Biostatistics for FCPS Part 1 and NRE: the marks you should never lose
Biostatistics is the most reliable scoring area in the paper. The same handful of calculations and definitions are asked again and again. Learn the 2 × 2 table and a few formulas and these marks are yours.
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Why this is the easiest section to secure
Biostatistics frightens people who have not touched maths since college. In the paper it is the opposite of frightening. The same calculations come back in almost every sitting, and the method never changes. A candidate who can do a 2 × 2 table calmly will rarely drop a mark here.
Give it three focused evenings and then practise one calculation a day until the exam.
Always draw the table the same way
| Disease present | Disease absent | |
|---|---|---|
| Test positive | a: true positive (TP) | b: false positive (FP) |
| Test negative | c: false negative (FN) | d: true negative (TN) |
Draw it this way every time, even when the question lays the data out differently. Most wrong answers in this topic come from putting a number in the wrong cell, not from the formula.
| Measure | Formula | What it answers |
|---|---|---|
| Sensitivity | a ÷ (a + c) | Of people with the disease, how many test positive? |
| Specificity | d ÷ (b + d) | Of people without the disease, how many test negative? |
| Positive predictive value | a ÷ (a + b) | If I test positive, how likely am I to have it? |
| Negative predictive value | d ÷ (c + d) | If I test negative, how likely am I to be clear? |
Worked example
A test is used on 100 people with a disease and 200 without. It is positive in 90 of those with the disease and in 30 of those without.
- TP = 90, FN = 10, FP = 30, TN = 170.
- Sensitivity = 90 ÷ 100 = 90%.
- Specificity = 170 ÷ 200 = 85%.
- PPV = 90 ÷ 120 = 75%.
- NPV = 170 ÷ 180 = about 94%.
Sensitivity and specificity belong to the test. Predictive values belong to the test and the population. When a disease becomes more common, PPV rises and NPV falls, while sensitivity and specificity stay the same.
Ruling in and ruling out
- A highly sensitive test, when negative, rules a disease out. It rarely misses anyone, so a negative result is reassuring.
- A highly specific test, when positive, rules a disease in. It rarely flags healthy people, so a positive result is convincing.
Screening tests should be sensitive. Confirmatory tests should be specific.
Measuring risk
| Measure | Formula | Study it comes from |
|---|---|---|
| Relative risk (RR) | Risk in exposed ÷ risk in unexposed | Cohort study or trial |
| Odds ratio (OR) | (a × d) ÷ (b × c) | Case-control study |
| Attributable risk | Risk in exposed − risk in unexposed | Cohort study |
| Absolute risk reduction (ARR) | Risk in control − risk in treated | Trial |
| Number needed to treat (NNT) | 1 ÷ ARR | Trial |
| Number needed to harm (NNH) | 1 ÷ (risk with drug − risk without) | Trial |
Worked examples
Odds ratio. In a case-control study, 40 of 100 lung cancer cases and 20 of 100 controls were exposed to asbestos. OR = (40 × 80) ÷ (60 × 20) = 3,200 ÷ 1,200 = 2.67.
Relative and attributable risk. In a cohort, 30 per 1,000 smokers and 10 per 1,000 non-smokers develop a disease. RR = 30 ÷ 10 = 3. Attributable risk = 30 − 10 = 20 per 1,000.
NNT. A stroke happens in 10% of the control group and 6% of the treated group. ARR = 4% = 0.04. NNT = 1 ÷ 0.04 = 25.
NNH. A rash occurs in 3% on the drug and 1% on placebo. The difference is 2%, so NNH = 1 ÷ 0.02 = 50.
Convert percentages to decimals before dividing. "1 ÷ 4" gives 0.25, not 25. That slip turns a correct method into a wrong option, and the examiners put that wrong number in the options on purpose.
Incidence and prevalence
- Incidence: new cases over a period, in people at risk.
- Prevalence: all existing cases at a point in time.
- In a stable population, prevalence ≈ incidence × average duration. An incidence of 10 per 1,000 per year with an average duration of 5 years gives a prevalence of about 50 per 1,000.
A new cure that shortens the illness lowers prevalence without changing incidence. A treatment that keeps people alive longer without curing them raises prevalence.
Study designs and which question each answers
| Design | Best for | Measure |
|---|---|---|
| Case-control | Rare diseases; several exposures | Odds ratio |
| Cohort | Rare exposures; incidence; several outcomes | Relative risk |
| Cross-sectional | Prevalence at one point in time | Prevalence |
| Randomised controlled trial | Whether a treatment works | RR, ARR, NNT |
| Ecological | Population-level patterns | Correlation (beware the ecological fallacy) |
Bias and confounding
- Recall bias: cases remember exposures better than controls. Typical of case-control studies.
- Selection bias: the groups differ in who was enrolled.
- Lead-time bias: screening finds a disease earlier, so survival looks longer even if death comes at the same time.
- Confounding: a third factor linked to both exposure and outcome. Randomisation is the only method that balances confounders you have not measured.
- Observer bias: reduced by blinding.
Errors, power and confidence intervals
- Type I error (α): rejecting a null hypothesis that is true. A false positive finding.
- Type II error (β): failing to reject a null hypothesis that is false. A missed real effect.
- Power = 1 − β. The simplest way to raise it is a larger sample.
- A 95% confidence interval for a ratio (RR or OR) that includes 1 means the result is not statistically significant. For a difference, the line of no effect is 0. An RR of 0.8 with a 95% CI of 0.6 to 1.1 is not significant.
Data and tests
| Data type | Example |
|---|---|
| Nominal | Blood group; vomiting present or absent |
| Ordinal | Pain mild, moderate or severe; cancer stage |
| Discrete | Number of children |
| Continuous | Blood pressure, height |
| Question | Test |
|---|---|
| Compare proportions (categorical data, 2 × 2 table) | Chi-square |
| Compare two means, independent groups | Unpaired t-test |
| Compare two means, same people before and after | Paired t-test |
| Compare three or more means | ANOVA |
| Compare two groups, data not normally distributed | Mann-Whitney U |
| Linear relationship between two continuous variables | Pearson correlation |
Averages, spread and the normal curve
- In a normal distribution, mean = median = mode.
- In a positively skewed distribution (a long tail to the right, like hospital stay), mean > median > mode.
- The median of an even number of values is the average of the middle two. For 20, 20, 25, 25, 30, 30, 35, 40, the median is (25 + 30) ÷ 2 = 27.5. Sort the numbers first.
- Variance and standard deviation measure spread. The standard error of the mean = SD ÷ √n.
- About 95% of values fall within 1.96 standard deviations of the mean.
- A correlation of −0.9 is a strong negative linear relationship. It says nothing about cause.
Validity, reliability and prevention
- Validity (accuracy): does the test measure the true value?
- Reliability (precision): does it give the same result when repeated?
- Primary prevention stops disease happening (vaccination). Secondary prevention catches it early (screening). Tertiary prevention limits the damage (stroke rehabilitation).
How to make these marks permanent
- Learn the 2 × 2 table and the risk formulas over two evenings.
- Do one calculation question every day until the exam. It takes two minutes.
- In the exam, write the table on your scratch sheet before you look at the options.
The FCPS-1 Prep question bank and the NRE-1 Prep question bank both include worked calculation questions with the full table in the explanation.
Read next: Past papers analysis · NRE Step 1 high-yield subjects · Study plan
Frequently asked questions
Do I need a calculator?
No. The numbers are chosen to divide cleanly. If your answer is an ugly decimal, check which cell you put each number in.
Is biostatistics in both papers?
It belongs to the general medical sciences, so expect it in Paper 1 for every group.
What is the most common mistake?
Mixing up predictive values with sensitivity and specificity. Ask yourself whether the question starts from the disease (sensitivity, specificity) or from the test result (predictive values).