Medical diagnostic testing
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(Medical) Diagnostic Testing. The situation. 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.

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(Medical) Diagnostic Testing

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Medical diagnostic testing

(Medical) Diagnostic Testing


The situation

The situation

  • 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).


Situation presented in a two way table

Situation presented in a two-way table

Test Result

True Disease

Diseased

Healthy

Status

(+)

(-)

False Negative

Diseased (+)

Correct

False Positive

Healthy (-)

Correct


Definitions

Definitions

  • False Positive: Healthy person incorrectly receives a positive (diseased) test result.

  • False Negative: Diseased person incorrectly receives a negative (healthy) test result.


Medical diagnostic testing

Goal

  • Minimize chance (probability) of false positive and false negative test results.

  • Or, equivalently, maximize probability of correct results.


Accuracy of tests in development

Accuracy of tests in development

  • 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.


In conditional probability notation

Sensitivity= P(Test +|True +)

= P(Test+ and True+) ÷ P(True +)

In conditional probability notation

Specificity= P(Test -|True -)

= P(Test- and True-) ÷ P(True -)


Example

Example


Example continued

Sensitivity = 49/85 = 0.58

Example (continued)

Specificity = 1475/2893 = 0.51

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


Interpretation of accuracy

Interpretation of accuracy

  • (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


Alternatively

False negative rate

= P(Test -|True +)

= 1 - P(Test +|True+)

= 1 - sensitivity

Alternatively

False positive rate

= P(Test +|True -)

= 1 - P(Test -|True -)

= 1 - specificity


Example1

Example


Example continued1

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

Example (continued)

False positive rate= 1 -1475/2893

= 1418/2893 = 0.49


Accuracy of tests in use

Accuracy of tests in use

  • 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.


In conditional probability notation1

Positive predictive value

= P(True +|Test +)

= P(True + and Test +) ÷ P(Test +)

In conditional probability notation

Negative predictive value

= P(True -|Test -)

= P(True - and Test -) ÷ P(Test -)


Example2

Example


Example continued2

Positive predictive value = 49/1467 = 0.033

Example (continued)

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.


Caution about predictive values

Caution about predictive values!

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!)


Example3

Example


Example continued3

Example (continued)

  • 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%


Example4

Example


Example continued4

Example (continued)

  • 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%.


Morals

Morals

  • 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.


Find correct predictive values by knowing

Find correct predictive values by knowing….

  • True proportion of diseased people in the population.

  • Sensitivity of the test

  • Specificity of the test


Example ppv of pap smears

Example: PPV of pap smears?

  • 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.


Example5

Example


Example6

Example


Example7

Example


Example8

Example


Example9

Example


Example continued5

Example (continued)

  • 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.


What to know

What to know

  • 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?


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