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Transcript of @2003 Martin L Lesser, PhD
SCREENING AND
DIAGNOSTIC TESTING
Martin L Lesser, PhDBiostatistics Unit
Feinstein Institute for Medical Research
North Shore – LIJ Health System
@2003 Martin L Lesser, PhD
OUTLINE• What is a Screening test? • Objectives of Screening• Features of a Good Screening test?• Diagnostic Testing• Calculations: Sensitivity, Specificity,
PPV, NPV, Accuracy, Prevalence, Bayes’ Theorem, ROC Curves
What is a Screening test?
• A test administered to a group of asymptomatic people to detect the signs of a disease (does not diagnose… if positive, need further evaluation)
• Usually a secondary prevention technique-improve outcome of illness in ‘affecteds’-reduce severity of disease-reduce mortality
SCREENING vs DIAGNOSIS-asymptomatic -possibly symptomatic -usually in a high risk -not necessarily in high
group (f-hx, lifestyle) risk group-community setting -clinical setting-inexpensive -can be expensive-easy to administer -may be complex-less invasive -may be invasive-relatively safe -may be risky-does not diagnose per se -goal is definitive
diagnosis
Features of a Good Screening Test
• Detects disease prior to clinical symptoms• Effective therapy or treatment must exist for
the disease detected (accessible and acceptable to ‘screenee’)
• Early detection would likely lead to a cure or effective treatment
• Safe to administer (and quick)• Not very costly• Must not cause undue anxiety• Preferably, follow-up diagnostic test must
not be harmful, cumbersome or expensive• Results must be valid, reliable and
reproducible
• Serious (important) disease
Screening Test Examples• Sphygmomanometer: Hypertension, CAD,
CVA• Pap Smear: Cervical Cancer• PPD Test: Tuberculosis• Cholesterol test: Hypercholesterolemia,
CAD• Mammogram: Breast Cancer• Chest X-ray: Lung Cancer• Fecal Occult Blood Test: Colon Cancer• PSA: Prostate Cancer
Who should be screened?
-NOBODY -EVERYBODY -SOME
-no benefit -wasteful (low risk)
-harmful (no cure)
-costly
-who might benefit?
-high risk grp! -family hx!
-cheap!
Diseases Appropriate for Screening
• Must be serious
• Beneficial pre-symptomatic treatment
• High prevalence of preclinical disease
Standard 2x2 Table
Disease
Test
Resu
lt
Disease +
Disease -
Test +
Test -
b (FP)
c (FN)
a (TP)
d (TN)
Sensitivity
=a/(a+c)
Specificity
=d/(b+d)
PPV***=a/(a+b)
NPV***=d/(c+d)
***formula applicable only when sampling is cross-sectional -may have to use Bayes’ Rule!!!
PPV***=a/(a+b)
SENSITIVITY
=Persons with the disease who test positive x 100%_______________________________________________
Total number of persons with the disease
=a x 100%
_______________
(a + c )
Standard 2x2 Table
Disease + Disease -
Test + a (TP) b (FP)
Test - c (FN) d (TN)
SPECIFICITY
=Persons without the disease who test negative x 100%_______________________________________________Total number of persons without the disease
=d x 100%
_______________ (b + d)
Standard 2x2 Table
Disease + Disease -
Test + a (TP) b (FP)
Test - c (FN) d (TN)
POSITIVE PREDICTIVE VALUE (PPV)
=Persons with a positive test who have the disease x 100%_______________________________________________
Total number of persons who test positive
=a x 100%
_______________
(a + b)
Standard 2x2 Table
Disease + Disease -
Test + a (TP) b (FP)
Test - c (FN) d (TN)
NEGATIVE PREDICTIVE VALUE (NPV)
=Persons with a negative test who don’t have disease x 100%_______________________________________________
Total number of persons who test negative
=d x 100%
_______________
(c + d)
Standard 2x2 Table
Disease + Disease -
Test + a (TP) b (FP)
Test - c (FN) d (TN)
ACCURACY
=Persons with a correct diagnosis x 100%_______________________________________________
Total number of persons tested
=(a+d) x
100%_______________(a + b + c +
d)
=(TP + TN) x
100%____________________
(a + b + c + d)
Standard 2x2 Table
Disease + Disease -
Test + a (TP) b (FP)
Test - c (FN) d (TN)
Test Characteristics• Fixe
d
• Relative
(Population Independent)
(Population Dependent)
-Sensitivity
-Likelihood that someone with disease has a positive test
-Specificity
-Likelihood that someone without disease has a negative test
-Positive Predictive Value
-Likelihood that someone with a positive test has the disease
-Negative Predictive Value
-Likelihood that someone with a negative test does not have the disease
Fixed Characteristics
• Screening Rule Out High Sensitivity• Diagnosis Rule In High Specificity
Highly Sensitive Test
-picks up most people with disease who truly have disease
Highly Specific Test
-unlikely to mislabel people as having disease when in fact they do not have the disease
-good for screening!!!
-avoid unnecessary treatment!!!
ExamplesExample 1 : PPD Test
for TB Diameter > 1 mm
=> TB+-results in too many
TB+’s (high FP)
Example 2 : CA125 in Ovarian Ca
-elevated CA125 even in non-Ovarian Cancer cases!!!
-unlikely to miss a true case of Ovarian Ca (high sensitivity)
-many people who don’t have the disease will test positive
(low specificity)
Relative Characteristics
PPV and NPV are related to the overall prevalence of the disease in the population you are testing!
NOTE! We normally assume that Sensitivity and Specificity remain constant regardless of the prevalence of the disease in the population you are testing .
Prevalence and PPV
Example: HIV Testing
1. Drug Rehab Center 2. Monastery of St. Claire
Bayes’ TheoremPPV/NPV: influenced by 3
quantities:
•Sensitivity
•Specificity
•Prevalence (prior odds)
**As Prevalence increases->
PPV increases!
**As Prevalence increases->
NPV decreases!
Bayes’ Formula for PPVPPV= Pr (D+| T+) x 100%
=Pr (T+|D+) x Pr (D+) x 100%_______________________________________________{Pr (T+|D+) x Pr (D+)} + {Pr(T+|D-) x
Pr(D-)}
=sens x prev x 100%
_____________________________________{sens x prev} + {(100-spec) x
(100-prev)}
Bayes’ Formula for NPVNPV= Pr (D-| T-) x 100%
=Pr (T-|D-) x Pr (D-) x 100%_______________________________________________{Pr (T-|D-) x Pr (D-)} + {Pr(T-|D+) x
Pr(D+)}
=spec x (100-prev) x 100%
_________________________________________{spec x (100-prev)} + {(100-
sens) x prev}
How to Set Cut Points
-It’s like tuning your radio!
-Want to pick up certain frequencies (disease)Want to catch disease, i.e. Minimize missing disease
Avoid too many false positives
Attain a balance of Sensitivity and Specificity!!!
Receiver Operating Characteristic Curves (ROC Curves)
Legend: England--Battle of Britain -performance of radar receiver
operators
TP: Correct early warning of German planes coming over the English Channel
FP: Receiver operator sent out alarm but no enemy planes appeared
FN: German planes appeared without previous warning from the radar operators.
Constructing an ROC Curve
Simply:
Plot Sensitivity on the Y-axisagainst FP (or 100-Specificity) on the X-axis
Hypothetical Example:Blood Pressure Screening to Predict 10-Year Stroke Risk in Subjects 50
Years and Older-Take single blood pressure measurement in a large number of subjects
-Follow subjects for 10 years to determine stroke status
Cutoff for + Test (SBP)
> 0 mm Hg
Sensitivity
100%
FP
100%
> 500 mm Hg
0% 0%
> 120 mm Hg
?? ??
> 130 mm Hg
?? ?? ?? > 140 mm
Hg
Specificity
0%
100%
??
?? ?? ??
CUTOFF SENSI TI VI TY SPECI FI CI TY FP 0 100 0 100
110 98 12 88 120 95 40 60 130 90 55 45 140 75 80 20 150 58 90 10 160 40 94 6 180 20 97 3 200 10 98 2 500 0 100 0
Competing Screening Tests
-Plot the ROC curves on the same graphExample: SBP vs. Cholesterol vs.
HgbA1c
-Area Under the ROC curve:
is the probability that a randomly selected pair of normal and abnormal subjects can be correctly classified
Do Screening Tests Work?
•Analysis of Outcomes
Survival of those diagnosed by screening prior to symptoms
versus
Survival of those diagnosed at the time of symptomatic presentation
•Other ways: (Randomized trial, Population based study)
Lead Time Bias
Precancerous
Cells
Small Nodule
Advanced Disease
Death
Time from Dx at Screening to Death
Time from Dx at Clinical Presentation to Death
Lead Time
Length Bias-------------------------------------------------------
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Other Sources of Bias (Source: Begg CB, Statistics in Medicine 1987)
Subject Selection•Case Mix•Verification bias•Uninterpretable test results•Inter-observer variation•Temporal changes
Methodology•Influence of clinical factors on interpretation•Variation in positivity criterion•Absence of a definitive reference test•Cutoff point validation bias
REFERENCES• Jekel, JK, Katz, DL, Elmore JG. Epidemiology,
Biostatistics, and Preventive Medicine. 2nd Ed. 2001. WB Saunders Company-Harcourt Health Sciences.
• Hennekens CH MD DrPH, Buring JE, ScD. Edited by Mayrent SL, PhD. Epidemiology in Medicine. 1st Ed. 1987. Little Brown and Company, Boston/Toronto.
• Dawson B, Trapp RG. Basic & Clinical Biostatistics.
3nd Ed. 2000. McGraw-Hill Medical Publishing Division.
• Lesser, ML in Fishman-Javitt MC, MD Stein HL, MD Lovecchio JL, MD (eds). 1990. Imaging of the Pelvis-MRI and Correlations to CT and Ultrasound.
@2002 Cristina P. Sison, PhD
Thanks!
For Statistical consulting, call:
NORTH SHORE-LIJ HEALTH SYSTEM: BIOSTATISTICS UNIT(516) 240-8300CORNELL PEOPLE: (212) 746-8544CORNELL GCRC: (212) 746-6291
@2002 Cristina P. Sison, PhD