Calculates the sample size for Lin’s concordance correlation coefficient (R.W. Payne).
Options
PRINT = string token |
What to print (replication, power); default repl, powe |
|---|---|
PROBABILITY = scalar |
Significance level at which the non-reproducibility is to be tested; default 0.05 |
POWER = scalar |
The required power (i.e. probability of detection) of the test; default 0.9 |
REPLICATION = variate |
Replication values for which to calculate and print or save the power; default * takes 11 replication values centred around the required number of replicates |
Parameters
CORRELATION = scalars |
Correlation for two samples with the smallest amount of non-reproducibility required to be detected |
|---|---|
CONCORDANCE = scalars |
Value of Lin’s concordance for two samples with the smallest amount of non-reproducibility required to be detected |
MEANSHIFT = scalars |
Value of the shift in means (divided by the harmonic mean of the standard deviations) for two samples with the smallest amount of non-reproducibility required to be detected |
SDRATIO = scalars |
Value of the ratio of the standard deviations for two samples with the smallest amount of non-reproducibility required to be detected |
NREPLICATES = scalars |
Saves the required number of replicates |
VREPLICATION = variates |
Numbers of replicates for which powers have been calculated |
VPOWER = variates |
Power (i.e. probability of detection) for the various numbers of replicates |
Description
Lin’s concordance correlation coefficient can be used to assess how well a new method of measurement reproduces the results provided by a standard method. To do this, you measure the same set of units using the two methods, and calculate the concordance between the resulting two sets of measurements. The methods are regarded as equivalent if the coefficient is greater than some threshold. SLCONCORDANCE helps you to decide how many units need to be measured to make a reliable assessment.
The concordance coefficient is defined by the equation
ρc = ρ × Cb
(see Lin 1989, 2000 or procedure LCONCORDANCE). The term ρ is the standard Pearson product-moment correlation coefficient, while Cb is a bias correction factor which is calculated by
Cb = 2 / (v + 1/v + u2)
v = s1 / s2
u = (m1 – m2) / √(s1 × s2)
where mi and si (i = 1,2) are the mean and standard deviation of the ith set of measurements. The quantity u represents the shift in the mean between the two sets of measurements divided by the harmonic mean of their standard deviations, while v is the ratio of the two standard deviations.
If the coefficient is given a Z-transformation, the result has an approximate Normal distribution, with a standard deviation that depends on ρc, ρ and u (see Lin 1989, 2000). So, to calculate the sample size, SLCONCORDANCE needs to know the values of these quantities for two sets of measurements displaying the smallest amount of non-reproducibility that is required to be detected. The correlation coefficient (ρ) is specified by the CORRELATION parameter, the concordance coefficient by the CONCORDANCE parameter, and u by the MEANSHIFT parameter. Alternatively, you can omit either CONCORDANCE or MEANSHIFT provided you specify the ratio of the standard deviations, v, using the SDRATIO parameter. (SLCONCORDANCE can then calculate the omitted quantity using the equations in the previous paragraph.)
The significance level for the test is specified by the PROBABILITY option (default 0.05 i.e. 5%). This is for a one-sided test, on the basis that you would not reject a new method for being too similar to the standard method. (Note, this also corresponds to a test for non-inferiority; see the Methods section of the documentation for procedure STTEST.) The required probability for detecting non-reproducibility (that is the power of the test) is specified by the POWER option (default 0.9).
The PRINT option controls printed output, with settings:
replication |
to print the required number of replicates to measure using each method (i.e. the sample size); |
|---|---|
power |
to print a table giving the power (i.e. probability of detection) provided by a range of numbers of replicates. |
By default both are printed.
The replications and corresponding powers can also be saved, in variates, using the VREPLICATION and VPOWER parameters. The REPLICATION option can specify the replication values for which to calculate and print or save the power; if this is not set, the default is to take 11 replication values centred around the required number of replicates.
Options: PRINT, PROBABILITY, POWER, RATIOREPLICATION, REPLICATION.
Parameters: CORRELATION, CONCORDANCE, MEANSHIFT, SDRATIO, NREPLICATES, VREPLICATION, VPOWER.
Method
The calculation uses the fact that the transformation
Z = 0.5 × (log(1 + ρc) / log(1 – ρc))
has an approximate Normal distribution, with a standard deviation defined by Lin (2000). Note, the results produced by SLCONCORDANCE do not match those of Lin (1992) firstly because of the correction to the equation for the standard deviation noted by Lin (2000), and secondly because the equation for n on page 601 of Lin (1992) should read
n = ( (EDNORMAL(1-β) + EDNORMAL(1-α)) * S / (Z – Zc,a) )2 + 2.
References
Lin, L.I. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics, 45, 255-268.
Lin, L.I. (1992). Assay validation using the concordance correlation coefficient. Biometrics, 48, 599-604.
Lin, L.I. (2000). A note on the concordance correlation coefficient. Biometrics, 56, 324-325.
See also
Procedure: LCONCORDANCE.
Commands for: Design of experiments.
Example
CAPTION 'SLCONCORDANCE example',!t(\
'Sample size required to detect non-reproducibility represented by',\
'a correlation of 0.95, a concordance of 0.9 and a shift in means',\
'(scaled by harmonic average s.d.) of 0.1.'); STYLE=meta,plain
SLCONCORDANCE CORRELATION=0.95; CONCORDANCE=0.9; MEANSHIFT=0.1