uisd {bayesmeta} | R Documentation |
Unit information standard deviation
Description
This function estimates the unit information standard deviation (UISD) from a given set of standard errors and associated sample sizes.
Usage
uisd(n, ...)
## Default S3 method:
uisd(n, sigma, sigma2=sigma^2, labels=NULL, individual=FALSE, ...)
## S3 method for class 'escalc'
uisd(n, ...)
Arguments
n |
vector of sample sizes or an |
sigma |
vector of standard errors associated with |
sigma2 |
vector of squared standard errors (variances) associated with |
labels |
(optional) a vector of labels corresponding to |
individual |
a |
... |
other |
Details
The unit information standard deviation (UISD) reflects the “within-study” variability, which, depending on the effect measure considered, sometimes is a somewhat heuristic notion (Roever et al., 2020). For a single study, presuming that standard errors result as
where is the within-study (population) standard
deviation, the UISD simply results as
This is often appropriate when assuming an (approximately) normal likelihood.
Assuming a constant value across studies, this
figure then may be estimated by
where is the average (arithmetic mean) of the
studies' sample sizes, and
is the
harmonic mean of the squared standard errors (variances).
The estimator is motivated via meta-analysis
using the normal-normal hierarchical model (NNHM). In the special case
of homogeneity (zero heterogeneity,
), the overall
mean estimate has standard error
Since this estimate corresponds to complete pooling, the standard error may also be expressed via the UISD as
Equating both above standard error expressions yields
as an estimator
of the UISD
(Roever et al, 2020).
Value
Either a (single) estimate of the UISD, or, if individual
was
set to ‘TRUE
’, a (potentially named) vector of UISDs for
each individual study.
Author(s)
Christian Roever christian.roever@med.uni-goettingen.de
References
C. Roever, R. Bender, S. Dias, C.H. Schmid, H. Schmidli, S. Sturtz, S. Weber, T. Friede. On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis. Research Synthesis Methods, 12(4):448-474, 2021. doi:10.1002/jrsm.1475.
See Also
Examples
# load data set:
data("CrinsEtAl2014")
# compute logarithmic odds ratios (log-ORs):
CrinsAR <- escalc(measure="OR",
ai=exp.AR.events, n1i=exp.total,
ci=cont.AR.events, n2i=cont.total,
slab=publication, data=CrinsEtAl2014)
# estimate the UISD:
uisd(n = CrinsAR$exp.total + CrinsAR$cont.total,
sigma = sqrt(CrinsAR$vi),
label = CrinsAR$publication)
# for an "escalc" object, one may also apply the function directly:
uisd(CrinsAR)
# compute study-specific UISDs:
uisd(CrinsAR, individual=TRUE)