Rates
The term rate is very widely used, but some indices called rates in demography are in fact ratios, proportions, or more complex measures. Strictly speaking, a rate is a measure of change in a population over a specified time period (usually a year).
When calculating a rate, the numerator is the number of events of interest (births, deaths, marriages, disease diagnoses etc.) that occur during the specified period of time. The denominator is either the number of person-years of exposure to risk during the time period, or an estimate of this. In demography, the mid-year population is often used as this estimate and is equivalent to the mean population for the period specified.
Examples of true demographic rates
Examples of true demographic rates, which use the population at risk as the denominator, include the Crude Death Rate and the General Fertility Rate among others. These are explained in more detail in later sessions.
The General Fertility Rate (GFR) is a true rate as the denominator only includes those who are at risk of the event (in this case giving birth) during the specified time period. The GFR is calculated as the number of births to women of reproductive age (taken as those aged 15-44, or 15-49) in a year divided by the mid-year population of women of reproductive age, and expressed per 1000 women.
Some demographic rates are called rates but are in fact ratios or proportions, for example, the Infant Mortality Rate.
The Infant Mortality Rate (IMR) is calculated as the number of deaths to infants less than 1 year old in a single year, divided by the number of live births in the same year. This is really a ratio as the denominator is not strictly the population at risk. If we took 2010 as the year of interest, some of infants who die in 2010 may have actually been born in the 2009, and are therefore not included in the denominator. On the other hand, some of the infants who are born in 2010, and are included in the denominator, may die in 2011 and therefore will not be included in the numerator. For this reason three-year averages of births and deaths are often used to calculate IMRs.
We will now look more closely at what is meant by ‘person time at risk’ or ‘person years of exposure to risk’, and why the mid-year population is a suitable proxy.