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The pipeline estimates a single pooled prevalence of inappropriate acid suppressor use by combining study-level proportions under a random-effects model. Because prevalence data violate the normality assumptions of standard models, the analysis applies a variance-stabilizing transformation before pooling and then back-transforms the result for reporting. The core function is fitMetaprop(), defined in src/R/meta-analysis.R, which wraps meta::metaprop() with a fixed set of options that enforce methodological consistency across all calls in the pipeline.

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Model specification

fitMetaprop() passes the cleaned data frame directly to meta::metaprop() and sets every modeling decision explicitly: 
fitMetaprop <- function(tbl, ...) {
  require("meta")

  mod <- meta::metaprop(
    data             = tbl,
    event            = Inappropriate_indication,
    n                = Sample_size,
    studlab          = Author,
    sm               = "PFT",
    method.tau       = "REML",
    method.random.ci = "HK",
    common           = FALSE,
    random           = TRUE,
    prediction       = TRUE,
    ...
  )

  return(mod)
}
ArgumentValueMeaning
sm"PFT"Freeman-Tukey double arcsine transformation
method.tau"REML"Restricted maximum likelihood for between-study variance
method.random.ci"HK"Hartung-Knapp confidence interval adjustment
commonFALSESuppress common-effect model output
randomTRUEFit random-effects model
predictionTRUECompute 95% prediction interval
The pipeline runs this function as a targets target: 
tar_target(mod_prop, fitMetaprop(tbl_clean))

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Why Freeman-Tukey transformation

Raw proportions near 0 or 1 produce asymmetric sampling distributions with variances that depend on the mean. The Freeman-Tukey double arcsine transformation (sm = "PFT") stabilizes those variances and ensures that the confidence interval boundaries, after back-transformation, always remain within the valid [0, 1] range. Without this step, naively pooling logit- or untransformed proportions can yield intervals that fall outside [0, 1] when prevalence is extreme.

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Hartung-Knapp adjustment

The standard DerSimonian-Laird approach underestimates the uncertainty in the pooled estimate when the number of studies is small or heterogeneity is high, inflating Type I error. Setting method.random.ci = "HK" applies the Hartung-Knapp-Sidik-Jonkman correction, which uses a t-distribution rather than a normal approximation for the confidence interval. The result is a more conservative interval that better reflects the actual sampling variability of the between-study variance estimate.

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Prediction interval

Because prediction = TRUE, the fitted model also returns a 95% prediction interval alongside the confidence interval for the pooled estimate. Where the confidence interval describes uncertainty about the mean prevalence across the studies already observed, the prediction interval estimates the range you would expect to see in a new, future study drawn from the same population of studies. In the presence of high heterogeneity this interval is substantially wider than the confidence interval and is the more practically relevant quantity for clinical planning.

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Accessing model output

Load the fitted model from the targets store and inspect it with standard meta methods: 
targets::tar_load(mod_prop)
summary(mod_prop)
Key fields on the returned object:
FieldDescription
mod_prop$TE.randomPooled effect (on the PFT scale)
mod_prop$lower.randomLower bound of the 95% CI (PFT scale)
mod_prop$upper.randomUpper bound of the 95% CI (PFT scale)
mod_prop$I2I² heterogeneity statistic (proportion, not percentage)
mod_prop$tau2Between-study variance estimate
mod_prop$HH statistic
mod_prop$QWald’s Q statistic
All effect estimates are stored on the Freeman-Tukey (PFT) scale. Use the pft2p() helper defined in docs/report.qmd to back-transform them to the original probability scale:
pft2p <- function(x, n) {
  harmonic_n <- {1 / mean(1 / n)}
  p <- meta::backtransf(x, sm = "PFT", n = harmonic_n)
  return(p)
}

# Example: back-transform the pooled estimate
pft2p(mod_prop$TE.random, n = mod_prop$n)

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