Incidence and prevalence
Incidence, prevalence, rates and ratios: measures of disease occurrence
Incidence, prevalence, attack rates, mortality rates, SMR, DALY and herd immunity explained with worked FCPS Part 1 examples. Prevalence is roughly incidence multiplied by duration, which explains most exam twists.
One of the most tested topics in past papers
Ratio, proportion and rate
| Measure | Numerator part of denominator? | Time built in? | Example |
|---|---|---|---|
| Ratio | No | No | Male to female ratio 2:1; maternal mortality ratio |
| Proportion | Yes | No | 20 of 100 patients anaemic = 20%; point prevalence |
| Rate | Yes (people at risk) | Yes | Deaths per 1,000 population per year; incidence rate |
Incidence and prevalence
| Measure | Counts | Formula |
|---|---|---|
| Incidence | New cases during a period | New cases ÷ population at risk during that period |
| Cumulative incidence (risk, attack rate) | Proportion of an at-risk group who become ill over a period | New cases ÷ people at risk at the start |
| Incidence density | New cases per person-time | New cases ÷ total person-years at risk |
| Point prevalence | All existing cases at one moment | Existing cases ÷ total population at that moment |
| Period prevalence | All cases present at any time in a period | Existing plus new cases in the period ÷ average population |
- People who already have the disease are not at risk and are removed from the incidence denominator.
- Prevalence ≈ incidence × average duration (for a stable, fairly rare disease). Prevalence is like water in a tank: incidence is the inflow tap, cure and death are the drains.
| Change | Effect on prevalence |
|---|---|
| Treatment that prolongs life without cure (insulin, antiretrovirals) | Rises; incidence unchanged |
| Faster cure, or a disease that kills quickly | Falls |
| Rising incidence | Rises |
| Better detection, screening, wider case definition | Rises |
| Immigration of cases or emigration of healthy people | Rises |
- Use incidence to study causes and risk (cohort studies, outbreaks, acute disease). Use prevalence to measure burden and plan services (cross-sectional surveys, chronic disease such as diabetes).
- Short diseases (common cold) have high incidence but low prevalence; long chronic diseases have prevalence far above incidence.
Attack rates and spread
- Attack rate: cumulative incidence during an outbreak = ill ÷ people exposed. If 50 of 200 wedding guests fall ill, the attack rate is 25%.
- Secondary attack rate (SAR): new cases among contacts within one incubation period ÷ susceptible contacts. The primary case is excluded, as are contacts already immune. In a family of 6 where one child has measles and 3 of the 5 susceptible members fall ill, SAR = 3 ÷ 5 = 60%. SAR measures how infectious an agent is.
- Basic reproduction number (R₀): average number of new infections from one case in a fully susceptible population. Herd immunity threshold = 1 − 1/R₀. Measles (R₀ about 15) needs about 93% immune; because vaccines are not 100% effective, coverage must be higher still (about 95%).
| Term | Meaning |
|---|---|
| Endemic | Constantly present at the usual expected level in an area (malaria in parts of Pakistan) |
| Epidemic | Clearly more cases than expected for that place and time; numbers need not be large |
| Pandemic | An epidemic spreading across countries or continents |
| Sporadic | Scattered cases with no clear link |
- Iceberg phenomenon: the cases a doctor sees (the tip) are a small fraction of all disease; the submerged part is subclinical, undiagnosed and carrier cases. It is large for hypertension, diabetes, TB and polio, and is the reason for screening.
Mortality and burden measures
| Measure | Formula |
|---|---|
| Crude death rate | Deaths in a year ÷ mid-year population × 1,000 |
| Age-specific death rate | Deaths in an age group ÷ population of that age group × 1,000 |
| Case fatality rate | Deaths from a disease ÷ cases of that disease × 100: measures severity |
| Proportional mortality | Deaths from one cause ÷ all deaths × 100 |
| Infant mortality rate | Deaths under 1 year ÷ live births × 1,000 |
| Neonatal mortality rate | Deaths in the first 28 days ÷ live births × 1,000 |
| Perinatal mortality rate | Stillbirths (28 weeks or more) plus deaths in the first 7 days ÷ (live births + stillbirths) × 1,000 |
| Maternal mortality ratio | Maternal deaths ÷ live births × 100,000 |
- Infant mortality rate is the best single indicator of a population's health and development.
- DALY (disability-adjusted life year) = years of life lost from premature death (YLL) + years lived with disability weighted for severity (YLD). One DALY is one lost year of healthy life; it lets fatal and disabling diseases be compared on one scale. QALY, used in health economics, counts years gained weighted for quality.
Standardisation and SMR
Crude rates mislead when populations differ in age structure: an older town has more deaths even if it is healthier.
- Direct standardisation: apply each population's age-specific rates to one standard population; needs the age-specific rates of the study group.
- Indirect standardisation: apply standard (national) age-specific rates to the study population to get expected deaths. Used for small groups such as an occupational cohort.
- Standardised mortality ratio = observed ÷ expected × 100. A factory with 30 deaths where 20 were expected has SMR = 150: 50% more deaths than expected. Above 100 means excess mortality.
Ratios that compare groups
Measures of occurrence feed into measures of association (detailed in the study design chapter).
| Study | Measure | Formula from a 2×2 table (a, b exposed cases and non-cases; c, d unexposed) |
|---|---|---|
| Cohort | Relative risk | [a ÷ (a + b)] ÷ [c ÷ (c + d)] |
| Case–control | Odds ratio | (a × d) ÷ (b × c), the cross-product |
- Case–control example: 40 of 100 cases and 20 of 100 controls were exposed. OR = (40 × 80) ÷ (60 × 20) = 2.67.
- With 160 of 200 cases and 80 of 200 controls smoking: OR = (160 × 120) ÷ (40 × 80) = 6.
- Case–control studies cannot give incidence, so they give odds ratios, which approximate relative risk when the disease is rare.
Sample size for a prevalence survey
To estimate a prevalence (for example anaemia in pregnant women) you need the expected prevalence (p), the acceptable precision or margin of error (d) and the confidence level (Z, 1.96 for 95%): n = Z² × p(1 − p) ÷ d². When p is unknown, 50% is used because it gives the largest sample.
Worked example
A town of 10,000 has 400 diabetics on 1 January and 100 new cases during the year. Point prevalence on 1 January = 400 ÷ 10,000 = 4%. Incidence = 100 ÷ (10,000 − 400) ≈ 1.04% per year. If incidence is 20 per 1,000 per year and the disease lasts 5 years, prevalence ≈ 100 per 1,000 (10%).
Remember Incidence for causes, prevalence for burden; prevalence ≈ incidence × duration.
Exam trap A treatment that prolongs life without cure increases prevalence and leaves incidence unchanged.
Exam trap The secondary attack rate excludes the primary case and immune contacts from the denominator.
How FCPS asks about this
- Effect of a new life-prolonging but non-curative drug: prevalence rises, incidence unchanged.
- Measure of disease severity: case fatality rate (deaths ÷ cases).
- Secondary attack rate calculation: new cases ÷ susceptible contacts (3 of 5 = 60%).
- SMR with 30 observed and 20 expected deaths: 150.
- Herd immunity for measles, R₀ 15: 1 − 1/15, about 93%.
- Disease constantly present at its usual level: endemic; the hidden mass of undetected cases is the iceberg phenomenon.
- Denominator of the maternal mortality ratio: 100,000 live births; DALY = YLL + YLD.
Test yourself on this topic
5 of the 41 questions in our bank on this topic. Choose an answer to see why every option is right or wrong.
How is the infant mortality rate defined?
Answer: Under-1 deaths per 1,000 live births
Infant mortality rate (IMR) = deaths under 1 year in a year ÷ live births in the same year × 1,000; a sensitive indicator of a community's health and socioeconomic development. Neonatal mortality: deaths in the first 28 days per 1,000 live births (early neonatal: first 7 days). Post-neonatal: 28 days to under 1 year. Perinatal mortality: stillbirths (after 28 weeks) plus early neonatal deaths per 1,000 total births. Under-5 mortality: deaths under 5 per 1,000 live births. Maternal mortality ratio is per 100,000 live births.
Child mortality indicators
- IMR: < 1 year per 1,000 live births
- Neonatal: < 28 days
- Perinatal: stillbirths (≥ 28 wk) + first 7 days, per 1,000 total births
- MMR: per 100,000 live births
Remember Infant: under one; neonate: under a month.
Why the other options are wrong
- Under-28-day deaths per 1,000 births That is neonatal mortality.
- Under-5 deaths per 1,000 population Under-5 mortality uses live births as denominator.
- Stillbirths per 1,000 total births That is the stillbirth rate.
- Under-1 deaths per 1,000 population Wrong denominator.
Two districts have the same population, but district A has many more elderly people. Crude cancer death rates are higher in A. How can their mortality be compared fairly?
Answer: Age-standardised rates
Crude rates are influenced by population structure; an older population will have more cancer deaths even if age-specific risks are identical. Standardisation removes confounding by age. Direct standardisation applies each population's age-specific rates to a standard population, giving age-standardised rates that can be compared. Indirect standardisation applies standard age-specific rates to the study population to calculate expected deaths; observed/expected gives the standardised mortality ratio (SMR), useful when age-specific rates are unstable (small populations, occupational studies). Specific rates (age- or sex-specific) are also informative.
Standardisation
- Crude rates confounded by age
- Direct: study rates applied to standard population
- Indirect: standard rates → expected deaths → SMR (observed/expected)
- SMR >100 → more deaths than expected
Remember Standardise before you compare.
Why the other options are wrong
- Crude rates only Confounded by age.
- Number of deaths only Ignores population size and structure.
- Case fatality rate Deaths among cases, not the population.
- Attack rate Used in outbreaks.
In a cohort, 20 new cases of diabetes occur over 4,000 person-years of follow-up. What is the incidence rate?
Answer: 5 per 1,000 person-years
Incidence rate (incidence density) = new cases ÷ total person-time at risk = 20 ÷ 4,000 = 0.005 per person-year = 5 per 1,000 person-years. Person-time accounts for people followed for different lengths of time (dropouts, late entry, deaths). Cumulative incidence (risk) is new cases ÷ population at risk at the start over a fixed period. Prevalence counts all existing cases at a point (point prevalence) or during a period (period prevalence).
Incidence
- Incidence rate = new cases ÷ person-time
- Cumulative incidence = new cases ÷ population at risk at start
- Prevalence = all existing cases ÷ population
Remember Incidence counts the new arrivals.
Why the other options are wrong
- 20 per 1,000 person-years Ignores person-time.
- 2 per 1,000 person-years Wrong calculation.
- 50 per 1,000 person-years Wrong calculation.
- 0.5 per 1,000 person-years Wrong calculation.
In a case–control study, 40 of 100 lung cancer cases and 20 of 100 controls were exposed to asbestos. What is the odds ratio?
Answer: 2.67
OR = (exposed cases × unexposed controls) ÷ (unexposed cases × exposed controls) = (40 × 80) ÷ (60 × 20) = 3,200 ÷ 1,200 = 2.67. The odds of exposure are about 2.7 times higher in cases than controls.
Odds ratio
- OR = (a × d) / (b × c)
- Case–control studies give odds ratios
- OR > 1 → exposure linked to disease
Remember Cross-multiply the 2 × 2 table.
Why the other options are wrong
- 2.0 Ratio of proportions exposed, not odds.
- 0.5 Inverted.
- 1.33 Not correct.
- 4.0 Not correct.
Two districts have the same maternal mortality ratio, but in district B women have twice as many pregnancies on average. A researcher divides maternal deaths by the number of women aged 15–49 years in each district. Which indicator has she calculated?
Answer: Maternal mortality rate
The maternal mortality rate uses women of reproductive age (15–49 years) as the denominator, usually per 100,000. It therefore reflects both the obstetric risk per pregnancy and how often women become pregnant. District B, with higher fertility, will have a higher maternal mortality rate even though its ratio (deaths per 100,000 live births) is the same. The ratio isolates the risk per birth; the rate shows the burden on the female population.
Ratio vs rate
- Ratio: per 100,000 live births
- Rate: per 100,000 women 15–49
- Rate rises with fertility
- Ratio = risk per birth
Remember Women in the denominator makes it a rate.
Exam trap Exam stems often call the ratio a rate; check the denominator before answering.
Why the other options are wrong
- Maternal mortality ratio The ratio uses live births as the denominator.
- General fertility rate This is live births per 1,000 women aged 15–49, not deaths.
- Lifetime risk of maternal death Lifetime risk is the probability of one woman dying of maternal causes over her reproductive life.
- Proportional maternal mortality This is maternal deaths as a percentage of all deaths of women 15–49.
Where this sits in the CPSP syllabus
- Paper 1: Epidemiology, Measures of disease occurrence: incidence, prevalence, rates and ratios
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