pubbias_meta {PublicationBias}

Estimate publication bias-corrected meta-analysis

Description

For a chosen ratio of publication probabilities, selection_ratio, estimates a publication bias-corrected pooled point estimate and confidence interval per Mathur and VanderWeele (2020). Model options include fixed-effects (a.k.a. "common-effect"), robust independent, and robust clustered specifications.

Usage

pubbias_meta(
  yi,
  vi,
  sei,
  cluster = 1:length(yi),
  selection_ratio,
  selection_tails = 1,
  model_type = "robust",
  favor_positive = TRUE,
  alpha_select = 0.05,
  ci_level = 0.95,
  small = TRUE,
  return_worst_meta = FALSE
)

corrected_meta(
  yi,
  vi,
  eta,
  clustervar = 1:length(yi),
  model,
  selection.tails = 1,
  favor.positive,
  alpha.select = 0.05,
  CI.level = 0.95,
  small = TRUE
)

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).

cluster

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).

selection_ratio

Ratio by which publication bias favors affirmative studies (i.e., studies with p-values less than alpha_select and estimates in the direction indicated by favor_positive).

selection_tails

1 (for one-tailed selection, recommended for its conservatism) or 2 (for two-tailed selection).

model_type

"fixed" for fixed-effects (a.k.a. "common-effect") or "robust" for robust random-effects.

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).

ci_level

Confidence interval level (as proportion) for the corrected point estimate. (The alpha level for inference on the corrected point estimate will be calculated from ci_level.)

small

Should inference allow for a small meta-analysis? We recommend always using TRUE.

return_worst_meta

Should the worst-case meta-analysis of only the nonaffirmative studies be returned?

eta

(deprecated) see selection_ratio

clustervar

(deprecated) see cluster

model

(deprecated) see model_type

selection.tails

(deprecated) see selection_tails

favor.positive

(deprecated) see favor_positive

alpha.select

(deprecated) see alpha_select

CI.level

(deprecated) see ci_level

Details

The selection_ratio represents the number of times more likely affirmative studies (i.e., those with a "statistically significant" and positive estimate) are to be published than nonaffirmative studies (i.e., those with a "nonsignificant" or negative estimate).

If favor_positive is 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 corrected estimate will be reported based on the recoded signs rather than the original sign convention.

Value

An object of class metabias::metabias(), a list containing:

data

A tibble with one row per study and the columns yi, yif, vi, affirm, cluster.

values

A list with the elements selection_ratio, selection_tails, model_type, favor_positive, alpha_select, ci_level, small, k, k_affirmative, k_nonaffirmative.

stats

A tibble with the columns model, estimate, se, ci_lower, ci_upper, p_value.

fit

A list of fitted models, if any.

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

# 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)

# first fit fixed-effects model without any bias correction
# since the point estimate is negative here, we'll assume publication bias
# favors negative log-RRs rather than positive ones
metafor::rma(yi, vi, data = dat, method = "FE")

# warmup
# note that passing selection_ratio = 1 (no publication bias) yields the naive
# point estimate from rma above, which makes sense
meta <- pubbias_meta(yi = dat$yi,
                     vi = dat$vi,
                     selection_ratio = 1,
                     model_type = "fixed",
                     favor_positive = FALSE)
summary(meta)

# assume a known selection ratio of 5
# i.e., affirmative results are 5x more likely to be published than
# nonaffirmative ones
meta <- pubbias_meta(yi = dat$yi,
                     vi = dat$vi,
                     selection_ratio = 5,
                     model_type = "fixed",
                     favor_positive = FALSE)
summary(meta)

# same selection ratio, but now account for heterogeneity and clustering via
# robust specification
meta <- pubbias_meta(yi = dat$yi,
                     vi = dat$vi,
                     cluster = dat$author,
                     selection_ratio = 5,
                     model_type = "robust",
                     favor_positive = FALSE)
summary(meta)

##### Make sensitivity plot as in Mathur & VanderWeele (2020) #####
# range of parameters to try (more dense at the very small ones)
selection_ratios <- c(200, 150, 100, 50, 40, 30, 20, seq(15, 1))

# compute estimate for each value of selection_ratio
estimates <- lapply(selection_ratios, function(e) {
  pubbias_meta(yi = dat$yi, vi = dat$vi, cluster = dat$author,
               selection_ratio = e, model_type = "robust",
               favor_positive = FALSE)$stats
})
estimates <- dplyr::bind_rows(estimates)
estimates$selection_ratio <- selection_ratios

require(ggplot2)
ggplot(estimates, aes(x = selection_ratio, y = estimate)) +
  geom_ribbon(aes(ymin = ci_lower, ymax = ci_upper), fill = "gray") +
  geom_line(lwd = 1.2) +
  labs(x = bquote(eta), y = bquote(hat(mu)[eta])) +
  theme_classic()