significance_funnel {PublicationBias}

Make significance funnel plot

Description

Creates a modified funnel plot that distinguishes between affirmative and nonaffirmative studies, helping to detect the extent to which the nonaffirmative studies' point estimates are systematically smaller than the entire set of point estimates. The estimate among only nonaffirmative studies (gray diamond) represents a corrected estimate under worst-case publication bias. If the gray diamond represents a negligible effect size or if it is much smaller than the pooled estimate among all studies (black diamond), this suggests that the meta-analysis may not be robust to extreme publication bias. Numerical sensitivity analyses (via pubbias_svalue()) should still be carried out for more precise quantitative conclusions.

Usage

significance_funnel(
  yi,
  vi,
  sei,
  favor_positive = TRUE,
  alpha_select = 0.05,
  plot_pooled = TRUE,
  est_all = NA,
  est_worst = NA,
  xmin = min(yi),
  xmax = max(yi),
  ymin = 0,
  ymax = max(sqrt(vi)),
  xlab = "Point estimate",
  ylab = "Estimated standard error"
)

Arguments

yi

A vector of point estimates to be meta-analyzed.

vi

A vector of estimated variances (i.e., squared standard errors) for the point estimates.

sei

A vector of estimated standard errors for the point estimates. (Only one of vi or sei needs to be specified).

favor_positive

TRUE if publication bias are assumed to favor significant positive estimates; FALSE if assumed to favor significant negative estimates.

alpha_select

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).

plot_pooled

Should the pooled estimates within all studies and within only the nonaffirmative studies be plotted as well?

est_all

Regular meta-analytic estimate among all studies (optional).

est_worst

Worst-case meta-analytic estimate among only nonaffirmative studies (optional).

xmin

x-axis (point estimate) lower limit for plot.

xmax

x-axis (point estimate) upper limit for plot.

ymin

y-axis (standard error) lower limit for plot.

ymax

y-axis (standard error) upper limit for plot.

xlab

Label for x-axis (point estimate).

ylab

Label for y-axis (standard error).

Details

By default (plot_pooled = TRUE), also plots the pooled point estimate within all studies, supplied by the user as est_all (black diamond), and within only the nonaffirmative studies, supplied by the user as est_worst (gray diamond). The user can calculate est_all and est_worst using their choice of meta-analysis model. If instead these are not supplied but plot_pooled = TRUE, these pooled estimates will be automatically calculated using a fixed-effects (a.k.a. "common-effect") model.

References

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.

Examples

##### Make Significance Funnel #####
# compute meta-analytic effect sizes for an example dataset
require(metafor)
dat <- metafor::escalc(measure = "RR", ai = tpos, bi = tneg, ci = cpos,
                       di = cneg, data = dat.bcg)

# favor_positive = FALSE since we think publication bias is in favor of negative
significance_funnel(yi = dat$yi, vi = dat$vi, favor_positive = FALSE)