Stats - evaluating clinical tests + disease rates

Question 1

How do you calculate the likelihood ratio of a positive test result?

Answer 1

Sensitivity / (1 - specificity)

Question 2

In a positive study result, what are the two outcomes?
How do we calculate the Positive Predictive Value (PPV)?

Answer 2

Study result positive:

True +ve (TP)
False +ve (FP)

PPV = TP/(TP+FP)

Question 3

In a negative study result, what are the two outcomes?
How do we calculate the Negative Predictive Value (NPV)?

Answer 3

Study result negative

False -ve (FN)
True -ve (TN)

NPV = TN/(FN+TN)

Question 4

What is the PPV and how is it calculated?

Answer 4

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 5

What is the NPV and how is it calculated?

Answer 5

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 6

What is the sensitivity?

How is it calculated?

Answer 6

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)

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

Question 7

What is the specificity?

How is it calculated?
How is the False positive rate calculated?

Answer 7

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)

NOTE: Specificity is a stable characteristic and is not affected by the prevalence of the condition under study.

Question 8

What is accuracy? How is this calculated in a 2x2 table?

Answer 8

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 9

Why are predictive values important, compared with sensitivity and specificity?
How do the PPV and NPV relate to the prevalence?

Answer 9

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 10

What is precision?
What 2 things are necessary to ensure precision in a test?

Answer 10

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

Both reproducibility and accuracy, are necessary to describe a measure as precise.

Question 11

What are likelihood ratios?

Answer 11

These are used for assessing the value of performing a diagnostic test They combine specificity and sensitivity into a single figure that is intended to be more clinically useful.

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

They involve the use of odds (rather than probabilities) or the use of simplifying aids such as Fagan’s nomogram.

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).

Question 12

Define the likelihood ratio for a positive test result (LR+)

Answer 12

(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
(sensitivity / (1 - specificity))

Question 13

What do the different levels of LR+ represent?
What level is needed to rule in a disease?

Answer 13

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

Define the likelihood ratio for a negative test result (LR-)

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
- (1 - sensitivity) / specificity

Question 15

What do the different levels of LR- represent?
What level is needed to rule out a disease?

Answer 15

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 16

What are the pre-test odds?
How are they calculated?

Answer 16

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]).

Question 17

What are the post-test odds?
How are they calculated?

Answer 17

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 18

What is the Odds Ratio?

Answer 18

Odds are calculated by dividing the number of times an event happens by the number of times is does not happen.

For example…

If 2 in every 100 patients treated with an antipsychotic have a seizure then the odds of developing a seizure if given an antipsychotic is 2/98 = 0.0204

IMPORTANT:

Odds - remember a ratio of the number of people who incur a particular outcome to the number of people who do not incur the outcome

NOT a ratio of the number of people who incur a particular outcome to the total number of people

Odds of stroke in group B (new drug) = 10/50 = 1/5 (60 PATIENTS)

Odds of stroke in group A (treatment as usual) = 20/80 = 1/4 (100 PATIENTS)

Odds ratio of having a stroke = 1/5 divided by 1/4 = 0.8

An odds ratio of < 1 implies that the risk of stroke is less in those exposed to the new drug compared to those receiving standard treatment.

Question 19

What is pre-test probability?

Answer 19

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).

Question 20

What is post-test probability? How is it calculated?

Answer 20

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 21

What diagram is used to calculate post-test probability? How does this work?

Answer 21

Fagan’s nomogram

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.

Question 22

What is the “attributable risk?” What does it tell you?

Answer 22

The attributable risk is the rate in the exposed group minus the rate in the unexposed group.

For example the attributable risk for lung cancer in smokers is the rate of lung cancer in smokers minus the rate of cancer in non smokers.
Essentially it tells you what proportion of deaths in the exposed group were due to the exposure

Question 23

What is the relative risk (RR)

What is this also known as (though not technically correct)?

Answer 23

The relative risk (RR) is the risk of an event relative to exposure. It is also known as the risk ratio

Note: Although risk ratio (RR) and relative risk (also abbreviated RR) are often used interchangeably, there are distinctions in specific contexts, especially in case-control studies where the odds ratio (OR) is more applicable. Therefore, equating these terms without proper context can be confusing in practice, particularly in research or clinical epidemiology.

Question 24

How is the RR calculated?

A = exposed and diseased
B = exposed and not diseased

C = not exposed and diseased
D = not exposed and not diseased

Answer 24

A/(A+B)
Divided by
C(C+D)

Question 25

How is the RR interpreted?

Answer 25

A relative risk of 1 means there is no difference between the two groups.

A relative risk of <1 means that the event is less likely to occur in the exposed group.

A relative risk of >1 means that the event is more likely to occur in the exposed group.

A RR of 20 = exposed group 20x more likely to have the disease/ effect

Question 26

What is the population attributable risk?

Answer 26

The population attributable risk can be described as the reduction in incidence that would be observed if the population were entirely unexposed. For instance how would the incidence of lung cancer change if everyone stopped smoking? It can be calculated by multiplying the attributable risk by the prevalence of exposure in the population.

Question 27

What is the null effect value for:

relative statistics e.g OR, RR
absolute statistics e.g ARR, SMD

Answer 27

Relative statistics like OR or RR have a null effect value of 1 whereas absolute statistics like Absolute Risk or ARR or SMD, have a null difference value of 0.