sigma_ref: Reference standard deviation

In pa4bayesmeta: Prior Accuracy for Bayesian Meta-Analysis

Description

Computes the reference standard deviation of the given meta-analysis data set. Depending on the argument type.sigma.ref, either the geometric or a weighted harmonic mean is used.

Usage

sigma_ref(df, type.sigma.ref = "geometric")

Arguments

df	data frame with one column "sigma" containing the standard errors of the estimates for the individual studies
type.sigma.ref	either "geometric" or "harmonic". Defaults to "geometric". Specifies if the geometric mean or a weighted harmonic mean is used to compute the reference standard deviation. See details for more information.

Details

If type.sigma.ref = "geometric", the reference standard deviation is given by the geometric mean of the standard deviations of the individual studies (Sorbye & Rue 2014 (equation (7)).
If type.sigma.ref = "harmonic", the reference standard deviation σ_{ref} is the square root of a weighted harmonic mean of the variances of the individual studies, as described in Hoaglin (2016, page 490). More precisely, we have

σ_{ref} = √{ (k-1) ∑ w_i /((∑ w_i)^2 - ∑ w_i^2)},

where k is the number of studies in the data frame df and the weights are w_i=σ_i^{-2}, i =1, ... , k, for the standard deviations σ_i (or standard errors) of the individual studies.

Value

The reference standard deviation of the data set. Non-negative real number.

References

Sorbye, S., Rue, H. (2014). Scaling intrinsic Gaussian Markov random field priors in spatial modelling. Spatial Statistics 8, 39–51. https://doi.org/10.1016/j.spasta.2013.06.004

Hoaglin, D. (2016). Misunderstandings about Q and "Cochran's Q test" in meta-analysis. Statistics in Medicine 35(4), 485–495. https://doi.org/10.1002/sim.6632

Examples

# load the steriod-resistant rejection (SRR) data analyzed in Friede et al. (2017)
data(srr)

# geometric mean of with-study standard deviations in SRR data
sigma_ref(df = srr)
# harmonic mean of with-study standard deviations in SRR data
sigma_ref(df = srr, type.sigma.ref = "harmonic")

pa4bayesmeta documentation built on Aug. 1, 2021, 3 p.m.