Clinical Test Evaluation

Question 1

Study result positive

Answer 1

Actual outcome presentTrue +ve (TP)
Actual outcome absentFalse +ve (FP)
PPV = TP/(TP+FP)

Question 2

Study result negative

Answer 2

Actual outcome presentFalse -ve (FN)
Actual outcome absentTrue -ve (TN)
NPV = TN/(FN+TN)

Question 3

Actual outcome present

Answer 3

Sensitivity= TP/(TP+FN)

Question 4

Actual outcome absent

Answer 4

Specificity= TN/(FP+TN)

Question 5

Sensitivity

Answer 5

The sensitivity of a test refers to the proportion of people with a condition which it correctly identifies (i.e. test positive). This is also known as the true positive rate.

Sensitivity is calculated by the following:

Sensitivity = TP/(TP+FN)

Sensitivity is a stable characteristic and is not affected by the prevalence of the condition under study.

Question 6

Specificity

Answer 6

The specificity of a test refers to the proportion of people without a condition which are correctly identified (i.e. test negative). This is also known as the true negative rate.The false positive rate can be calculated by the following:

False positive rate = 1 - specificity

Specificity is calculated by the following:

Specificity = TN/(FP+TN)

Specificity is a stable characteristic and is not affected by the prevalence of the condition under stud

Question 7

Accuracy

Answer 7

Accuracy tell us how closely to its true value something is measured. In a 2 by 2 table it is given by the following equation, basically the proportion of results that are correct.

Accuracy = (TP + TN) / (TP + FP + TN + FN)

Put simply, this means how many times the result of the test was ‘right’.

Question 8

Predictive values

Answer 8

Sensitivity and specificity give us an indication as to the accuracy of a test. These are important but don’t help us make sense of test results. If a patient gets a positive test result then what they want to know is what this means to their likelihood of having the disease. Predictive values assist with this.

Important note: the sensitivity and specificity of a test are unaffected by the prevalence of a condition. The PPV and NPV are affected by the prevalence. As the prevalence of a condition falls the PPV falls and the NPV rises.

Question 9

Positive predictive value

Answer 9

This refers to the proportion of those scoring positive that actually have a condition (i.e. The chance that a positive result will be correct).

PPV = TP/(TP+FP)

If a test has a PPV of 10% then this means that among those who have a positive screening test, the probability of disease is 10%.

Question 10

Negative predictive value

Answer 10

This refers to the proportion of those scoring negative that don’t have a condition (i.e. The chance that a negative result will be correct).

NPV = TN/(FN+TN)

If a test has a NPV of 90% then this means that among those who have a negative screening test, the probability of not having the disease is 90%.

Question 11

Precision

Answer 11

The precision quantifies a tests ability to produce the same measurements with repeated tests

Question 12

Likelihood ratios

Answer 12

Likelihood ratios are much underused. This probably relates to their complexity as they involve the use of odds (rather than probabilities) or the use of simplifying aids such as Fagan’s nomogram.

Likelihood ratios tell us how much we should shift our suspicion for a particular test result. They combine specificity and sensitivity into a single figure that is intended to be more clinically useful. Unlike predictive values they are not affected by the prevalence of the condition. They can be used to refine our estimation of the probability of the disease being present by combing them with our initial estimation (pre test odds) to produce an aggregate figure (post test odds).

A likelihood ratio is the percentage of ill people with a given test result divided by the percentage of well individuals with the same result. Ideally, abnormal test results should be much more typical in ill individuals than in those who are well (high likelihood ratio) and normal test results should be most frequent in well people than in sick people (low likelihood ratio).

Question 13

Likelihood ratio for a positive result

Answer 13

Likelihood ratio for a positive test result (LR+) = probability of a patient with a disease having a positive test divided by the probability of a patient without the disease having a positive test result

LR+ = true positive rate / false positive rate

Or can be put another way

LR+ = sensitivity / (1 - specificity)

So if a test has a LR+ of 13 this means that a person with a disease is 13 times more likely to have a positive test result than a person without the disease

LR+ > 1 means that a positive test is more likely to occur in a person with a disease than in people without

LR+ < 1 means that a positive test is less likely to occur in a person with the disease than in a person without

Generally speaking a LR+ of 10 or more is considered to significantly increase the probability of a disease (rule in disease).

Question 14

Likelihood ratio for a negative result

Answer 14

Likelihood ratio for a negative test result (LR-) = probability of an individual with disease having a negative test divided by the probability of an individual without disease having a negative test.

LR- = false negative rate / true negative rate

Or

LR- = (1 - sensitivity) / specificity

So for a LR- of 0.2. This means that the probability of having a negative test for individuals with the disease is 0.2 times or about one-fifth of that of those without the disease. Put in another way, individuals without the disease are about five times more likely to have a negative test than individuals with the disease.

A LR- > 1 means that a negative test is more likely to occur in people with the disease than in people without the disease.

A LR- < 1 means that a negative test is less likely to occur in people with the disease compared to people without the disease.

Generally speaking, for patients who have a negative test, a LR- of more than 10 significantly increase the probability of disease (rule in disease) whilst a very low LR- (below 0.1) virtually rules out the chance that a person has the disease.

Question 15

Pre and post test odds

Answer 15

The pre test odds is the odds that the patient has the target disorder before the test is carried out (pre-test probability/ [1 - pre-test probability]).

The post test odds is the odds that the patient has the target disorder after the test is carried out (pre-test odds x likelihood ratio).

Question 16

Pre and post test probabilities

Answer 16

The pre-test probability is the proportion of people with the target disorder in the population at risk at a specific time (point prevalence) or time interval (period prevalence).

The post test probability is the proportion of patients with that particular test result who have the target disorder (post test odds/[1 + post-test odds]).

Question 17

Fagan’s nomogram

Answer 17

The use of odds rather than probabilities makes the calculations complex because pre-test probabilities must be converted to pre-test odds which is multiplied by the likelihood ratio to get the post-test odds which is then converted into post-test probabilities.

An easier method uses probabilities and Fagan’s nomogram.

In the nomogram, a straight line drawn from a patients pre-test probability through the likelihood ratio gives the post-test probability