pimeta packageThe pimeta package is easy. Load your data and then pass it the pima function!
require("pimeta")## Loading required package: pimetadata(sbp, package = "pimeta")
# a parametric bootstrap prediction interval
out <- pima(
y = sbp$y, # effect size estimates
se = sbp$sigmak, # within studies standard errors
B = 25000, # number of bootstrap samples
seed = 14142135, # random number seed
parallel = 4 # multi-threading
)
out##
## Prediction & Confidence Intervals for Random-Effects Meta-Analysis
##
## A parametric bootstrap prediction and confidence intervals
## Heterogeneity variance: DerSimonian-Laird
## Variance for average treatment effect: Hartung (Hartung-Knapp)
##
## No. of studies: 10
##
## Average treatment effect [95% prediction interval]:
## -0.3341 [-0.8807, 0.2240]
## d.f.: 9
##
## Average treatment effect [95% confidence interval]:
## -0.3341 [-0.5613, -0.0985]
## d.f.: 9
##
## Heterogeneity measure
## tau-squared: 0.0282
## I-squared: 70.5%plot(out, base_size = 10, studylabel = sbp$label)
Several type of methods are supported.
# Higgins-Thompson-Spiegelhalter prediction interval
pima(sbp$y, sbp$sigmak, method = "HTS")##
## Prediction & Confidence Intervals for Random-Effects Meta-Analysis
##
## Higgins-Thompson-Spiegelhalter prediction and confidence intervals
## Heterogeneity variance: DerSimonian-Laird
## Variance for average treatment effect: approximate
##
## No. of studies: 10
##
## Average treatment effect [95% prediction interval]:
## -0.3341 [-0.7598, 0.0917]
## d.f.: 8
##
## Average treatment effect [95% confidence interval]:
## -0.3341 [-0.5068, -0.1613]
## d.f.: 9
##
## Heterogeneity measure
## tau-squared: 0.0282
## I-squared: 70.5%# Partlett-Riley prediction interval (Hartung and Knapp's variance)
pima(sbp$y, sbp$sigmak, method = "HK")##
## Prediction & Confidence Intervals for Random-Effects Meta-Analysis
##
## Partlett-Riley prediction and confidence intervals
## Heterogeneity variance: REML
## Variance for average treatment effect: Hartung (Hartung-Knapp)
##
## No. of studies: 10
##
## Average treatment effect [95% prediction interval]:
## -0.3287 [-0.9887, 0.3312]
## d.f.: 8
##
## Average treatment effect [95% confidence interval]:
## -0.3287 [-0.5761, -0.0814]
## d.f.: 9
##
## Heterogeneity measure
## tau-squared: 0.0700
## I-squared: 85.5%# Partlett-Riley prediction interval (Sidik and Jonkman's variance)
pima(sbp$y, sbp$sigmak, method = "SJ")##
## Prediction & Confidence Intervals for Random-Effects Meta-Analysis
##
## Partlett-Riley prediction and confidence intervals
## Heterogeneity variance: REML
## Variance for average treatment effect: bias corrected Sidik-Jonkman
##
## No. of studies: 10
##
## Average treatment effect [95% prediction interval]:
## -0.3287 [-0.9835, 0.3261]
## d.f.: 8
##
## Average treatment effect [95% confidence interval]:
## -0.3287 [-0.5625, -0.0950]
## d.f.: 9
##
## Heterogeneity measure
## tau-squared: 0.0700
## I-squared: 85.5%# Partlett-Riley prediction interval (Kenward and Roger's variance)
pima(sbp$y, sbp$sigmak, method = "KR")##
## Prediction & Confidence Intervals for Random-Effects Meta-Analysis
##
## Partlett-Riley prediction and confidence intervals
## Heterogeneity variance: REML
## Variance for average treatment effect: Kenward-Roger
##
## No. of studies: 10
##
## Average treatment effect [95% prediction interval]:
## -0.3287 [-1.0280, 0.3706]
## d.f.: 5.9508
##
## Average treatment effect [95% confidence interval]:
## -0.3287 [-0.5815, -0.0759]
## d.f.: 6.9508
##
## Heterogeneity measure
## tau-squared: 0.0700
## I-squared: 85.5%The convert_bin() function converts binary outcome data to effect size estimates and within studies standard errors vectors. A data set of 13 placebo-controlled trials with cisapride that was reported by Hartung and Knapp (Stat Med., 2001, doi:10.1002/sim.1009) was analyzed below.
m1 <- c(15,12,29,42,14,44,14,29,10,17,38,19,21)
n1 <- c(16,16,34,56,22,54,17,58,14,26,44,29,38)
m2 <- c( 9, 1,18,31, 6,17, 7,23, 3, 6,12,22,19)
n2 <- c(16,16,34,56,22,55,15,58,15,27,45,30,38)
dat <- convert_bin(m1, n1, m2, n2, type = "logOR")
dat## y se
## 1 2.0989861 0.9847737
## 2 3.3570262 1.0165653
## 3 1.5652318 0.5747840
## 4 0.8640463 0.4042977
## 5 1.4656407 0.6332968
## 6 2.2325713 0.4481371
## 7 1.5465488 0.7782417
## 8 0.4125323 0.3721812
## 9 2.1202635 0.8265438
## 10 1.8071598 0.6022988
## 11 2.7646729 0.5382109
## 12 -0.3544099 0.5555283
## 13 0.2058521 0.4541130pibin <- pima(dat$y, dat$se, seed = 2236067, parallel = 4)
pibin##
## Prediction & Confidence Intervals for Random-Effects Meta-Analysis
##
## A parametric bootstrap prediction and confidence intervals
## Heterogeneity variance: DerSimonian-Laird
## Variance for average treatment effect: Hartung (Hartung-Knapp)
##
## No. of studies: 13
##
## Average treatment effect [95% prediction interval]:
## 1.4209 [-0.6283, 3.5173]
## d.f.: 12
##
## Average treatment effect [95% confidence interval]:
## 1.4209 [0.7992, 2.0567]
## d.f.: 12
##
## Heterogeneity measure
## tau-squared: 0.7176
## I-squared: 69.9%binlabel <- c(
"Creytens", "Milo", "Francois and De Nutte", "Deruyttere et al.",
"Hannon", "Roesch", "De Nutte et al.", "Hausken and Bestad",
"Chung", "Van Outryve et al.", "Al-Quorain et al.", "Kellow et al.",
"Yeoh et al.")
plot(pibin, digits = 2, base_size = 10, studylabel = binlabel)