Biostatistics for EMREE: sensitivity, predictive value, NNT and bias with worked examples

What to expect

EMREE is reported to include public health and preventive medicine, which covers biostatistics and epidemiology. At exam level, this means a short list of calculations and ideas that repeat. This guide covers them with small numbers. It is revision material, not a replacement for a textbook, and the questions in the exam are not reproduced here.

The 2 by 2 table

Nearly every diagnostic test question can be answered from one table. Imagine 1,000 people. In 100 of them the disease is present and in 900 it is absent. The test is positive in 90 of the 100 diseased people (true positives) and negative in 10 (false negatives). Among the 900 without the disease, it is positive in 90 (false positives) and negative in 810 (true negatives).

• Sensitivity = true positives divided by all with disease = 90 / 100 = 90 percent.
• Specificity = true negatives divided by all without disease = 810 / 900 = 90 percent.
• Positive predictive value = true positives divided by all positive tests = 90 / 180 = 50 percent.
• Negative predictive value = true negatives divided by all negative tests = 810 / 820, about 98.8 percent.
• Positive likelihood ratio = sensitivity / (1 − specificity) = 0.9 / 0.1 = 9.

Why prevalence matters

Sensitivity and specificity are properties of the test. Predictive values change with how common the disease is. In the example, disease prevalence is 10 percent and the positive predictive value is 50 percent. If the same test were used in a group where only 1 percent have the disease, the positive predictive value would fall sharply, because false positives would swamp true positives. Exam questions like to test this: “what happens to the PPV when prevalence falls?”. It falls, and the NPV rises.

A useful memory hook: a highly sensitive test is good for ruling out disease when negative, and a highly specific test is good for ruling in disease when positive. Many students use the mnemonics SnNout and SpPin for this.

Risk, relative risk and NNT

Suppose a drug trial finds that 10 percent of controls had an event and 6 percent of treated patients did.

• Absolute risk reduction (ARR) = 10 − 6 = 4 percentage points.
• Relative risk (RR) = 6 / 10 = 0.6.
• Relative risk reduction (RRR) = 1 − 0.6 = 40 percent.
• Number needed to treat (NNT) = 1 / ARR = 1 / 0.04 = 25.

Odds ratio and study design

An odds ratio compares the odds of exposure in cases and controls, and is the usual measure in case-control studies. A cohort study follows exposed and unexposed people over time and gives a relative risk. A randomised controlled trial allocates people by chance, which reduces confounding. Cross-sectional studies measure prevalence at one point in time. Remember that the order of strength for causal questions generally puts randomised trials above cohort studies, and cohort above case-control, although the right design depends on the question, for example a rare disease suits a case-control design.

Confidence intervals and p values

A 95 percent confidence interval is a range that, if the study were repeated many times, would contain the true value in about 95 percent of the intervals. If a confidence interval for a relative risk includes 1, or for a difference includes 0, the result is not statistically significant at the 5 percent level. A p value below 0.05 means that a difference at least this large would be unlikely if there were no true difference. It does not tell you how big or important an effect is. Type I error is a false positive finding. Type II error is missing a real effect, and power is the chance of detecting one.

Bias and confounding

Questions often ask you to name a bias from a short description.

• Selection bias: the people studied differ systematically from the target population.
• Recall bias: cases remember past exposures differently from controls, typical in case-control studies.
• Lead-time bias: screening seems to lengthen survival only because the disease is found earlier.
• Confounding: a third factor linked to both exposure and outcome distorts the association.
• Observer or measurement bias: the way outcomes are assessed differs between groups.

Screening concepts

Public health sections often ask about screening. Know the difference between primary prevention, which stops disease occurring, secondary prevention, which finds disease early, and tertiary prevention, which reduces harm in established disease. Screening is secondary prevention. A good screening test is sensitive, acceptable and cheap, and the condition should be important, with an accepted treatment and a detectable early stage. Lead-time bias and length bias distort apparent survival gains from screening, so a question that shows longer survival after screening may be testing whether you realise that survival was lengthened only by earlier diagnosis.

The Wilson and Jungner criteria are the classic list of conditions for a screening programme, and your course may expect you to know them in outline.

A second worked calculation

A test is used on 2,000 people. 200 have the disease. The test detects 180 of them. Among the 1,800 without the disease, the test correctly gives a negative result in 1,620. Draw the table. True positives are 180, false negatives 20, true negatives 1,620 and false positives 180. Sensitivity is 180 over 200, which is 90 percent. Specificity is 1,620 over 1,800, which is 90 percent. Positive predictive value is 180 over 360, which is 50 percent. Negative predictive value is 1,620 over 1,640, about 98.8 percent.

Notice that these are the same percentages as the first example, but the population is twice the size. The ratios depend on prevalence, not on how many people you test. Now imagine the same test used where prevalence is 1 percent. With 2,000 people, 20 have the disease and 18 are detected. Of 1,980 without disease, 198 are false positives. The positive predictive value is now 18 over 216, about 8 percent.

Pitfalls in exam questions

Several traps recur. Mixing up sensitivity and positive predictive value is the most common, so write the denominator of each measure every time. Forgetting that a confidence interval that crosses 1 for a ratio, or 0 for a difference, means no statistical significance is another. Reading “relative risk reduction of 50 percent” as a large absolute benefit without checking the baseline risk is a third: halving a risk of 2 in 1,000 is a small absolute change. And confusing a study’s design with its analysis, for example calling a cohort study a trial because it followed patients, can cost marks.

When you do a question, say aloud which measure is asked for, which table cells it uses and what the units are. This habit prevents most careless slips.

How to practise

Draw a 2 by 2 table for every question until you no longer need to. Redo the calculations with different numbers, and say each formula aloud. Read the EMREE guide for what is known about the exam. Add the formulas to flashcards as small cards, one per measure, and practise a few questions on public health each week, as suggested in the 12-week plan. Where a formula is stated in your course notes in a different form, use the form your exam source uses.

Two shortcuts worth keeping

Two hooks save time on the 2 by 2 table, and each has a limit.

• SnNout and SpPin: a Sensitive test, when Negative, helps rule a condition OUT, and a Specific test, when Positive, helps rule it IN. It works best when sensitivity or specificity is very high, and it ignores how likely the disease was before the test.
• Cohort gives Risk, case-control gives Odds: use relative risk for a cohort study or trial, and the odds ratio for a case-control study. The odds ratio is close to the relative risk only when the disease is rare.

Frequently asked questions