1 / 27

What’s wrong with correlation analysis?

What’s wrong with correlation analysis?. Friedo Dekker ERA-EDTA Registry / LUMC. Nothing!. Unless…. How large do you estimate the correlation between MDRD and Cockcroft-Gault?. 0.2 0.4 0.6 0.8. It depends….  On what?. N=100. N=10. 10. 20. 30. 10. 20. 30.

phuc
Download Presentation

What’s wrong with correlation analysis?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. What’s wrong with correlation analysis? Friedo Dekker ERA-EDTA Registry / LUMC Nothing! Unless….

  2. How large do you estimate the correlation between MDRD and Cockcroft-Gault? • 0.2 • 0.4 • 0.6 • 0.8 FWD

  3. It depends….  On what? FWD

  4. N=100 N=10 10 20 30 10 20 30 What influences the size of the correlation coefficient? Example: Correlation between MDRD and C-G • Sample size? • Statistical significance? (p-value) • Measurement error? (random error, variability) No No Yes FWD

  5. 10 20 30 50 60 70 What influences the size of the correlation coefficient? Example: Correlation between MDRD and C-G • Mean eGFR of population? (e.g., 20 vs 60 ml/min) No FWD

  6. 10 20 30 10 20 50 30 40 60 50 70 60 What influences the size of the correlation coefficient? Example: Correlation between MDRD and C-G • Range of GFR in population? (e.g., 10-30 vs 10-60 ml/min)  What influences the range of GFR?? Yes Researcher! FWD

  7. 10 20 30 10 20 30 What influences the size of the correlation coefficient? • systematic difference or bias? No FWD

  8. 10 20 30 10 20 30 What influences the size of the correlation coefficient? • Slope of the relationship? (slope of regression line) No FWD

  9. What is a correlation coefficient? • Ranges from -1 to 0 to +1 • Measure of linear association • Extent to which data are on ‘a’ straight line • [PM clinical relevant? Most of the time perhaps we want to know ‘on which line’ data are] • R2 = % explained variance: if all data are on straight line  100% of variation in one variable is explained by variation in the other variable FWD

  10. Y X Correlation coefficient “has something to do with length and width” FWD

  11. Correlation coefficient (1) r = 0 r = 1.0 r = 0.5 r = - 0.5 FWD

  12. Correlation coefficient (2) r = 0 r = 0 FWD

  13. Y X How to calculate a Correlation coefficient FWD

  14. Y +/+ -/+ -/- +/- X Correlation coefficient is sum of cross-products* r = Σ(X*Y)/n * r = Σ(X*Y)/n with both X and Y standardized towards mean=0 and SD = 1 FWD

  15. What’s wrong with correlation analysis? (1) • As a researcher, I can directly influence the size of the correlation coefficientby increasing range (low through high GFR values) • As a researcher, I can directly influence the statistical significance of the correlation coefficient by increasing sample size (even very low correlations become significant) FWD

  16. What’s wrong with correlation analysis? (2) When measuring agreement, the correlation coefficient is NOT influenced if: • Mean difference between measures ≠ 0 (systematic difference or bias) • Slope of the relationship ≠ 1 (over or underestimation at higher values) FWD

  17. All these scatterplots have same correlation coefficient: FWD

  18. What’s wrong with correlation analysis? (3) The correlation coefficient DOES tell me: • To what extent data are on ‘a’ straight line The correlation coefficient does NOT tell me: • What line fits best through the data • Size of the error you make if you use one method in stead of the other method FWD

  19. Which correlation is highest? Children vs Adults Children Adults “The coefficients of correlation were even better (…) in children than in adults”. Kidney International 2003 FWD

  20. WHYis correlation higher in children than in adults? Children Adults “The coefficients of correlation were even better (…) in children than in adults”. Kidney International 2003 FWD

  21. WHY is correlation higher in children than in adults? Children 180 180 Adults “The coefficients of correlation were even better (…) in children than in adults”. Kidney International 2003 FWD

  22. Which agreement is best? Cockcroft-Gault vs Schwartz in children Kidney International 2003 FWD

  23. Bland – Altman plot Lancet 1986 • Agreement difficult to see from scatterplot • Regressionline is somewhat better than sole correlation coefficient • Even better to plot difference against the mean • 95% of differences are between ‘limits of agreement’ (mean +/- 2 SD) • Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; i, 307-310. • Most cited paper of The Lancet (>10,000 times cited) FWD

  24. Bland – Altman plot Lancet 1986 • Mean difference between Schwartz and Inulin clearance = 20 ml/min • 95% of differences between -60 and 20 (limits of agreement) • Larger difference at higher values Kidney International 2003 FWD

  25. Which agreement is best? Cockcroft-Gault vs Schwartz in children Cockcroft Gault Schwartz Kidney International 2003 FWD

  26. Assessing agreement between measurements • Use Bland-Altman plot in stead of correlation • Clinical interpretation of expected differences FWD

  27. What’s wrong with correlation analysis? Nothing! Unless…. F.W.Dekker@lumc.nl FWD

More Related