TESTING A TEST

Ian McDowellDepartment of Epidemiology &

Community MedicineJanuary 2008

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The Challenge of Clinical Measurement

• Diagnoses are based on information, from formal measurements and/or from your clinical judgment

• This information is seldom perfectly accurate:– Random errors can occur (machine not working?)– Biases in judgment or measurement can occur (“this kid

doesn’t look sick”)– Due to biological variability, this patient may not fit the

general rule– Diagnosis (e.g., hypertension) involves a categorical

judgment; this often requires dividing a continuous score (blood pressure) into categories. Choosing the cutting-point is challenging

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Therefore…

• You need to be aware … – That we express these complexities in terms of

probabilities

– That using a quantitative approach is better than just guessing!

– That you will gradually become familiar with the typical accuracy of measurements in your chosen clinical field

– That the principles apply to both diagnostic and screening tests

– Of some of the ways to describe the accuracy of a measurement

Attributes of Tests or Measures• Safety, Acceptability, Cost, etc.• Reliability: consistency or reproducibility;

this considers chance or random errors (which sometimes increase, sometimes decrease, scores)

• Validity: “Is it measuring what it is supposed to measure?” By extension, “what diagnostic conclusion can I draw from a particular score on this test?” Validity may be affected by bias, which refers to systematic errors (these fall in a certain direction)

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Reliability and ValidityReliability

Low High

Validity Low

High

•

••

•

•

•

•

• •

••

•

•••• ••

•••••

•

Biasedresult!

☺Average of these inaccurate results is not bad. This is probably how screening questionnaires (e.g., for depression) work

Ways of Assessing Validity

• Content or “Face” validity: does it make clinical or biological sense? Does it include the relevant symptoms?

• Criterion: comparison to a “gold standard” definitive measure (e.g., biopsy, autopsy)– Expressed as sensitivity and specificity

• Construct validity (this is used with abstract themes, such as “quality of life” for which there is no definitive standard)

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Criterion, or “Gold Standard”

The clinical observation or simple test is judged against

• More definitive (but expensive or invasive) tests, such as a complete work-up,

Or against

• Eventual outcome (for screening tests, when workup of well patients is unethical)

Sensitivity and specificity are calculated7

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2 x 2 Table for Testing a Test

TP = true positive; FP = false positive…

Golden Rule: always calculate based on the gold standard

Gold standard

Disease DiseasePresent AbsentTest score:

Test positive Test negative

a (TP) b (FP)

c (FN) d (TN)

Validity: Sensitivity Specificity = a/(a+c) = d/(b+d)

A Bit More on Sensitivity

= Test’s ability to detect disease when it is present

a/(a+c) = TP/(TP+FN)Mnemonics:

- a sensitive person is one who is aware of your feelings- (1 – seNsitivity) = false Negative rate = how many cases are missed by the screening test?

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…and More on SpecificityAbility to detect absence of disease when it is

truly absent (can it detect non-disease?)d/(b+d) = TN/(FP+TN)

• Mnemonics: – a specific test would identify only that type of

disease. “Nothing else looks like this”– (1- sPecificity) = false Positive rate (How many

are falsely classified as having the disease?)

• The FP idea will arise again, so keep it in mind!

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Most Tests Provide a Continuous Score. Selecting a Cutting Point

Pathologicalscores

Healthyscores

Move this way to increase sensitivity(include more of

sick group)

Move this way toincrease specificity

(exclude healthy people)

Test scores for a healthy population

Sick population

Crucial issue: changing cut-point can improve sensitivity or specificity, but never both

Possible cut-point

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Clinical applications• A specific test can be useful to

rule in a disease. Why?

– Very specific tests give few false positives.So, if the result is positive, you can be sure the patient has the condition (‘nothing else would give this result’): “SpPin”

D + D -

a bc d

T +T -

• A sensitive test can be useful for ruling a disease out:

–A negative result on a very sensitive test (which detects all true cases) reassures you thatthe patient does not have the disease: “SnNout”

Problems with Wrong Results

• False Positives can arise due to other factors (such as taking other medications, diet, etc.) They entail cost and danger of investigations, labeling, worry – This is similar to Type I or alpha error in a test of

statistical significance: the possibility of falsely concluding that there is an effect of an intervention.

• False Negatives imply missed cases, so potentially bad outcomes if untreated– cf Type II or beta error: the chance of missing a true

difference13

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Practical Question:“Doctor, how likely am I to have this disease?”

= Predictive Values

• Sensitivity & specificity don’t tell you this, because they work from the gold standard.

• Now you need to work from the test result, but you won’t know whether this person is a true positive or a false positive (or a true or false negative). Hmmm…

How accurately will a positive (or negative) result predicts disease (or health)?

Positive and Negative Predictive Values• Based on rows, not columns

• Positive Predictive Value (PPV) = a/(a+b) = Probability that a positive score is a true positive

• NPV = d/(c+d); same for a negative test result

• BUT… there’s a big catch:

• We are now working across the columns, so PPV & NPV depend critically on how many cases of disease there are (prevalence).

• As prevalence goes down, PPV goes down (it’s harder to find the smaller number of cases) and NPV rises.

• So, PPV and NPV must be determined for each clinical setting,

• But this is then immediately useful to clinician: reflects this population, so tell us about this patient

D + D -

a b

c dT +T -

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D + D -

T +

T -

50

5

10

100

Sensitivity = 50/55 = 91%Specificity = 100/110 = 91%

Prevalence = 55/165 = 33%

A. Specialist referral hospital

PPV = 50/60 = 83%NPV = 100/105 = 95%

D + D -

T +

T -

50

5

100

1000

Sensitivity = 50/55 = 91%Specificity = 1000/1100 = 91%

Prevalence = 55/1155 = 3%

B. Primary care

PPV = 50/150 = 33%NPV = 1000/1005 = 99.5%

Prevalence and Predictive Values

Imagine you know Sensitivity & Specificity. To work out PPV and NPV you need to guess

prevalence, then work backwards:

Fill cells in following order:

“Truth”Disease Disease Total PVPresent Absent

Test Pos

Test Neg

Total 1st2nd 3rd

4th

5th

(from sensitivity) (from specificity)

7th6th

8th

9th10th

11th

(from estimated prevalence)

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Gasp…! Isn’t there an easier way to do all this…?

Yes (good!)

But first, you need a couple more concepts (less good…)

• Before you apply a diagnostic test, prevalence gives your best guess about the chances that this patient has the disease.

• This is known as “Pretest Probability of Disease”: (a+c) / N in the 2 x 2 table:

• It can also be expressed as odds of disease: (a+c) / (b+d), as long asthe disease is rare

a b

c dN

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Test scores are continuous scales. You can use this to combine sensitivity and specificity:

Meet Receiver Operating Characteristic Curves

Work out Sen and Spec for every possible cut-point, then plot these.Area under the curve indicates the information provided by the test

1-Specificity ( = false positives)

Sens

itiv

ity

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Note: the theme ofsensitivity &(1-specificity) will appearagain!

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This Leads to … Likelihood Ratios

• Defined as the odds that a given level of a diagnostic test result would be expected in a patient with the disease, as opposed to a patient without: true positives / false positives. [TP / FP]

• Advantages:– Combines sensitivity and specificity into one number

– Can be calculated for many levels of the test

– Can be turned into predictive values

• LR for positive test = Sensitivity / (1-Specificity)• LR for negative test = (1-Sensitivity) / Specificity

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Practical application: a Nomogram

1) You need the LR for this test

2) Plot the likelihood ratio on

center axis (e.g., LR+ = 20)

Example:

Post-test probability = 91%

▪3) Select pretest probability

(prevalence) on left axis

(e.g. Prevalence = 30%) ▪4) Draw line through these points to right axis to indicate post-test probability of disease

Chaining LRs Together (1)

• Example: 45 year-old woman presents with “chest pain”

– Based on her age, pretest probability that a vague chest pain indicates CAD is about 1%

• Take a fuller history. She reports a 1-month history of intermittent chest pain, suggesting angina (substernal pain; radiating down arm; induced by effort; relieved by rest…)

– LR of this history for angina is about 100

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The previous example:1. From the

History:

Pretest probabilityrises to 50%

based on history

She’s young;pretest

probabilityabout 1%

LR 100

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Chaining LRs Together (2)

45 year-old woman with 1-month history of intermittent chest pain…After the history, post test probability is now about

50%. What will you do?Something more precise (but also more costly):

• Record an ECG– Results = 2.2 mm ST-segment depression.

LR for ECG 2.2 mm result = 10.– Overall post test probability is now >90% for

coronary artery disease (see next slide)

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The previous example: ECG Results

Now start pretest probability (i.e. 50%, prior to ECG, based onhistory)

Post-test probabilitynow rises

to 90%