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