pima: Calculating Prediction Intervals
In nshi-stat/pimeta: Prediction Intervals for Random-Effects Meta-Analysis

Description Usage Arguments Details Value References See Also Examples

This function can estimate prediction intervals (PIs) as follows: A parametric bootstrap PI based on confidence distribution (Nagashima et al., 2018). A parametric bootstrap confidence interval is also calculated based on the same sampling method for bootstrap PI. The Higgins–Thompson–Spiegelhalter (2009) prediction interval. The Partlett–Riley (2017) prediction intervals.

pima(y, se, v = NULL, alpha = 0.05, method = c("boot", "HTS", "HK",
  "SJ", "KR", "CL", "APX", "WL"), theta0 = 0, side = c("lt", "gt"),
  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 error estimates 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 prediction interval (Nagashima et al., 2018). `HTS`: the Higgins–Thompson–Spiegelhalter (2009) prediction interval / (the DerSimonian & Laird estimator for τ^2 with an approximate variance estimator for the average effect, (1/∑{\hat{w}_i})^{-1}, df=K-2). `HK`: Partlett–Riley (2017) prediction interval (the REML estimator for τ^2 with the Hartung (1999)'s variance estimator [the Hartung and Knapp (2001)'s estimator] for the average effect, df=K-2). `SJ`: Partlett–Riley (2017) prediction interval / (the REML estimator for τ^2 with the Sidik and Jonkman (2006)'s bias coreccted variance estimator for the average effect, df=K-2). `KR`: Partlett–Riley (2017) prediction interval / (the REML estimator for τ^2 with the Kenward and Roger (1997)'s approach for the average effect, df=ν-1). `APX`: Partlett–Riley (2017) prediction interval / (the REML estimator for τ^2 with an approximate variance estimator for the average effect, df=K-2). for the average effect, df=ν-1). `WL`: Wang–Lee (2019) prediction interval / (a method of sample quantiles of ensemble estimates).
`theta0`	threshold θ_0, for the cumulative probability of effect θ_{new} less or greater than θ_0; \Pr(θ_{new} < θ_0) or \Pr(θ_{new} > θ_0).
`side`	either the cumulative probability of effect less (default = "lt") or greater ("gt") then θ_0
`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 upper limit 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

The functions bootPI, pima_boot, pima_hts, htsdl, pima_htsreml, htsreml are deprecated, and integrated to the pima function.

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.
lpi, upi: the lower and upper prediction limits \hat{c}_l and \hat{c}_u.
tau2h: the estimate for τ^2.
i2h: the estimate for I^2.
nup: degrees of freedom for the prediction interval.
nuc: degrees of freedom for the confidence interval.
vmuhat: the variance estimate for \hat{μ}.

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

Nagashima, K., Noma, H., and Furukawa, T. A. (2019). Prediction intervals for random-effects meta-analysis: a confidence distribution approach. Stat Methods Med Res. 28(6): 1689-1702. https://doi.org/10.1177/0962280218773520.

Wang, C-C and Lee, W-C. (2019). A simple method to estimate prediction intervals and predictive distributions. Res Syn Meth. 30(28): 3304-3312. https://doi.org/10.1002/jrsm.1345.

Hartung, J. (1999). An alternative method for meta-analysis. Biom J. 41(8): 901-916. https://doi.org/10.1002/(SICI)1521-4036(199912)41:8<901::AID-BIMJ901>3.0.CO;2-W.

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.

Kenward, M. G., and Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics. 53(3): 983-997. https://www.ncbi.nlm.nih.gov/pubmed/9333350.

DerSimonian, R., and Laird, N. (1986). Meta-analysis in clinical trials. Control Clin Trials. 7(3): 177-188.

print.pima, plot.pima, cima.

data(sbp, package = "pimeta")

# Nagashima-Noma-Furukawa prediction interval
# is sufficiently accurate when I^2 >= 10% and K >= 3
pimeta::pima(sbp$y, sbp$sigmak, seed = 3141592, parallel = 4)

# Higgins-Thompson-Spiegelhalter prediction interval and
# Partlett-Riley prediction intervals
# are accurate when I^2 > 30% and K > 25
pimeta::pima(sbp$y, sbp$sigmak, method = "HTS")
pimeta::pima(sbp$y, sbp$sigmak, method = "HK")
pimeta::pima(sbp$y, sbp$sigmak, method = "SJ")
pimeta::pima(sbp$y, sbp$sigmak, method = "KR")
pimeta::pima(sbp$y, sbp$sigmak, method = "APX")