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(Medical) Diagnostic Testing

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(Medical) Diagnostic Testing

- Patient presents with symptoms, and is suspected of having some disease. Patient either has the disease or does not have the disease.
- Physician performs a diagnostic test to assist in making a diagnosis.
- Test result is either positive (diseased) or negative(healthy).

Test Result

True Disease

Diseased

Healthy

Status

(+)

(-)

False Negative

Diseased (+)

Correct

False Positive

Healthy (-)

Correct

- False Positive: Healthy person incorrectly receives a positive (diseased) test result.
- False Negative: Diseased person incorrectly receives a negative (healthy) test result.

- Minimize chance (probability) of false positive and false negative test results.
- Or, equivalently, maximize probability of correct results.

- Sensitivity: probability that a person who truly has the disease correctly receives a positive test result.
- Specificity: probability that a person who is truly healthy correctly receives a negative test result.

Sensitivity= P(Test +|True +)

= P(Test+ and True+) ÷ P(True +)

Specificity= P(Test -|True -)

= P(Test- and True-) ÷ P(True -)

Sensitivity = 49/85 = 0.58

Specificity = 1475/2893 = 0.51

CDC screening questionnaire about as good as tossing a coin in identifying kids with elevated and normal lead levels.

- (Conditional) probabilities, so numbers between 0 and 1
- Closer sensitivity is to 1, the more accurate the test is in identifying diseased individuals
- Closer specificity is to 1, the more accurate the test is in identifying healthy individuals

False negative rate

= P(Test -|True +)

= 1 - P(Test +|True+)

= 1 - sensitivity

False positive rate

= P(Test +|True -)

= 1 - P(Test -|True -)

= 1 - specificity

False negative rate = 1 - 49/85 = 36/85 = 0.42

False positive rate= 1 -1475/2893

= 1418/2893 = 0.49

- Positive predictive value: probability that a person who has a positive test result really has the disease.
- Negative predictive value: probability that a person who has a negative test result really is healthy.

Positive predictive value

= P(True +|Test +)

= P(True + and Test +) ÷ P(Test +)

Negative predictive value

= P(True -|Test -)

= P(True - and Test -) ÷ P(Test -)

Positive predictive value = 49/1467 = 0.033

Negative predictive value = 1475/1511 = 0.98

Kids who test positive have small chance in having elevated lead levels, while kids who test negative can be quite confident that they have normal lead levels.

Reading positive and negative predictive values directly from table is accurate only if the proportion of diseased people in the sample is representative of the proportion of diseased people in the population. (Random sample!)

- Sens = 392/400 = 0.98
- Spec = 576/600 = 0.96
- PPV = 392/416 = 0.94
- NPV = 576/584 = 0.99

Looks good?

Note prevalence of disease is 400/1000 or 40%

- Sens = 49/50 = 0.98
- Spec = 912/950 = 0.96
- PPV = 49/87 = 0.56
- NPV = 912/913 = 0.999

Sensitivity and specificity the same, and yet PPV smaller -- because prevalence of disease is smaller, namely 50/1000 or 5%.

- Don’t recklessly read PPV and NPV directly from tables without knowing prevalence of disease.
- PPV in screening tests naturally low, but not all that bad since NPV generally high.

- True proportion of diseased people in the population.
- Sensitivity of the test
- Specificity of the test

- Rate of atypia in normal population is 0.001
- Sensitivity = 0.70
- Specificity = 0.90

Find probability that a woman will have atypical cervical cells given that she had a positive pap smear.

- PPV = 70/10,060 = 0.00696
- NPV = 89,910/89,940 = 0.999

Person with positive pap has tiny chance (0.6%) of truly having disease, while person with negative pap almost certainly will be disease free.

- How to calculate sensitivity and specificity
- Relationship between false negative (positive) rate and sensitivity (specificity)
- How disease prevalence affects predictive values
- How to calculate predictive values correctly
- Methodological standards…how good is that test?