Definition

 

We assume that, at a certain period of time (for example, a given year), every living individual of a population on which we want to calculate the Sullivan indicator can be unambiguously described as being in exactly one of a fixed number of states of health.

Consider a collection of individuals classified in increasing W+1 age groups (numbered from i=0 to i=W) and a particular health state which has been located on some of them. Suppose you want to have a health indicator on the whole population which doesn't depend on its age structure. Using a common notation [4], let:

=number of survivors of age (beginning of the age interval i). In other words, it is assumed that of every persons alive at age will survive until age .

=number of person years (see section 3.2.1) lived in the age group i. That is to say the number of years lived by the persons in the interval i. Each member of the cohort who survives the interval i contributes to , each member of the cohort who have died during the interval i contributes only a part of that time.

=prevalence of the particular health state for age group i (that is to say the percentage of persons in this health state in the whole population of the age interval i).

The health state indicator proposed by Sullivan can be calculated as:

 

Values of can be estimated from a cross-sectional health survey on the whole population. and are provided by an ordinary current life table.