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"), 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)the effect size estimates vector
the within studies standard error estimates vector
the within studies variance estimates vector
the alpha level of the prediction interval
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 \(\tau^2\) with
an approximate variance estimator for the average effect,
\((1/\sum{\hat{w}_i})^{-1}\), \(df=K-2\)).
HK: Partlett--Riley (2017) prediction interval
(the REML estimator for \(\tau^2\) 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 \(\tau^2\) 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 \(\tau^2\) with
the Kenward and Roger (1997)'s approach
for the average effect, \(df=\nu-1\)).
APX: Partlett--Riley (2017) prediction interval /
(the REML estimator for \(\tau^2\) with
an approximate variance estimator for the average
effect, \(df=K-2\)).
the number of bootstrap samples
the number of threads used in parallel computing, or FALSE that means single threading
set the value of random seed
the maximum number of iteration for the exact distribution function of \(Q\)
the desired level of accuracy for the exact distribution function of \(Q\)
the lower limit of random numbers of \(\tau^2\)
the upper limit of random numbers of \(\tau^2\)
the maximum number of iteration for numerical inversions
the desired level of accuracy for numerical inversions
a vector of random numbers from the exact distribution of \(\tau^2\)
the maximum number of iteration for REML estimation
K: the number of studies.
muhat: the average treatment effect estimate \(\hat{\mu}\).
lci, uci: the lower and upper confidence limits \(\hat{\mu}_l\) and \(\hat{\mu}_u\).
lpi, upi: the lower and upper prediction limits \(\hat{c}_l\) and \(\hat{c}_u\).
tau2h: the estimate for \(\tau^2\).
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 \(\hat{\mu}\).
The functions bootPI, pima_boot,
pima_hts, htsdl, pima_htsreml, htsreml
are deprecated, and integrated to the pima function.
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. (2018). Prediction intervals for random-effects meta-analysis: a confidence distribution approach. Stat Methods Med Res. In press. https://doi.org/10.1177/0962280218773520.
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.
# NOT RUN {
data(sbp, package = "pimeta")
# Nagashima-Noma-Furukawa prediction interval
# is sufficiently accurate when I^2 >= 10% and K >= 3
# }
# NOT RUN {
pimeta::pima(sbp$y, sbp$sigmak, seed = 3141592, parallel = 4)
# }
# NOT RUN {
# 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")
# }
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