Incidence

Incidence is the measure of new cases (new cases = incident cases).

There are 2 measures of incidence: risk and rate.

Risk
Risk is the probability of new occurrence of disease among individuals in an initially disease-free population during a defined time period.

To calculate a risk (r), we divide the number of new cases (d) in the defined period by the population at risk at the beginning of the period (N): r = d/N (over a defined period). Risk is a probability but is often multiplied by a suitable number (e.g.: 100000), giving rise to examples such as: “Annual risk of death was 14 per 1000 in Kenya in 1 year”

Odds of disease/survival
It is a related measure of disease occurrence. For a defined population and time period, it is the number of cases divided by the number of people who did not become a case: Odds = Cases/Non-cases (in specified observed period of time). Also can be defined as: Odds = risk/(1-risk)

Rate
Rate is a measure of the frequency of occurrence of new cases. Rate relates the number of new cases to the person-time (Y) at risk = a measure that takes into account changes in the size of the population at risk during the follow-up period. In a defined population followed up for a period of time, we establish the total person-years at risk (Y).

The observed rate (r) is: r = d/Y (where d is number of new cases arising in the population)

We can also use person-months or person-days instead of person-years. The relationship between risk, rate and prevalence:
 * Both measures of incidence, risk and rate, have as numerator the number of new cases occurring in a population, however they have different denominators
 * (point) prevalence depends on the duration of disease (T) and on the rate of disease (r);
 * In special conditions (when disease is stable = both incidence rate and duration are stable) prevalence approximates the product of mean duration and incidence rate:
 * Prevalence ~ rate * duration (proved by the units: time * new cases / person*time = new cases/people = prevalence)
 * Therefore: Duration ~ prevalence/rate
 * Example: If we have population of 10000 people, 10 new cases of cancer a year and 20 registered cases at any time, then the average duration of (survival from) the cancer is 20/10 (prevalence/rate) = 2 years