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Evidence Based Medicine

Statistics

Question 9 of 180

Which of the following best describes the positive predictive value of a diagnostic test:

Answer:

Positive predictive value (PPV) is the proportion of individuals with a positive test result who actually have the disease.

Characteristics of Diagnostic Tests

Those with disease Those without disease Total
Test positive a b a+b
Test negative c d c+d
Total a+c b+d n=a+b+c+d

Test Characteristics

Sensitivity is the proportion of patients WITH the disease (true positives) who have a POSITIVE test result i.e. that are correctly identified by the test as having the disease = true positive rate.

“If I have Disease X, what is the likelihood I will test positive for it?”

Sensitivity = a/(a+c)

Specificity is the proportion of patients WITHOUT the disease (true negatives) who have a NEGATIVE test result i.e. that are correctly identified by the test as not having the disease = true negative rate.

"If I do not have disease X, what is the likelihood I will test negative for it?"

Specificity = d/(b+d)

Positive predictive value (PPV) is the proportion of individuals with a POSITIVE test result who HAVE the disease.

"If I have a positive test, what is the likelihood I have disease X?"

PPV = a/(a+b)

Negative predictive value (NPV) is the proportion of individuals with a NEGATIVE test result who DO NOT HAVE the disease.

“If I have a negative test, what is the likelihood I do not have Disease X?”

NPV = d/(c+d)

In a perfect test, the sensitivity, specificity, PPV and NPV would be 1 (100%). The lower the value (the closer to 0), the less useful the test.

When a highly specific test is used, a positive test result tends to rule in the disorder - SpPin

When a highly sensitive test is used, a negative test tends to rule out the disorder - SnNout

N.B. Predictive values are dependent on the prevalence of the disease in the population being studied (PPV will decrease as a disease becomes rarer in the population whereas NPV will increase). Sensitivity and specificity are independent of prevalence.

Test Characteristic Definition Formula
Point prevalence The proportion of people diagnosed by the gold standard as having the disease at that time. Point prevalence = (a+c)/n
Sensitivity The proportion of patients with the disease (true positives) who are correctly identified by the test as having the disease = true positive rate. Sensitivity = a/(a+c)
Specificity The proportion of patients without the disease (true negatives) who are correctly identified by the test as not having the disease = true negative rate. Specificity = d/(b+d)
Positive predictive value (PPV) The proportion of individuals with a positive test result who actually have the disease. PPV = a/(a+b)
Negative predictive value The proportion of individuals with a negative test result who do not have the disease. NPV = d/(c+d)
Positive likelihood ratio (LR+) The ratio of the chance of a positive result if the patient has the disease to the chance of a positive result if they do not have the disease. LR+ = sensitivity/(1 - specificity)
Negative likelihood ratio (LR-) The ratio of the chance of a negative result if the patient has the disease to the chance of a negative result if they do not have the disease. LR- = (1 -sensitivity)/specificity
Accuracy of a test The proportion of patients given the correct result. Accuracy = (a+d)/n

Likelihood Ratios

A likelihood ratio is a measure of the diagnostic value of a test. Likelihood ratios show how many times more likely patients with a disease are to have a particular test result than patients without the disease. Likelihood ratios are more useful than predictive values because they are calculated from sensitivity and specificity and therefore remain constant even when the prevalence of the disorder changes.

The likelihood ratio for a positive test result (LR+) is the ratio of the chance of a positive result if the patient has the disease to the chance of a positive result if they do not have the disease.

For ruling in a diagnosis, LR+ = sensitivity/(1 - specificity)

The likelihood ratio for a negative test result (LR-) is the ratio of the chance of a negative result if the patient has the disease to the chance of a negative result if they do not have the disease.

For ruling out a diagnosis, LR- = (1 - sensitivity)/specificity

A test with a high LR+ (>5) is good at increasing certainty about the presence of a disease and a low LR- (<0.2) is good at increasing certainty about the absence of a disorder. LRs around 1 are unhelpful.

Use of Likelihood Ratios

Knowing the LR+ gives a simple way to estimate how likely someone is to have the disease, if one knows the prevalence, or probability of disease before the test, without having to set up a contingency table.

Patient Risk & Odds Description Formula
Pre-test probability (equivalent to the prevalence) The probability that a patient will have the disease (a+c)/n
Pre-test odds The odds that a patient will have the disease pre-test probability/(1 - pre-test probability)
Post-test odds The odds a patient with a positive test result actually has the disease pre-test odds x LR+
Post-test probability The probability that a patient with a positive test result actually has the disease post-test odds/(post-test odds + 1)

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  • Biochemistry
  • Blood Gases
  • Haematology
Biochemistry Normal Value
Sodium 135 – 145 mmol/l
Potassium 3.0 – 4.5 mmol/l
Urea 2.5 – 7.5 mmol/l
Glucose 3.5 – 5.0 mmol/l
Creatinine 35 – 135 μmol/l
Alanine Aminotransferase (ALT) 5 – 35 U/l
Gamma-glutamyl Transferase (GGT) < 65 U/l
Alkaline Phosphatase (ALP) 30 – 135 U/l
Aspartate Aminotransferase (AST) < 40 U/l
Total Protein 60 – 80 g/l
Albumin 35 – 50 g/l
Globulin 2.4 – 3.5 g/dl
Amylase < 70 U/l
Total Bilirubin 3 – 17 μmol/l
Calcium 2.1 – 2.5 mmol/l
Chloride 95 – 105 mmol/l
Phosphate 0.8 – 1.4 mmol/l
Haematology Normal Value
Haemoglobin 11.5 – 16.6 g/dl
White Blood Cells 4.0 – 11.0 x 109/l
Platelets 150 – 450 x 109/l
MCV 80 – 96 fl
MCHC 32 – 36 g/dl
Neutrophils 2.0 – 7.5 x 109/l
Lymphocytes 1.5 – 4.0 x 109/l
Monocytes 0.3 – 1.0 x 109/l
Eosinophils 0.1 – 0.5 x 109/l
Basophils < 0.2 x 109/l
Reticulocytes < 2%
Haematocrit 0.35 – 0.49
Red Cell Distribution Width 11 – 15%
Blood Gases Normal Value
pH 7.35 – 7.45
pO2 11 – 14 kPa
pCO2 4.5 – 6.0 kPa
Base Excess -2 – +2 mmol/l
Bicarbonate 24 – 30 mmol/l
Lactate < 2 mmol/l

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