cima: Calculating Confidence Intervals
In pimeta: Prediction Intervals for Random-Effects Meta-Analysis

Description Usage Arguments Details Value References See Also Examples

This function calculates confidence intervals.

cima(y, se, v = NULL, alpha = 0.05, method = c("boot", "DL", "HK",
  "SJ", "KR", "APX", "PL", "BC"), B = 25000, parallel = FALSE,
  seed = NULL, maxit1 = 1e+05, eps = 10^(-10), lower = 0,
  upper = 1000, maxit2 = 1000, tol = .Machine$double.eps^0.25,
  rnd = NULL, maxiter = 100)

`y`	the effect size estimates vector
`se`	the within studies standard errors vector
`v`	the within studies variance estimates vector
`alpha`	the alpha level of the prediction interval
`method`	the calculation method for the pretiction interval (default = "boot"). `boot`: A parametric bootstrap confidence interval (Nagashima et al., 2018). `DL`: A Wald-type t-distribution confidence interval (the DerSimonian & Laird estimator for τ^2 with an approximate variance estimator for the average effect, (1/∑{\hat{w}_i})^{-1}, df=K-1). `HK`: A Wald-type t-distribution confidence interval (the REML estimator for τ^2 with the Hartung (1999)'s varance estimator [the Hartung and Knapp (2001)'s estimator] for the average effect, df=K-1). `SJ`: A Wald-type t-distribution confidence interval (the REML estimator for τ^2 with the Sidik and Jonkman (2006)'s bias coreccted SE estimator for the average effect, df=K-1). `KR`: Partlett–Riley (2017) confidence interval / (the REML estimator for τ^2 with the Kenward and Roger (1997)'s approach for the average effect, df=ν). `APX`: A Wald-type t-distribution confidence interval / (the REML estimator for τ^2 with an approximate variance estimator for the average effect, df=K-1). `PL`: Profile likelihood confidence interval (Hardy & Thompson, 1996). `BC`: Profile likelihood confidence interval with Bartlett-type correction (Noma, 2011).
`B`	the number of bootstrap samples
`parallel`	the number of threads used in parallel computing, or FALSE that means single threading
`seed`	set the value of random seed
`maxit1`	the maximum number of iteration for the exact distribution function of Q
`eps`	the desired level of accuracy for the exact distribution function of Q
`lower`	the lower limit of random numbers of τ^2
`upper`	the lower upper of random numbers of τ^2
`maxit2`	the maximum number of iteration for numerical inversions
`tol`	the desired level of accuracy for numerical inversions
`rnd`	a vector of random numbers from the exact distribution of τ^2
`maxiter`	the maximum number of iteration for REML estimation

Excellent reviews of heterogeneity variance estimation have been published (e.g., Veroniki, et al., 2018).

K: the number of studies.
muhat: the average treatment effect estimate \hat{μ}.
lci, uci: the lower and upper confidence limits \hat{μ}_l and \hat{μ}_u.
tau2h: the estimate for τ^2.
i2h: the estimate for I^2.
nuc: degrees of freedom for the confidence interval.
vmuhat: the variance estimate for \hat{μ}.

Veroniki, A. A., Jackson, D., Bender, R., Kuss, O., Langan, D., Higgins, J. P. T., Knapp, G., and Salanti, J. (2016). Methods to calculate uncertainty in the estimated overall effect size from a random-effects meta-analysis Res Syn Meth. In press. https://doi.org/10.1002/jrsm.1319.

Nagashima, K., Noma, H., and Furukawa, T. A. (2018). Prediction intervals for random-effects meta-analysis: a confidence distribution approach. Stat Methods Med Res. In press. https://doi.org/10.1177/0962280218773520.

Higgins, J. P. T, Thompson, S. G., Spiegelhalter, D. J. (2009). A re-evaluation of random-effects meta-analysis. J R Stat Soc Ser A Stat Soc. 172(1): 137-159. https://doi.org/10.1111/j.1467-985X.2008.00552.x

Partlett, C, and Riley, R. D. (2017). Random effects meta-analysis: Coverage performance of 95 confidence and prediction intervals following REML estimation. Stat Med. 36(2): 301-317. https://doi.org/10.1002/sim.7140

Hartung, J., and Knapp, G. (2001). On tests of the overall treatment effect in meta-analysis with normally distributed responses. Stat Med. 20(12): 1771-1782. https://doi.org/10.1002/sim.791

Sidik, K., and Jonkman, J. N. (2006). Robust variance estimation for random effects meta-analysis. Comput Stat Data Anal. 50(12): 3681-3701. https://doi.org/10.1016/j.csda.2005.07.019

Noma H. (2011) Confidence intervals for a random-effects meta-analysis based on Bartlett-type corrections. Stat Med. 30(28): 3304-3312. https://doi.org/10.1002/sim.4350

pima

data(sbp, package = "pimeta")
set.seed(20161102)

# Nagashima-Noma-Furukawa confidence interval
pimeta::cima(sbp$y, sbp$sigmak, seed = 3141592)

# A Wald-type t-distribution confidence interval
# An approximate variance estimator & DerSimonian-Laird estimator for tau^2
pimeta::cima(sbp$y, sbp$sigmak, method = "DL")

# A Wald-type t-distribution confidence interval
# The Hartung variance estimator & REML estimator for tau^2
pimeta::cima(sbp$y, sbp$sigmak, method = "HK")

# A Wald-type t-distribution confidence interval
# The Sidik-Jonkman variance estimator & REML estimator for tau^2
pimeta::cima(sbp$y, sbp$sigmak, method = "SJ")

# A Wald-type t-distribution confidence interval
# The Kenward-Roger approach & REML estimator for tau^2
pimeta::cima(sbp$y, sbp$sigmak, method = "KR")

# A Wald-type t-distribution confidence interval
# An approximate variance estimator & REML estimator for tau^2
pimeta::cima(sbp$y, sbp$sigmak, method = "APX")

# Profile likelihood confidence interval
# Maximum likelihood estimators of variance for the average effect & tau^2
pimeta::cima(sbp$y, sbp$sigmak, method = "PL")

# Profile likelihood confidence interval with a Bartlett-type correction
# Maximum likelihood estimators of variance for the average effect & tau^2
pimeta::cima(sbp$y, sbp$sigmak, method = "BC")