Concordance correlation coefficient calculation in R

The Concordance Correlation Coefficient (CCC) is a widely used statistic in various fields, including medical research, biology, psychology, and more.

It quantifies the agreement and reliability between two continuous measurements or observations.

In this article, we will explore what CCC is, how to calculate it using R, interpret its outcomes, and provide case examples of when to use it.

What is the Concordance Correlation Coefficient?

The CCC, introduced by Lin in 1989, measures the degree of agreement and correlation between two sets of data points.

It provides a single numerical value that ranges from -1 to 1, where:

1 indicates perfect positive agreement.

-1 indicates perfect negative agreement (i.e., one set of data is the exact opposite of the other).

0 indicates no agreement.

In practical terms, CCC combines both the correlation and bias between two sets of measurements, making it a robust measure of agreement.

Calculating CCC in R

To calculate the CCC in R, two frequently used R libraries are “epiR” (also computes limits of agreement and Bland-Altman plot, as demonstrated in the previous Medium article) and “SimplyAgree”.

# Example dataset
observed <- c(3, 4, 5, 6, 7)
predicted <- c(2, 4.9, 6, 6.8, 9)

# Calculate CCC using library epiR
install.packages("epiR")
ccc <- epiR::epi.ccc(observed, predicted, ci="z-transform", conf.level=0.95)
ccc.result <- ccc$rho.c
ccc.result

estimate Lower 95% Upper 95%
0.8101911 0.4415887 0.9447991

# Calculate CCC using library SimplyAgree
install.packages("SimplyAgree")
SimplyAgree::jmvagree(method1=observed, method2=predicted, ciWidth=95,
                      agreeWidth=95, CCC=T, plotbland=F)

Concordance Correlation Coefficient             
 ─────────────────────────────────────────────── 
          Estimate     Lower C.I.    Upper C.I   
 ─────────────────────────────────────────────── 
   CCC    0.8101911     0.4415887    0.9447991   
 ───────────────────────────────────────────────

Interpreting CCC Outcomes

Interpreting CCC results is crucial to understanding the agreement between two sets of measurements.

The CCC value ranges from -1 to 1, as previously mentioned:

- A CCC value close to 1 indicates high positive agreement between the two datasets, signifying a strong linear relationship and little bias.

- A CCC value close to -1 indicates high negative agreement, suggesting a strong linear relationship, but one dataset is the mirror image of the other.

- A CCC value close to 0 suggests no agreement or a very weak linear relationship between the datasets.

It’s important to interpret CCC in the context of your specific field and data.

What is considered a “good” CCC may vary depending on your research area and the nature of the measurements.

Examples of Lin’s concordance correlation coefficients between 2-day (A) and 3-day (B) average counts per minute versus 7-day average counts per minute among adults aged 65 and older in National Health and Nutrition Examination Survey 2003±4 and 2005±6 accelerometry sub-study. Credit: Kocherginsky et al. (2017). Measuring Physical Activity with Hip Accelerometry among U.S. Older Adults: How Many Days Are Enough? PLoS ONE 12(3): e0174739. https://doi.org/10.1371/journal.pone.0174739.g001

Case Examples of When to Use CCC

1. Medical Research

In clinical studies, CCC is used to assess the agreement between measurements taken by different instruments or observers.

For instance, you might use CCC to evaluate the agreement between two blood pressure monitoring devices or the inter-rater reliability of two radiologists interpreting medical images.

2. Environmental Monitoring

Environmental scientists often use CCC to assess the agreement between field measurements and remote sensing data.

This can help determine the accuracy of satellite data in estimating environmental variables such as land cover, temperature, or pollution levels.

3. Psychological Testing

Psychologists use CCC to assess the agreement between test scores obtained from different raters or on different occasions.

This is crucial in test-retest reliability studies and when comparing results from multiple raters in psychological assessments.

4. Quality Control

Manufacturing and quality control industries employ CCC to measure the agreement between measurements taken by different instruments or operators.

It ensures consistency and reliability in production processes.

Conclusion

The Concordance Correlation Coefficient (CCC) is a valuable statistic for assessing agreement and reliability between two sets of continuous measurements.

In R, the “epiR” and “SimplyAgree” libraries provide a convenient way to calculate CCC.

Understanding CCC’s interpretation and applications is essential for researchers and professionals in various fields.

By using CCC, you can confidently assess the agreement and reliability of your data, making informed decisions and drawing meaningful conclusions in your research or professional practice.

Reference:

Lawrence, I., & Lin, K. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics, 255–268.