1. The Statistically Meaningful Display of Analog Data Robert A. Warner, MD Laboratory of Logic and Experimental Philosophy Simon Fraser University Vancouver, BC, Canada

2. Interpreting Analog Displays Do any parts of the display differ from a reference standard? Are the differences genuine or merely variants of normal?

3. An Individual Value vs. A Reference Population Population Mean A Individ. Value A Individ. Value B Population Mean B Measurement Units 1.0 SD 1.0 SD

4. Standard (Z) Scores (Individual Value – Population Mean) Population S.D. Positive Z score: individual value>mean Negative Z score: individual value<mean Differences are in S.D. of the population

5. Advantages of Z Scores All parameters are on the same scale (the S.D. of the population) No compression at the extremes of a distribution (unlike percentiles) Can use demographically specific normal reference populations Directly translatable to P values

6. Z Scores, P Values & Coding Z ScoreP ValueB&W Code >3.080.001 >2.330.01 >1.650.05 -1.64 to 1.64NS <-1.650.05 <2.330.01 <3.080.001

7. Colors On the Tracing Refer To Amplitudes Colors Above the Tracing Refer to Durations Analog ECG Display PR = 230 Msec. Q = 34 Msec. S = 0 Msec.

8. Colored Z Score Matrix To Accompany a Standard ECG Diagnosis: Acute Inferior MI

9. B & W Z Score Matrix To Accompany a Standard ECG Diagnosis: Acute Inferior MI

10. Validation of the Z Score Method Compared abilities of Z scores vs. 2 widely- used commercial ECG algorithms to detect prior inferior and anterior MI 1138 patients (mean age 53, 426 females), 497 cath-proven normals, 366 prior inferior MI, 275 prior anterior MI Used Z scores of Q waves in aVF and initial R waves in V2 The commercial algorithms use voltages, not Z scores.

11. Inferior MI Z Scores vs. Algorithms Sensitivities @ 95% Specificity Z vs. Algorithm 1 Chi Square = 43.9 P<0.0000001 Z vs. Algorithm 2 Chi Square = 20.3 P<0.000001

12. Anterior MI Z Scores vs. Algorithms Sensitivities @ 95% Specificity Z vs. Algorithm 1 Chi Square = 24.1 P<0.000001 Z vs. Algorithm 2 Chi Square = 9.2 P<0.002

13. Z Scores in Long Recordings Objective and quantifiable comparisons to normal reference and baseline data Statistically meaningful results Cost-Effective –Rapid interpretation –Doesn’t require highly trained personnel Full disclosure of data Permits multiparameter recordings

14. Rapid Review of Data Ischemia Monitoring – 24 Hour Display March 4 to March 5, 2010 Colors = Maximum ST Segment Displacement Ischemia Monitoring – 1 Hour Display March, 2010 – 6:00 to 7:00 PM

15. Multiparameter Monitoring Maximizes the types of useful data provided Concordant orthogonal parameters increase the accuracy of diagnosis Parameters measured in different units are hard to display simultaneously and to interpret

16. Importance of Similar Scales Raw Data A Raw Data B Z Scores A Z Scores B

17. Z Scores in Acute Anterior MI MI Onset

18. Z Scores in Acute Anterior MI MI Onset

19. Exploratory Analysis What can Z scores teach us? Absolute Z scores of 159 known normals vs. 103 known healed anterior MI’s. Which parts of which leads discriminate the best?

20. Some Uses of Z Scores Medical practice and research Physical, biological and behavioral science Engineering, industrial processes and quality control Assessing the performance of mechanical and electrical equipment Economics, finance and investing Teaching the interpretation of analog displays Biofeedback

21. Thank you!