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The Statistically Meaningful Display of Analog Data

The Statistically Meaningful Display of Analog Data. Robert A. Warner, MD Laboratory of Logic and Experimental Philosophy Simon Fraser University Vancouver, BC, Canada. Interpreting Analog Displays. Do any parts of the display differ from a reference standard?

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The Statistically Meaningful Display of Analog Data

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

  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

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

  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 MIZ Scores vs. AlgorithmsSensitivities @ 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 MIZ Scores vs. AlgorithmsSensitivities @ 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!

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