Evidence Based Medicine
Statistics
A new test is being developed to diagnose chlamydia. 1000 people aged 15 – 35 years attending a GUM clinic undergo the new test and the current gold standard nucleic acid amplification test (NAAT) to confirm the diagnosis. Of the 1000 people, 250 are diagnosed with chlamydia. Of the patients diagnosed with chlamydia, 240 test positive with the new diagnostic test and of the patients not diagnosed with chlamydia, 150 test positive with the new diagnostic test. What is the positive likelihood ratio (LR+) for this test:
| Chlamydia Yes | Chlamydia No | Total | |
|---|---|---|---|
| Positive test | a= 240 | b = 150 | 390 |
| Negative test | c = 10 | d = 600 | 610 |
| Total | 250 | 750 | 1000 |
Answer:
- Sensitivity = a/(a+c) = 240/250 = 0.96 = 96%
- This means that if the patient has chlamydia, there is a 96% chance of the test being positive. The test will only have a 4% false negative rate.
- Specificity = d/(b+d) = 600/750 = 0.8 = 80%
- This means if the patient does not have chlamydia, there is an 80% chance of the test being negative. The test will have a 20% false positive result.
- Positive likelihood ratio (LR+) = sensitivity/(1-specificity) = 0.96/(1 - 0.8) = 4.8
- This means that a positive test result is 4.8 times more likely to be seen in a patient who has chlamydia than in a patient who does not have chlamydia.
Characteristics of Diagnostic Tests
Evidence Based Medicine / Statistics
Last Updated: 24th July 2020
| 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 |
