A test result does not tell you on its own whether someone has a condition; it shifts the probability you had before the test. The post-test probability combines that pre-test probability – often the prevalence in similar patients, adjusted for symptoms – with the strength of the test, summarised by its likelihood ratio.
The calculation is easiest in odds. Convert the pre-test probability to odds, multiply by the likelihood ratio and convert back. A positive result uses the positive likelihood ratio LR+ = sensitivity ÷ (1 − specificity); a negative result uses LR− = (1 − sensitivity) ÷ specificity. LR+ above 10 or LR− below 0.1 are usually considered strong evidence; values near 1 barely change anything.
The calculator offers three starting points: a known pre-test probability and likelihood ratio, a pre-test probability with the test’s sensitivity and specificity, or a 2 × 2 table of true and false positives and negatives, in which case the prevalence, sensitivity and specificity are taken from the table. It is an educational tool – clinical decisions also depend on context and should be made with a clinician.
How to use the Post-Test Probability Calculator
- What do you know?
- Pre-test probability (prevalence)
- Likelihood ratio
- Sensitivity
- Specificity
- True positives (TP)
- False positives (FP)
- False negatives (FN)
- True negatives (TN)
- Test result
Results update as you type, and everything is calculated in your browser.
How it works
The pre-test probability p is turned into odds p/(1 − p), multiplied by the likelihood ratio for the result observed, and converted back with odds/(1 + odds). When a table is entered, prevalence = (TP + FN)/N, sensitivity = TP/(TP + FN) and specificity = TN/(TN + FP).
Worked example
Pre-test probability 20% and a positive test with sensitivity 85% and specificity 90%. LR+ = 0.85 ÷ 0.10 = 8.5. Pre-test odds = 0.2 ÷ 0.8 = 0.25; post-test odds = 0.25 × 8.5 = 2.125; post-test probability = 2.125 ÷ 3.125 = 68%. A negative result instead uses LR− = 0.15 ÷ 0.90 = 0.1667, giving odds 0.0417 and a probability of 4%.
Rough guide to likelihood ratios
| LR+ | LR− | Effect on probability |
|---|---|---|
| > 10 | < 0.1 | Large, often conclusive |
| 5–10 | 0.1–0.2 | Moderate |
| 2–5 | 0.2–0.5 | Small |
| 1–2 | 0.5–1 | Rarely important |
Inputs explained
| Field | What to enter |
|---|---|
| What do you know? | Choose one: Pre-test probability and likelihood ratio, Pre-test probability, sensitivity and specificity, 2 × 2 table of test results |
| Pre-test probability (prevalence) | In % |
| Likelihood ratio | A number |
| Sensitivity | In % |
| Specificity | In % |
| True positives (TP) | A number |
| False positives (FP) | A number |
| False negatives (FN) | A number |
| True negatives (TN) | A number |
| Test result | Choose one: Positive, Negative |
What each result means
- Post-test probability = [o1]÷(1 + [o1])×100
- Pre-test probability used = [p0]
- Sensitivity = [se]
- Specificity = [sp]
- Positive likelihood ratio (LR+) = [Sensitivity]÷(100 – [Specificity])
- Negative likelihood ratio (LR−) = (100 – [Sensitivity])÷[Specificity]
- Likelihood ratio used = [lr]
- Pre-test odds = [Pre-test probability used]÷(100 – [Pre-test probability used])
- Post-test odds = [o1]
- Change in probability = [Post-test probability] – [Pre-test probability used]
Formula
Pre-test odds = pre-test probability ÷ (1 − pre-test probability)
Post-test odds = pre-test odds × likelihood ratio
Post-test probability = post-test odds ÷ (1 + post-test odds)
LR+ = sensitivity ÷ (1 − specificity) · LR− = (1 − sensitivity) ÷ specificity
Worked example
Inputs — What do you know?: Pre-test probability and likelihood ratio; Pre-test probability (prevalence): 20 %; Likelihood ratio: 6.
Results — Post-test probability = 60 %; Pre-test probability used = 20 %; Likelihood ratio used = 6; Pre-test odds = 0.25; Post-test odds = 1.5; Change in probability = 40 percentage points.
Key terms
- Pre-test probability
- The probability of the condition before the test, often the prevalence.
- Likelihood ratio
- How many times more likely a result is in people with the condition than without it.
- Post-test probability
- The updated probability after taking the test result into account.
- Odds
- Probability ÷ (1 − probability).
Frequently asked questions
How do you calculate post-test probability?
Convert the pre-test probability to odds, multiply by the likelihood ratio and convert back. 20% → odds 0.25; × 6 = 1.5; 1.5 ÷ 2.5 = 60%.
What is the difference between pre-test odds and pre-test probability?
Probability is cases ÷ everyone; odds are cases ÷ non-cases. A 29% prevalence is odds of 0.29 ÷ 0.71 = 0.41 (or about 2.4 to 1 against).
What is a good likelihood ratio?
LR+ above 10 or LR− below 0.1 make large, often decisive changes; 2–5 and 0.2–0.5 make small changes; values near 1 are useless.
Can a likelihood ratio be negative?
No. It is a ratio of two probabilities and is always 0 or more.
Is the post-test probability the same as the positive predictive value?
Yes, when the pre-test probability equals the prevalence in the population where PPV was measured.
Why does the same test mean different things for different patients?
Because the pre-test probability differs. A positive result moves 2% to about 15% but 50% to about 89% with LR+ = 8.5.
Can I apply several tests in a row?
Yes, if they are independent: the post-test probability of one test becomes the pre-test probability of the next.