cima {pimeta} | R Documentation |
Calculating Confidence Intervals
Description
This function calculates confidence intervals.
Usage
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)
Arguments
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").
|
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 |
eps |
the desired level of accuracy for the exact distribution function of |
lower |
the lower limit of random numbers of |
upper |
the lower upper of random numbers of |
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 |
maxiter |
the maximum number of iteration for REML estimation |
Details
Excellent reviews of heterogeneity variance estimation have been published (e.g., Veroniki, et al., 2018).
Value
-
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
. -
tau2h
: the estimate for\tau^2
. -
i2h
: the estimate forI^2
. -
nuc
: degrees of freedom for the confidence interval. -
vmuhat
: the variance estimate for\hat{\mu}
.
References
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
See Also
Examples
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")