The Statistically MeaningfulDisplay of Analog Data

Robert A. Warner, MD

Laboratory of Logic and ExperimentalPhilosophy

Simon Fraser University

Vancouver, BC, Canada

Interpreting Analog Displays

• Do any parts of the display differfrom a reference standard?

• Are the differences genuine ormerely 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 adistribution (unlike percentiles)

• Can use demographically specificnormal reference populations

• Directly translatable to P values

Z Scores, P Values & Coding

0.001<3.08

0.01<2.33

0.05<-1.65

NS-1.64 to 1.64

0.05>1.65

0.01>2.33

0.001>3.08

B&W CodeP ValueZ Score

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

Analog ECG Display

COLOR CODESZ Score P Value

3.08 .0012.33 .011.65 .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 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 # # # # #

Validation of the Z Score Method

• Compared abilities of Z scores vs. 2 widely-used commercial ECG algorithms to detectprior inferior and anterior MI

• 1138 patients (mean age 53, 426 females),497 cath-proven normals, 366 prior inferiorMI, 275 prior anterior MI

• Used Z scores of Q waves in aVF and initialR waves in V2

• The commercial algorithms use voltages, notZ scores.

Inferior MIZ Scores vs. AlgorithmsSensitivities @ 95% Specificity

0

10

20

30

40

50

60

70

80

90

100

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

10

20

30

40

50

60

70

80

90

100

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 comparisonsto 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 9

AM AM AM PM PM PM PM PM PM PM PM PM

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

PM PM PM AM AM AM AM AM AM AM AM AM

6

PM

7:00

PM

PM PM

6:20 6:25

PM

6:30 6:45

PM

6:05 6:10 6:15

PM

PM

6:35

PM

6:40

PM PM

6:50

PM

6:55

PM

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 dataprovided

• Concordant orthogonal parametersincrease the accuracy of diagnosis

• Parameters measured in differentunits are hard to displaysimultaneously and to interpret

Importance of Similar Scales

0.00

5.00

10.00

15.00

20.00

25.001 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

ZS

co

re

ST_V2

ST_aVF

S4 Conf

S3 Conf

HEARTRATE

MI Onset

Z Scores in Acute Anterior MI

COLOR CODESZ Score P Value

3.08 .0012.33 .011.65 .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 159known normals vs. 103known healed anterior MI’s.Which parts of which leadsdiscriminate the best?

Some Uses of Z Scores

• Medical practice and research

• Physical, biological and behavioral science

• Engineering, industrial processes and qualitycontrol

• Assessing the performance of mechanicaland electrical equipment

• Economics, finance and investing

• Teaching the interpretation of analog displays

• Biofeedback

Thank you!