*! version 1.0.0 13Aug2023

Title

repeatability -- Repeatability coefficient

Syntax

repeatability
rating1
rating2
[rating3 ...]
[if] [in]
[, level(#)
onesided
]

repeatability

level(#) set confidence level; default is level(95)

onesided one-sided test; default is two sided

by is allowed with repeatability; see [D] by.

Description

repeatability computes the repeatability coefficient (RC) which has been described as the "consistency of quantitative results obtained when the same imaging
test is performed at short intervals on the same subjects or test objects using the same equipment in the same center" (Barnhart & Barboriak 2009), or
interpreted as the "smallest detectable difference between a test and retest measurement for a given subject, defined as a 100(1−α/2)% quantile of the
distribution of test-retest differences" (Baumgartner et. al. 2018). More specifically, the interpretation of RC is that the difference between any two
readings on the same subject is expected to be from −RC to RC for 95% (or whatever level is specified) of subjects (Barnhart & Barboriak 2009; Bland & Altman 1996).

repeatability computes confidence intervals based on the chi2 method described by Barnhart & Barboriak (2009), but I recommend using the bootstrap as
shown in the example below.

Options

level(#) specifies the confidence level, as a percentage, for confidence intervals. The default is level(95).

onesided indicates a one-sided test. The default is two-sided.

Examples

Setup

. use lungfunction.dta

Compute repeatability across four measurements of lung function in each of 20 schoolchildren (data are from Bland & Altman [1996]).

. repeatability rating1 - rating4

Same as above but set CI level to 99.

. repeatability rating1 - rating4, level(99)

We now rerun repeatability and apply the bootstrap to compute 95% confidence intervals

. bootstrap repeatability = r(repeat), reps(1000): repeatability rating1 - rating4

. estat bootstrap, all

Stored results

repeatability stores the following in r():

Scalars

r(ntar) number of targets (observations)

r(nrat) number of ratings

r(wssd) within-subject standard deviation

r(repeat) repeatability coefficient

r(lcl) lower confidence limit

r(ucl) upper confidence limit

References

Barnhart, H. X., and D. P. Barboriak. 2009. Applications of the repeatability of quantitative
imaging biomarkers: a review of statistical analysis of repeat data sets.
Translational Oncology 2: 231–5.

Baumgartner, R., Joshi, A., Feng, D., Zanderigo, F. and R. T. Ogden. 2018. Statistical evaluation of test-retest
studies in PET brain imaging. EJNMMI Research 8: 1-9.

Bland, J. M. and D. G. Altman. 1996. Statistics notes: measurement error. BMJ 312: 1654.

Citation of repeatability

repeatability is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such:

Linden A. (2023). REPEATABILITY: Stata module to compute the repeatability coefficient.

Authors

Ariel Linden

President, Linden Consulting Group, LLC

alinden@lindenconsulting.org

Also see

Online: icc, finn (if installed), robinson (if installed), bhapkar (if installed), iota (if installed),
maxwell (if installed), wscv (if installed), kappaetc (if installed)