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 |

`sigma` |
vector of standard errors associated with |

`sigma2` |
vector of |

`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)

[Package *bayesmeta* version 2.7 Index]