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.

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Diagnostic Testing

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Diagnostic testing

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

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 dilemma1

The Provider Dilemma

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


Diagnostic testing

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 Thought Process

  • Clinician derives patient prior prob. of disease:

    • H & P

    • Literature

    • Experience

  • “Index of Suspicion”

    • 0% - 100%

    • “Low, Med., High”


Threshold approach to diagnostic testing

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


Threshold approach to diagnostic testing1

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


Test characteristics

Reliability

Inter observer

Intra observer

Correlation

B&A Plot

Simple Agreement

Kappa Statistics

Validity

Sensitivity

Specificity

NPV

PPV

ROC Curves

Test Characteristics


Reliability

Reliability

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


Reliability1

Reliability

Not Reliable

Reliable


Intra rater reliability

Intra rater reliability

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


Inter rater reliability

Inter rater reliability

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


Correlation r

Correlation (r)

  • For continuous data

  • r = 1 perfect

  • r = 0 none

O1

O1 = O2

O2

Bland & Altman, 1986


Correlation r1

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

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


Simple agreement

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


Kappa

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


Interpreting kappa values

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


Weighted kappa

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

Validity

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

  • Internal Validity

  • External Validity


Validity1

Validity

Valid, not reliable

Reliable and Valid


Internal validity

Internal Validity

  • Performance Characteristics

  • Sensitivity

  • Specificity

  • NPV

  • PPV

  • ROC Curves


2 x 2 table

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

Gold Standard

  • Definitive test used to identify cases

  • Example: traditional agar culture

  • The dipstick and dipslide are measured against the gold standard


Sensitivity sn

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

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

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

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

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


Predictive value problems

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

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 pain1

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


Receiver operator curve

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 curve1

Receiver Operator Curve

  • Avoids the “single cutoff trap”

Sepsis

Effect

No Effect

WBC Count

Gallagher, 1998


Area under the curve

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

Problem with ROC curves

  • Same problems as SN and SP “Reverse Logic”

  • Mainly used to describe Dx test performance


Appendicitis example

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 example1

Appendicitis Example

SN 76% (65%-84%)

SP 52% (45%-60%)

PPV 42% (35%-51%)

NPV 82% (74%-89%)

Cardall, 2004


Appendicitis example2

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

Abdominal CT


Follow up

Follow UP

  • CT result: acute appendicitis

  • Patient taken to OR for appendectomy


Diagnostic testing

But, was WBC necessary?

Answer given in talk on Likelihood Ratios


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