pima() R function from [pimeta]

Calculating Prediction Intervals

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)

Arguments

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 $\tau^2$ 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, $df=K-2$ ).
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 $\tau^2$
upper: the upper limit of random numbers of $\tau^2$
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 $\tau^2$
maxiter: the maximum number of iteration for REML estimation

Returns

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 $\hat{\mu}$ .

Details

The functions bootPI, pima_boot, pima_hts, htsdl, pima_htsreml, htsreml

are deprecated, and integrated to the pima function.

Examples


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")

References

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.

pima function