uisd {bayesmeta}

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 escalc object.

sigma

vector of standard errors associated with n.

sigma2

vector of squared standard errors (variances) associated with n.

labels

(optional) a vector of labels corresponding to n and sigma.

individual

a logical flag indicating whether individual (study-specific) UISDs are to be returned.

...

other uisd arguments.

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

\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).

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 [e-mail]

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

escalc.

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)