Introduction to the Overall Concordance Correlation Coefficient

 

5/2/03

Oral Exam Presentation

 

 

 

 

 

 

 

Can a new technique or instrument reproduce the results of a “gold-standard”?

 

Examples:

 

 

 

 

How would a graduate student explore the question? I surveyed 18 graduate students and the responses were:

 

Paired t-test: 55.56%

Linear regression: 22.22%

Only graphs: 11.11%

Other: 11.11%

 

By a paired t-test, testingby the test statistic

 

By linear regression, we want slope = 1, and intercept = 0, by the test statistics

 

By the Pearson correlation coefficient,, testingby the test statistic

 

Problems:

 

Paired t-test 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 coefficientincludes 1

 

The Pearson correlation coefficient only measures linear correlation, but fails to detect departure from theline

 

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 best-fit line)

 

is a measure of accuracy (deviation fromline)

 

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