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!