uisd | R Documentation |
This function estimates the unit information standard deviation (UISD) from a given set of standard errors and associated sample sizes.
uisd(n, ...)
## Default S3 method:
uisd(n, sigma, sigma2=sigma^2, labels=NULL, individual=FALSE, ...)
## S3 method for class 'escalc'
uisd(n, ...)
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 |
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
\sigma_i=\frac{\sigma_\mathrm{u}}{\sqrt{n_i}},
where \sigma_\mathrm{u}
is the within-study (population) standard
deviation, the UISD simply results as
\sigma_\mathrm{u} = \sqrt{n_i \, \sigma_i^2}.
This is often appropriate when assuming an (approximately) normal likelihood.
Assuming a constant \sigma_\mathrm{u}
value across studies, this
figure then may be estimated by
s_\mathrm{u} \;=\; \sqrt{\bar{n} \, \bar{s}^2_\mathrm{h}} \;=\; \sqrt{\frac{\sum_{i=1}^k n_i}{\sum_{i=1}^k \sigma_i^{-2}}},
where \bar{n}
is the average (arithmetic mean) of the
studies' sample sizes, and \bar{s}^2_\mathrm{h}
is the
harmonic mean of the squared standard errors (variances).
The estimator s_\mathrm{u}
is motivated via meta-analysis
using the normal-normal hierarchical model (NNHM). In the special case
of homogeneity (zero heterogeneity, \tau=0
), the overall
mean estimate has standard error
\left(\sum_{i=1}^k\sigma_i^{-2}\right)^{-1/2}.
Since this estimate corresponds to complete pooling, the standard error may also be expressed via the UISD as
\frac{\sigma_\mathrm{u}}{\sqrt{\sum_{i=1}^k n_i}}.
Equating both above standard error expressions yields
s_\mathrm{u}
as an estimator
of the UISD \sigma_\mathrm{u}
(Roever et al, 2020).
Either a (single) estimate of the UISD, or, if individual
was
set to ‘TRUE
’, a (potentially named) vector of UISDs for
each individual study.
Christian Roever christian.roever@med.uni-goettingen.de
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jrsm.1475")}.
escalc
.
# 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)
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