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 |

`sigma` |
vector of standard errors associated with |

`sigma2` |
vector of |

`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

`\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 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)
```

*bayesmeta*version 3.4 Index]