*! version 1.0.0 22Sept2023

Title

power concord -- Power analysis for Lin's concordance correlation coefficient

Syntax

Compute sample size

power concord concord0 concord1
, [ power(numlist) alpha(numlist) onesided graph[(graphopts)] ]

Compute power

power concord concord0 concord1
, [ n(numlist) alpha(numlist) onesided graph[(graphopts)] ]

where concord0 is the null (hypothesized) concordance coefficient and
concord1 is the alternative (target) concordance coefficient. concord0 and concord1 may each be
specified either as one number or as a list of values in parentheses
(see numlist).

* alpha(numlist) significance level; default is alpha(0.05)

* power(numlist) power; default is power(0.80)

* n(numlist) total sample size; required to compute power

onesided one-sided test; default is two sided

graph[(graphopts)] graph results; see [PSS-2] power, graph

* Specifying a list of values in at least two starred options, or
two command arguments, or at least one starred option and one argument
results in computations for all possible combinations of the values; see
numlist.

Description

power concord computes power and sample size for Lin's concordance coefficient using the "simplifed method" described in Lin et al. (2012).
For the case of two raters with a single reading per rater, the computations of the power and sample size are simplified by using the upper
bound of the variance of each estimate of the agreement indices (see page 72 of Lin et al. [2012] for details).

Options

alpha(numlist) sets the significance level of the test. The
default is alpha(0.05).

power(numlist) specifies the desired power at which sample size is to be computed.
If power() is specified in conjunction with n(),
then the actual power of the test is presented.

n(numlist) specifies the total number of subjects in the study to be used for determining power.

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

graph, graph(); see [PSS-2] power, graph.

Examples

Examples: Computing sample size

We want to use Lin's concordance correlation coefficient to compare a new measurement method to the "gold standard" method
to determine whether the new method can replace the gold standard method. We assume that the concordance coefficient
is 0.95 under the null hypothesis and 0.97 under the alternative hypothesis. We specify a one-sided test, a 5% significance level
and 80% power (the defaults).

. power concord 0.95 0.97, onesided

Same as above, using a power of 90%, an alpha of 1% and a two-sided test

. power concord 0.95 0.97, power(0.90) alpha(0.01)

Same as above, but testing power at both 80% and 90% and alpha at the 1% and 5% level

. power concord 0.95 0.97, alpha(0.01 0.05) power(0.80 0.90)

Same as above, but applying a range of concordance coefficient values under the alternative hypothesis
and setting alpha levels to 1% and 5%; and graphing the results

. power concord 0.95 0.96(0.01)0.99, power(0.80) alpha(0.01 0.05) graph

Examples: Computing power

For a total sample of 94 subjects, compute the power of a one-sided test to
detect a concordance of 0.97 given a null concordance of 0.95
at a 5% significance level (the default)

. power concord 0.95 0.97, onesided n(94)

Same as above but test alpha levels of 1%, 5% and 10%

. power concord 0.95 0.97, onesided n(94) alpha(0.01 0.05 0.10)

Compute powers for a range of sample sizes at alpha 1% and 5%,
graphing the results

. power concord 0.95 0.97, onesided n(70(5)160) alpha(0.01 0.05) graph

Stored results

power concord stores the following in r():

Scalars

r(alpha) significance level

r(concord0) null concordance coefficient

r(concord1) alternative concordance coefficient

r(beta) probability of a type II error

r(delta) effect size

r(divider) 1 if divider is requested in the table, 0 otherwise

r(N) total sample size

r(onesided) 1 for a one-sided test, 0 otherwise

r(power) power

Macros

r(type) test

r(method) concord

r(columns) displayed table columns

r(labels) table column labels

r(widths) table column widths

r(formats) table column formats

Matrices

r(pss_table) table of results

References

Lin, L., Hedayat, A. S., and W. Wu. 2012. Statistical Tools for Measuring Agreement. Springer, New York.

Citation of power concord

power concord 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., and L. Lin. 2023. POWER CONCORD: Stata module to compute power and sample size for Lin's concordance correlation coefficient

Authors

Ariel Linden

President, Linden Consulting Group, LLC

alinden@lindenconsulting.org

Lawrence Lin

equeilin@gmail.com

Also see

Online: power, concord (if installed)