Community medicine chapters
Incidence, prevalence and measures of risk
The difference between incidence and prevalence and how they are linked, attack rates, and the measures of risk and effect used in studies: relative risk, attributable risk, odds ratio, absolute and relative risk reduction, and number needed to treat, all with worked examples.
- Incidence counts new cases in a period (risk of getting the disease); prevalence counts all existing cases at a time (burden of disease); prevalence ≈ incidence × duration.
- Relative risk (from cohort studies) = incidence in exposed ÷ incidence in unexposed; odds ratio (from case-control studies) = ad ÷ bc.
- Attributable risk = incidence in exposed − unexposed; in trials, NNT = 1 ÷ absolute risk reduction.
On this page
Overview
To compare the health of groups, we need to count disease in relation to the population (incidence and prevalence) and to compare risk between groups (relative risk, odds ratio and others).
Incidence
Incidence = number of new cases during a period ÷ population at risk during that period (× 1,000 or another constant).
- Measures the risk of developing disease.
- Useful for studying causes and acute diseases.
- Cumulative incidence uses the population at risk at the start; incidence density uses person-time (for example cases per 1,000 person-years) when people are followed for different lengths of time.
Attack rate: the incidence during an epidemic or outbreak, usually expressed as a percentage.
Secondary attack rate: new cases among susceptible contacts of a primary case ÷ number of susceptible contacts × 100. It measures infectiousness.
Prevalence
Prevalence = number of all existing cases (new and old) ÷ total population at that time.
- Point prevalence: at a single point in time.
- Period prevalence: during a period (for example a year).
- Measures the burden of disease; useful for planning services, especially for chronic diseases.
- Found from cross-sectional surveys.
Linking incidence and prevalence
Prevalence ≈ Incidence × Duration (P = I × D), when the situation is stable.
| Change | Effect on prevalence |
|---|---|
| More new cases (higher incidence) | ↑ |
| Longer duration (better survival without cure) | ↑ |
| Faster cure or more deaths (shorter duration) | ↓ |
| Immigration of cases or emigration of healthy people | ↑ |
A treatment that prolongs life but does not cure (insulin for diabetes, antiretrovirals for HIV) increases prevalence without changing incidence.
For a short, acute disease (common cold) prevalence is low even if incidence is high. For a long chronic disease (diabetes) prevalence is high even if incidence is low.
A town of 50,000 has 500 people with diabetes on 1 January
Point prevalence = 500 ÷ 50,000 × 1,000 = 10 per 1,000
During the year, 100 new cases arise among the 49,500 at risk
Incidence = 100 ÷ 49,500 × 1,000 = about 2 per 1,000 per year
Check with P = I × D: if average duration = 5 years → 2 × 5 = 10 per 1,000 (matches)
Case fatality rate
Case fatality rate = deaths from a disease ÷ number of cases of that disease × 100. It shows the killing power (severity) of a disease, for example in an outbreak.
The 2 × 2 table
| Disease present | Disease absent | |
|---|---|---|
| Exposed | a | b |
| Not exposed | c | d |
Relative risk (risk ratio)
RR = incidence in exposed ÷ incidence in unexposed = [a ÷ (a + b)] ÷ [c ÷ (c + d)]
- Calculated from cohort studies (and trials), because they measure incidence.
- RR = 1: no association. RR > 1: exposure increases risk. RR < 1: exposure is protective.
- It measures the strength of association (useful for judging causation).
Attributable risk (risk difference)
AR = incidence in exposed − incidence in unexposed
- The extra disease in exposed people that is due to the exposure.
- Attributable risk per cent = (Ie − Iu) ÷ Ie × 100: the proportion of disease in the exposed that could be prevented by removing the exposure.
- Population attributable risk = incidence in the whole population − incidence in the unexposed: the disease in the whole community that could be prevented. Most useful for public health planning.
1,000 smokers followed: 30 develop lung cancer → Ie = 30 ÷ 1,000 = 0.030
2,000 non-smokers followed: 10 develop it → Iu = 10 ÷ 2,000 = 0.005
RR = 0.030 ÷ 0.005 = 6 (smokers have 6 times the risk)
AR = 0.030 − 0.005 = 0.025 = 25 per 1,000 smokers
AR% = 0.025 ÷ 0.030 × 100 = 83.3% of cases in smokers are due to smoking
Odds ratio
OR = (a × d) ÷ (b × c) (the cross-product ratio)
- Calculated from case-control studies, which cannot measure incidence.
- The odds of exposure among cases ÷ the odds of exposure among controls.
- When the disease is rare, the OR is a good estimate of the RR.
- OR = 1: no association; > 1: risk factor; < 1: protective.
Cohort → relative risk. Case-control → odds ratio.
100 cases: 60 exposed (a), 40 not exposed (c)
200 controls: 50 exposed (b), 150 not exposed (d)
OR = (a × d) ÷ (b × c) = (60 × 150) ÷ (50 × 40) = 9,000 ÷ 2,000 = 4.5
The odds of exposure are 4.5 times higher in cases than in controls
Measures of treatment effect (trials)
- Control event rate (CER): proportion with the outcome in the control group.
- Experimental event rate (EER): proportion in the treated group.
- Absolute risk reduction (ARR) = CER − EER.
- Relative risk reduction (RRR) = ARR ÷ CER.
- Number needed to treat (NNT) = 1 ÷ ARR: the number of patients who must be treated to prevent one bad outcome. Round up to a whole number.
- Number needed to harm (NNH) = 1 ÷ absolute risk increase for a side effect.
Stroke in 5 years: 20% on placebo (CER = 0.20), 15% on the drug (EER = 0.15)
ARR = 0.20 − 0.15 = 0.05 (5%)
RRR = 0.05 ÷ 0.20 = 0.25 (25%)
NNT = 1 ÷ 0.05 = 20: treat 20 people for 5 years to prevent one stroke
A large relative risk reduction can sound impressive while the absolute benefit is small. Always look at the ARR and NNT.
Expect: definitions of incidence and prevalence, P = I × D and what happens to prevalence with better survival, attack rate and secondary attack rate, case fatality rate, RR from cohort and OR from case-control, interpreting RR or OR below and above 1, attributable risk, and ARR, RRR and NNT calculations.
Quick revision
- Incidence: new cases ÷ population at risk. Prevalence: all cases ÷ population.
- P ≈ I × D; survival without cure raises prevalence.
- RR = Ie ÷ Iu (cohort). OR = ad ÷ bc (case-control).
- RR or OR = 1: no association; < 1: protective.
- AR = Ie − Iu; AR% = AR ÷ Ie.
- ARR = CER − EER; RRR = ARR ÷ CER; NNT = 1 ÷ ARR.
Written by The House Job from Excel Community Medicine and Park's Textbook of Preventive and Social Medicine (named in the UHS PGET syllabus).
FAQ
What is the difference between incidence and prevalence?
Incidence counts new cases over a period among people at risk; prevalence counts all existing cases at a point or period of time.
What is the relationship between incidence and prevalence?
Prevalence is approximately incidence multiplied by the average duration of the disease.
Which measure is used in case-control studies?
The odds ratio, calculated as ad ÷ bc.
How is the number needed to treat calculated?
NNT = 1 ÷ absolute risk reduction.