Introduction to the Overall Concordance Correlation Coefficient
Oral Exam Presentation
Can a new technique or instrument reproduce the results of a "goldstandard"?
Examples:
How would a graduate student explore the question? I surveyed 18 graduate students and the responses were:
Paired ttest: 55.56%
Linear regression: 22.22%
Only graphs: 11.11%
Other: 11.11%
By a paired ttest, testing_{}by the test statistic_{}
By linear regression, we want slope = 1, and intercept = 0, by the test statistics_{}
By the Pearson correlation coefficient,_{}, testing_{}by the test statistic_{}
Problems:
Paired ttest tests only whether the means are equal
Least squares regression analysis is typically misused by regressing one measurement on the other and declaring them equivalent if and only if the confidence interval for the regression coefficient_{}includes 1
The Pearson correlation coefficient only measures linear correlation, but fails to detect departure from the_{}line
The Concordance Correlation Coefficient (CCC) addresses these issues
Consider pairs of samples_{}
It is natural to consider the expected squares difference
_{}
To scale it between 1 and 1
CCC =_{}
_{}
_{}is a measure of precision (deviation from bestfit line)
_{}is a measure of accuracy (deviation from_{}line)
_{}is a scale shift
_{}is a location shift relative to the scale
Characteristics
The CCC
The estimate_{}
Inference
Overall Concordance Correlation Coefficient
OCCC =_{}, where
_{}
OCCC can be interpreted as the weighted average of all pairwise CCC's
We can rewrite the OCCC as a function of means, variances, and covariances as:
_{}
And we can also rewrite as product of precision and accuracy:
_{}
Simulation
Table 1 (p. 1023)
True_{} 
True_{} 
N 
Mean 
SD 
Mean SE 
.5 
.469 
100 
.4636 
.0502 
.0512 


50 
.4582 
.0735 
.0719 


25 
.4486 
.1016 
.1012 
.7 
.656 
100 
.6489 
.0404 
.0401 


50 
.6455 
.0585 
.0558 


25 
.6355 
.0887 
.0866 
.9 
.844 
100 
.8409 
.0224 
.0224 


50 
.8372 
.0336 
.0323 


25 
.8337 
.0451 
.04505 
Extending the OCCC