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

 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?

• Are the differences genuine or merely variants of normal?

An Individual Value vs. A Reference Population

PopulationMean

A

Individ.Value

A

Individ.Value

B

PopulationMean

B

Measurement Units

1.0SD

1.0SD

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

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

Z Scores, P Values & Coding

Z Score P Value B&W Code

>3.08 0.001

>2.33 0.01

>1.65 0.05

-1.64 to 1.64 NS

<-1.65 0.05

<2.33 0.01

<3.08 0.001

Colors On the Tracing Refer To Amplitudes Colors Above the Tracing Refer to Durations

Analog ECG Display  

COLOR CODES Z Score P Value

3.08 .001 2.33 .01 1.65 .05

-1.64 to 1.64 NS -1.65 .05 -2.33 .01 -3.08 .001

PR = 230Msec.

Q = 34Msec.

S = 0Msec.

Colored Z Score Matrix

To Accompany a Standard ECG

Diagnosis: Acute Inferior MI

Q Q R R S S ST T

Lead Amp Dur Amp Dur Amp Dur Amp Amp

I # # # # # # # #

II # # # # # # # #

III # # # # # # # #

aVR # # # # # # # #

aVL # # # # # # # #

aVF # # # # # # # #

V1 # # # # # # # #

V2 # # # # # # # #

V3 # # # # # # # #

V4 # # # # # # # #

V5 # # # # # # # #

V6 # # # # # # # #

B&W Z Score MatrixTo Accompany a Standard ECG

Diagnosis: Acute Inferior MI

Q Q R R S S ST T

Lead Amp Dur Amp Dur Amp Dur Amp Amp

I # # # # # #

II # # # #

III # # # #

aVR # # # # # # # #

aVL # # # # # #

aVF # # # #

V1 # # # # # # # #

V2 # # # # # # # #

V3 # # # # # # # #

V4 # # # # # # # #

V5 # # # # #

V6 # # # # #

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.

Inferior MIZ Scores vs. AlgorithmsSensitivities @ 95% Specificity

0

1020

3040

5060

7080

90100

Z Score Alg. 1 Alg. 2

• Z vs. Algorithm 1

Chi Square = 43.9

P<0.0000001

• Z vs. Algorithm 2

Chi Square = 20.3

P<0.000001

Anterior MIZ Scores vs. AlgorithmsSensitivities @ 95% Specificity

0

1020

3040

5060

7080

90100

Z Score Alg. 1 Alg. 2

• Z vs. Algorithm 1

Chi Square = 24.1

P<0.000001

• Z vs. Algorithm 2

Chi Square = 9.2

P<0.002

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

Rapid Review of Data

10 11 12 1 2 3 4 5 6 7 8 9AM AM AM PM PM PM PM PM PM PM PM PM

10 11 12 1 2 3 4 5 6 7 8 9PM PM PM AM AM AM AM AM AM AM AM AM

6PM

7:00PM

PM PM6:20 6:25

PM

6:30 6:45

PM6:05 6:10 6:15PM

PM6:35PM

6:40PM PM

6:50PM

6:55PM

Ischemia Monitoring – 24 Hour DisplayMarch 4 to March 5, 2010

Colors = Maximum ST Segment Displacement

Ischemia Monitoring – 1 Hour DisplayMarch, 2010 – 6:00 to 7:00 PM

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

Importance of Similar Scales

0.00

5.00

10.00

15.00

20.00

25.00

1 5 9

13

17

21

25

29

33

37

41

45

49

53

57

61

65

69

73

77

81

85

89

93

97

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

1 5 9

13

17

21

25

29

33

37

41

45

49

53

57

61

65

69

73

77

81

85

89

93

97

Raw Data A

Raw Data B

Z Scores AZ Scores B

Z Scores in Acute Anterior MI

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

Time

Z S

core

ST_V2

ST_aVF

S4 Conf

S3 Conf

HEARTRATE

MI Onset

Z Scores in Acute Anterior MI

COLOR CODES Z Score P Value

3.08 .001 2.33 .01 1.65 .05

-1.64 to 1.64 NS -1.65 .05 -2.33 .01 -3.08 .001

MI Onset

Exploratory AnalysisWhat 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?

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

Thank you!