.e., those with a "nonsignificant" or negative estimate) to
attenuate the pooled point estimate to
favor_positive = FALSE, such that publication bias is assumed to favor
negative rather than positive estimates, the signs of
yi will be reversed
prior to performing analyses. The returned number of affirmative and
nonaffirmative studies will reflect the recoded signs.
return_worst_meta = TRUE, also returns the worst-case meta-analysis of
only the nonaffirmative studies. If
model_type = "fixed", the worst-case
meta-analysis is fit by
model_type = "robust",
it is fit by
robumeta::robu(). Note that in the latter case, custom
inverse-variance weights are used, which are the inverse of the sum of the
study's variance and a heterogeneity estimate from a naive random-effects
meta-analysis (Mathur & VanderWeele, 2020). This is done for consistency
with the results of
pubbias_meta(), which is used to determine
sval_ci. Therefore, the worst-case meta-analysis results may differ
slightly from what you would obtain if you simply fit
the nonaffirmative studies with the default weights.
Mathur MB, VanderWeele TJ (2020). “Sensitivity analysis for publication bias in meta-analyses.” Journal of the Royal Statistical Society: Series C (Applied Statistics), 69(5), 1091--1119.
# calculate effect sizes from example dataset in metafor require(metafor) dat <- metafor::escalc(measure = "RR", ai = tpos, bi = tneg, ci = cpos, di = cneg, data = dat.bcg) ##### Fixed-Effects Specification ##### # S-values and worst-case meta-analysis under fixed-effects specification svals_fixed_0 <- pubbias_svalue(yi = dat$yi, vi = dat$vi, q = 0, model_type = "fixed", favor_positive = FALSE) # publication bias required to shift point estimate to 0 svals_fixed_0$stats$sval_est #>  "Not possible" # and to shift CI to include 0 svals_fixed_0$stats$sval_ci #>  7.58431 # now try shifting to a nonzero value (RR = 0.90) svals_fixed_q <- pubbias_svalue(yi = dat$yi, vi = dat$vi, q = log(.9), model_type = "fixed", favor_positive = FALSE) # publication bias required to shift point estimate to RR = 0.90 svals_fixed_q$stats$sval_est #>  8.261336 # and to shift CI to RR = 0.90 svals_fixed_q$stats$sval_ci #>  3.406779 ##### Robust Clustered Specification ##### svals <- pubbias_svalue(yi = dat$yi, vi = dat$vi, q = 0, model_type = "robust", favor_positive = FALSE) summary(svals) #> # A tibble: 1 × 2 #> sval_est sval_ci #> <chr> <dbl> #> 1 Not possible 4.17