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Diagnostic Testing. Ethan Cowan, MD, MS Department of Emergency Medicine Jacobi Medical Center Department of Epidemiology and Population Health Albert Einstein College of Medicine. The Provider Dilemma.

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Diagnostic Testing

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Diagnostic Testing

Ethan Cowan, MD, MS

Department of Emergency Medicine

Jacobi Medical Center

Department of Epidemiology and Population Health

Albert Einstein College of Medicine


The Provider Dilemma

  • A 26 year old pregnant female presents after twisting her ankle. She has no abdominal or urinary complaints. The nurse sends a UA and uricult dipslide prior to you seeing the patient. What should you do with the results of these tests?


The Provider Dilemma

  • Should a provider give antibiotics if either one or both of these tests come back positive?


Why Order a Diagnostic Test?

  • When the diagnosis is uncertain

  • Incorrect diagnosis leads to clinically significant morbidity or mortality

  • Diagnostic test result changes management

  • Test is cost effective


Clinician Thought Process

  • Clinician derives patient prior prob. of disease:

    • H & P

    • Literature

    • Experience

  • “Index of Suspicion”

    • 0% - 100%

    • “Low, Med., High”


Probability of Disease

0%

100%

Testing Zone

P(+)

P(-)

Threshold Approach to Diagnostic Testing

  • P < P(-)Dx testing & therapy not indicated

  • P(-) < P < P(+)Dx testing needed prior to therapy

  • P > P(+) Only intervention needed

Pauker and Kassirer, 1980, Gallagher, 1998


Probability of Disease

0%

100%

Testing Zone

P(+)

P(-)

Threshold Approach to Diagnostic Testing

  • Width of testing zone depends on:

    • Test properties

    • Risk of excess morbidity/mortality attributable to the test

    • Risk/benefit ratio of available therapies for the Dx

Pauker and Kassirer, 1980, Gallagher, 1998


Reliability

Inter observer

Intra observer

Correlation

B&A Plot

Simple Agreement

Kappa Statistics

Validity

Sensitivity

Specificity

NPV

PPV

ROC Curves

Test Characteristics


Reliability

  • The extent to which results obtained with a test are reproducible.


Reliability

Not Reliable

Reliable


Intra rater reliability

  • Extent to which a measure produces the same result at different times for the same subjects


Inter rater reliability

  • Extent to which a measure produces the same result on each subject regardless of who makes the observation


Correlation (r)

  • For continuous data

  • r = 1 perfect

  • r = 0 none

O1

O1 = O2

O2

Bland & Altman, 1986


Correlation (r)

  • Measures relation strength, not agreement

  • Problem: even near perfect correlation may indicate significant differences between observations

O1

r = 0.8

O1 = O2

O2

Bland & Altman, 1986


Bland & Altman Plot

O1 – O2

  • For continuous data

  • Plot of observation differences versus the means

  • Data that are evenly distributed around 0 and are within 2 STDs exhibit good agreement

10

0

-10

[O1 + O2] / 2

Bland & Altman, 1986


a

b

c

d

Simple Agreement

Rater 1

Rater 2

  • Extent to which two or more raters agree on the classifications of all subjects

  • % of concordance in the 2 x 2 table (a + d) / N

  • Not ideal, subjects may fall on diagonal by chance

-

+

total

-

a + b

+

c + d

total

a + c

b + d

N


a

b

c

d

Kappa

Rater 1

Rater 2

  • The proportion of the best possible improvement in agreement beyond chance obtained by the observers

  • K = (pa – p0)/(1-p0)

  • Pa = (a+d)/N (prop. of subjects along the main diagonal)

  • Po = [(a + b)(a+c) + (c+d)(b+d)]/N2 (expected prop.)

-

+

total

-

a + b

+

c + d

total

a + c

b + d

N


K=1

K > 0.80

0.60 < K < 0.80

0.40 < K < 0.60

0 < K < 0.40

K = 0

K < 0

Perfect

Excellent

Good

Fair

Poor

Chance (pa = p0)

Less than chance

Interpreting Kappa Values


n11

n12

...

n1C

n21

n22

...

n2C

 . .

 . .

...

...

 . .

nC1

nC2

...

nCC

Weighted Kappa

Rater 1

Rater 2

1

2

...

C

total

  • Used for more than 2 observers or categories

  • Perfect agreement on the main diagonal weighted more than partial agreement off of it.

1

n1.

2

n2.

 . .

 . .

C

nC.

total

n.1

n.2

...

n.C

N


Validity

  • The degree to which a test correctly diagnoses people as having or not having a condition

  • Internal Validity

  • External Validity


Validity

Valid, not reliable

Reliable and Valid


Internal Validity

  • Performance Characteristics

  • Sensitivity

  • Specificity

  • NPV

  • PPV

  • ROC Curves


2 x 2 Table

Disease Status

TP = True Positives

FP = False Positives

total

noncases

cases

positives

Test Result

+

TP

FP

negatives

-

FN

TN

total

cases

noncases

N

TN = True Negatives

FN = False Negatives


Gold Standard

  • Definitive test used to identify cases

  • Example: traditional agar culture

  • The dipstick and dipslide are measured against the gold standard


Sensitivity (SN)

Disease Status

  • Probability of correctly identifying a true case

  • TP/(TP + FN) = TP/ cases

  • High SN, Negative test result rules out Dx (SnNout)

total

noncases

cases

positives

Test Result

+

TP

FP

negatives

-

FN

TN

total

cases

noncases

N

Sackett & Straus, 1998


Specificity (SP)

Disease Status

  • Probability of correctly identifying a true noncase

  • TN/(TN + FP) = TN/ noncases

  • High SP, Positive test result rules in Dx (SpPin)

total

noncases

cases

positives

Test Result

+

TP

FP

negatives

-

FN

TN

total

cases

noncases

N

Sackett & Straus, 1998


Problems with Sensitivity and Specificity

  • Remain constant over patient populations

  • But, SN and SP convey how likely a test result is positive or negative given the patient does or does not have disease

  • Paradoxical inversion of clinical logic

  • Prior knowledge of disease status obviates need of the diagnostic test

Gallagher, 1998


Positive Predictive Value (PPV)

Disease Status

  • Probability that a labeled (+) is a true case

  • TP/(TP + FP) = TP/ total positives

  • High SP corresponds to very high PPV (SpPin)

total

noncases

cases

positives

Test Result

+

TP

FP

negatives

-

FN

TN

total

cases

noncases

N

Sackett & Straus, 1998


Negative Predictive Value (NPV)

Disease Status

  • Probability that a labeled (-) is a true noncase

  • TN/(TN + FN) = TP/ total negatives

  • High SN corresponds to very high NPV (SnNout)

total

noncases

cases

positives

Test Result

+

TP

FP

negatives

-

FN

TN

total

cases

noncases

N

Sackett & Straus, 1998


Vulnerable to Disease Prevalence (P) Shifts

Do not remain constant over patient populations

As PPPV NPV

As PPPV NPV

Predictive Value Problems

Gallagher, 1998


Flipping a Coin to Dx AMI for People with Chest Pain

ED AMI Prevalence 6%

SN = 3 / 6 = 50%SP = 47 / 94 = 50%

PPV= 3 / 50 = 6%NPV = 47 / 50 = 94%

Worster, 2002


Flipping a Coin to Dx AMI for People with Chest Pain

CCU AMI Prevalence 90%

SN = 45 / 90 = 50% SP = 5 / 10 = 50%

PPV= 45 / 50 = 90%NPV = 5 / 50 = 10%

Worster, 2002


1.0

Sensitivity

(TPR)

0.0

0.0

1.0

1-Specificity (FPR)

Receiver Operator Curve

  • Allows consideration of test performance across a range of threshold values

  • Well suited for continuous variable Dx Tests


Receiver Operator Curve

  • Avoids the “single cutoff trap”

Sepsis

Effect

No Effect

WBC Count

Gallagher, 1998


Area Under the Curve (θ)

1.0

  • Measure of test accuracy

  • (θ) 0.5 – 0.7 no to low discriminatory power

  • (θ) 0.7 – 0.9 moderate discriminatory power

  • (θ) > 0.9 high discriminatory power

Sensitivity

(TPR)

0.0

0.0

1.0

1-Specificity (FPR)

Gryzybowski, 1997


Problem with ROC curves

  • Same problems as SN and SP “Reverse Logic”

  • Mainly used to describe Dx test performance


Physical Exam

+

OR

CT Scan

-

-

+

No Appy

Appy

Appendicitis Example

  • Study design:

  • Prospective cohort

  • Gold standard:

  • Pathology report from appendectomy or CT finding (negatives)

  • Diagnostic Test:

  • Total WBC

Cardall, 2004


Appendicitis Example

SN 76% (65%-84%)

SP 52% (45%-60%)

PPV 42% (35%-51%)

NPV 82% (74%-89%)

Cardall, 2004


Physical Exam

+

OR

CT Scan

-

-

+

No Appy

Appy

Appendicitis Example

  • Patient WBC:

  • 13,000

  • Management:

  • Get CT with PO & IV Contrast

Cardall, 2004


Abdominal CT


Follow UP

  • CT result: acute appendicitis

  • Patient taken to OR for appendectomy


But, was WBC necessary?

Answer given in talk on Likelihood Ratios


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