Incidence, Prevalence & Mortality Rates

Incidence: new cases among people at risk

Definition. Incidence is the number of new cases arising during a defined period divided by the population at risk at the start of that period. Anyone who already has the disease is removed from the denominator, as is anyone who cannot develop it; a woman who has had a hysterectomy is not at risk for uterine cancer. Incidence expresses the risk of acquiring disease and is estimated by cohort studies.

Cumulative incidence. Also called the incidence proportion or risk: new cases ÷ people at risk at the outset, over a stated interval. It is a proportion between 0 and 1 that assumes complete follow-up; an outbreak attack rate is one.

Incidence density. Also called the incidence rate: new cases ÷ total person-time at risk, reported per 100 or per 1,000 person-years. Each participant contributes time only while at risk and under observation (until diagnosis, death, loss to follow-up, or study end), so the measure copes with staggered entry and dropouts. For example, 200 people followed a mean of 2.5 disease-free years contribute 500 person-years; 10 new cases give 2 per 100 person-years.

Prevalence and the incidence–duration link

Definition. Prevalence is all existing cases divided by the total population at a given time. Point prevalence refers to a single moment such as a survey day; period prevalence counts anyone who had the disease at any time during an interval such as a year. Prevalence measures burden and is what a cross-sectional survey captures. It is a proportion without time units, and it sets the pretest probability that drives a test's predictive values.

P ≈ I × D. In a steady state with a fairly uncommon disease, prevalence approximately equals incidence multiplied by average duration: incidence of 2 per 1,000 per year lasting 10 years on average gives a prevalence near 20 per 1,000. Think of a bathtub: incidence is the faucet, prevalence is the water level, and recovery or death is the drain.

• Prevalence rises, incidence unchanged: longer survival without cure, such as a drug that extends life in metastatic cancer.
• Prevalence falls, incidence unchanged: a cure (direct-acting antivirals for hepatitis C) or faster death.
• Incidence falls, then prevalence: primary prevention such as vaccination or smoking cessation.
• Both rise: a more sensitive test, a new screening program, or a broader case definition identifies more cases.

Conditions that are controlled but not cured (type 1 diabetes on insulin, HIV on ART, osteoarthritis) have prevalence far above incidence. Rapidly fatal pancreatic cancer has a prevalence not much larger than its annual incidence, whereas highly survivable prostate cancer accumulates many prevalent cases. ART also suppresses viral load and prevents transmission, so over time it lowers HIV incidence as well; a question about a noncurative drug that prolongs survival wants prevalence up, incidence unchanged.

Mortality and case-fatality

Population mortality rates. Crude mortality is all deaths in a year divided by the midyear population, usually per 1,000 or 100,000; it ignores age structure. Cause-specific mortality divides deaths from one cause by the whole population. Age-specific mortality restricts both numerator and denominator to one age band (deaths at ages 65–74 ÷ people aged 65–74) and is the building block of age adjustment.

Case-fatality rate. Deaths from a disease divided by the people who have it over a period, a proportion (often a percentage) that measures lethality rather than population burden. Rabies has a CFR near 100% but, being rare, a tiny mortality rate; influenza has a low CFR yet causes many deaths because so many people are infected.

Infant and maternal mortality

Infant mortality rate. Deaths before age 1 year divided by live births in the same year, per 1,000 live births; it is a sensitive index of a population's overall health. Neonatal mortality covers days 0–27 and is driven mainly by prematurity, low birth weight, and congenital anomalies; postneonatal mortality runs from day 28 to the first birthday. A death at 6 weeks is therefore an infant and postneonatal death, not a neonatal one. Perinatal mortality combines late fetal deaths (stillbirths) with deaths in the first week of life.

Maternal mortality ratio. Deaths from causes related to or aggravated by pregnancy, occurring during pregnancy or within 42 days of its end and excluding accidental or incidental causes, per 100,000 live births. Live births stand in for the true at-risk group (all pregnancies), so strictly it is a ratio. US review committees track pregnancy-related deaths for 1 year postpartum because cardiomyopathy and mental health–related deaths often occur after day 42.

Age adjustment: direct and indirect standardization

Why crude rates mislead. Death rates climb steeply with age, so a retirement community shows a higher crude mortality than a college town even when every age-specific rate is identical. Age is acting as a confounder; compare age-specific or age-adjusted rates instead.

Direct standardization. Each population's own age-specific rates are applied to one standard population (for US statistics, the 2000 standard population). Expected deaths are summed and divided by the standard's size, giving age-adjusted rates that can be compared head-to-head. The method needs reliable age-specific rates for every population, and the adjusted rate is a hypothetical summary rather than an actual rate.

Indirect standardization. When a group is small or its age-specific rates are unknown or unstable, as in an occupational cohort, the standard population's age-specific rates are applied to the group's own age structure to calculate expected deaths. The standardized mortality ratio (SMR) is observed ÷ expected deaths: 45 observed against 30 expected gives an SMR of 1.5, a 50% excess. An SMR above 1 signals excess mortality; below 1 means fewer deaths than expected, often reflecting the healthy worker effect.