rma.exact {rma.exact}

Compute an exact confidence interval for the grand mean in a normal-normal random effects meta-analysis.

Description

Compute an exact confidence interval for the grand mean in a normal-normal random effects meta-analysis.

Usage

rma.exact(yi, vi, c0 = 1, level = 0.05, mu.bounds = NULL,
  tau2.bounds = NULL, resolution = 100, resolution.mu = resolution,
  resolution.tau2 = resolution, Z = NULL, B = 3000, mu.alpha = 0.995,
  tau2.alpha = 0.995, plot = TRUE, test.stat = NULL, ...)

Arguments

yi

a vector containing the primary study measurements

vi

a vector of the same length as yi containing the variances of the of the primary study measurements contained in yi

c0

a vector containing the mixing parameters for the test statistics

level

the level of the confidence interval; set to NULL to plot a confidence region, otherwise rma.exact.fast is called using the specified level

mu.bounds

upper and lower bounds for the range of population effect values for constructing the confidence region; if NULL, value will be calculated from mu.alpha

tau2.bounds

upper and lower bounds for the range of population variance values for constructing the confidence region; if NULL, value will be calculated from tau2.alpha

resolution

resolution of the population mean and variance values within the bounding box

resolution.mu

resolution of the population mean values within the bounding box

resolution.tau2

resolution of the population variance values within the bounding box

Z

a matrix of length(yi) rows with each row consisting of standard normal samples to be used in the monte carlo estimation of the null distribution of the test statistic; if NULL, B values will be sampled per row

B

the number of monte carlo replicates per primary study observation to be used

mu.alpha

the level of the exact CI for constructing the bounds on the population mean dimension of the bounding box

tau2.alpha

the level of the exact CI for constructing the bounds on the population variance dimension of the bounding box

plot

whether to plot the confidence region (if level is not NULL) or its boundary (if level is NULL)

test.stat

(currently for internal use)

...

(currently for internal use)

Details

Computes an exact (up to monte carlo error), unconditional, non-randomized CI for the grand mean in a random effects meta-analysis assuming a normal-normal model for the primary study observations. This function implements the algorithm described in:

Michael, Thornton, Xie, and Tian (2017). Exact Inference on the Random Effects Model for Meta-Analyses with Few Studies. (Submitted.)

If the parameter "level" is not NULL (the default value is .05), this function passes the call down to rma.exact.fast, which computes a CI at the specified level. If "level" is set to NULL, an entire 2-dimensional grid of p-values is estimated. In the latter case, an RMA.Exact object is returned, which may be passed to a plot routine to plot contours of confidence regions.

Value

if "level" is not NULL, a named vector of CI endpoints; otherwise, an object of class RMA.Exact

See Also

rma.exact.fast for computing confidence intervals at specified levels, plot.RMA.Exact, confint.RMA.Exact

Examples

set.seed(1)

K <- 5
c0 <- 1
mu0 <- 0
tau2 <- 12.5
vi <- (seq(1, 5, length=K))^2
yi <- rnorm(K)*sqrt(vi+tau2)+mu0
rma.exact(yi=yi,vi=vi)

## plotting a conifdence region and printing CIs with an RMA.Exact object
rma0 <- rma.exact(yi=yi,vi=vi,level=NULL)
plot(rma0)
confint(rma0)


## confidence region with multiple c0 values using an RMA.Exact object
c0 <- c(0,.25,1)
tau2 <- 12.5
vi <- (seq(1, 5, length=K))^2
yi=rnorm(K)*sqrt(vi+tau2)+mu0
rma0 <- rma.exact(yi=yi,vi=vi,c0=c0,level=NULL)
plot(rma0)
confint(rma0)

## setting tau2.bounds and other parameters to non-default values using an RMA.Exact object
Z <- matrix(rnorm(K*5e3),nrow=K)
B <- ncol(Z)
resolution <- 3e2
rma0 <- rma.exact(yi=yi,vi=vi,level=NULL,Z=Z,resolution=resolution,c0=c0,
tau2.bounds=c(1,120),resolution.tau2=1e3,resolution.mu=1e2)
plot(rma0)

c0 <- 1:4
rma0 <- rma.exact(yi=yi,vi=vi,level=NULL,Z=Z,resolution=resolution,c0=c0,
tau2.bounds=c(1,450),resolution.tau2=1e3,resolution.mu=1e2)
plot(rma0)
confint(rma0,level=c(.05))