uisd {bayesmeta} | 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] = sigma[u] / sqrt(n[i]),
where sigma[u] is the within-study (population) standard deviation, the UISD simply results as
sigma[u] = sqrt(n[i] * sigma[i]^2).
This is often appropriate when assuming an (approximately) normal likelihood.
Assuming a constant sigma[u] value across studies, this figure then may be estimated by
s[u] = sqrt(mean(n) * hmean(sigma^2)) = sqrt(sum(n)/sum(sigma^-2)),
where mean(n) is the average (arithmetic mean) of the studies' sample sizes, and hmean(sigma^2) is the harmonic mean of the squared standard errors (variances).
The estimator s[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
sqrt(1/sum(sigma^(-2))).
Since this estimate corresponds to complete pooling, the standard error may also be expressed via the UISD as
sigma[u] / sqrt(sum(n)).
Equating both above standard error expressions yields s[u] as an estimator of the UISD sigma[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. doi: 10.1002/jrsm.1475.
# 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)