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Definitions and description
Rates, and ratios are key cornerstones in understanding the health, morbidity, and mortality of populations. Plain numbers of events, such as deaths, or births, or hospital admissions have very little meaning in themselves, lacking a context in which they can be interpreted. Calculating rates supplies such a context, by transforming the data in terms of the population at risk and the time period relevant.
A Rate is a quantity in one dimension divided by a quantity in (usually) another dimension, with an indication of time. For example,
The Annual Incidence Rate of an acute disease is = number of new cases of that disease during a particular year/ estimated or counted average population at risk, observed within that year.
The Point Prevalence Rate of a condition is the number of cases of that condition at a particular point in time / population at risk at that point in time.
Note that in the case of incidence we are concerned only with the start of an illness, so we need to specify the period of observation (x cases per thousand people per year) while in the case of point prevalence we are looking at a snapshot, and the item is expressed in terms of cases per thousand people, or percentage of the population with the condition at any one time.
The distinction is especially important in conditions such as HIV, where incidence rates describe the pattern of new cases, while prevalence describes the population living with the condition.
The Period Prevalence Rate is the number of cases of that condition during a particular period in time / average population at risk for that period.
Methods of comparison - Standardisation
Rates may be expressed as 'crude rates' where the denominator includes all the population, particularly all age groups. An example is ‘All Age All-Cause Mortality’, much used as a rough headline figure for assessing overall public health. Crude rates may hide significant differences in risk between subgroups of the populations where there are large differences in the make-up of populations, especially in terms of age. More generally useful are rates which have been stratified in such a way as to present separately data where there are significant differences among different sectors of the population. The most commonly used stratifications are by age (or more often, age-band) and sex, these being both the most important determinants of many health issues and also the most complete data items available, but given sufficient reliable data, other groupings such as ethnicity or socio-economic status can be used in the calculations.
Such stratified data can then be used in conjunction with similarly stratified data for other populations, to derive what are known as ‘Standardised Rates’. These enable comparison of local data with other areas, including nationally. Comparison is done between observed data and 'expected' data. The two methods of standardisation, Direct and Indirect, both generate population-weighted averages, but differ in their expected data and in the inferences that may be drawn from them.
Direct Standardisation
This requires:
- a local 'index' population, stratified as required (here we will use age band only, for simplicity), e.g. CCG, Local Authority, or ward population.
- age-specific counts for the event of interest (e.g. mortality) in the index population.
- a 'reference' population for comparison purposes. This can be a 'real' population (e.g. England & Wales Office of National Statistics mid-year estimates, or an artificial population such as the 'Standard European Population', which is used by the Department of Health for its national standardised data but the documents are not available on the NHS Digital webpage-.
https://www.gov.uk/government/statistics/nhs-outcomes-framework-indicators-november-2015-release [accessed 20/08/2018]
Further details of the recent Standard European Population can be found at
The method is to derive for each stratum, e.g. age group, the age-specific rate for the event, then apply the result to the equivalent stratum of the reference population, then sum the strata to get the total expected deaths and divide by the total reference population to get the rate. If there are ‘n’ age-bands, ‘indo’p is the stratified index population and reference pop the similarly stratified ‘refpop’, the Directly Age Standardised Rate (DASR) is
This is the expected mortality rate in the reference population if it were to experience the mortality observed in the index population. It is typically expressed in terms of per 1000.
The main advantage of using DASRs is that by performing these calculations for several index populations (e.g. CCGs or, possibly more validly, LAs) the mortalities in these populations can be compared without the confounding factor of age. A potential disadvantage is that when based on very small numbers of deaths (or other events) the rates can become unstable.
Indirect Standardisation
Where age group data required for direct standardisation are not available, it is possible to standardise using Indirect standardisation, which applies a similar process, in reverse. Age-stratified incidence rates for a known reference population are applied to local index population structures, to arrive at mortality rates which would have been experienced locally if the index population had experienced mortality at the reference rates. The results are summed, and the ratio of the locally observed to the expected mortality calculated to give the Standardised Mortality Ratio (SMR), often multiplied by 100. An SMR>100 implies higher mortality than the national average, and vice versa.
| SMR = | Observed | x 100 |
| Expected |
Issues Relating to Selection of Data
Choice of reference population
- For both sorts of standardisation, ranks can be affected by the structure of the reference population.
- For direct standardisation the reference population need not be a real population (nationally presented figures often are issued using artificially constructed populations such as the 'Standard European Population', but many people prefer to use the complete population of England or England and Wales.
- For indirect standardisation it is essential to use the same population as the reference mortality rates were calculated from. It is important to be sure whether incidence figures are for England, England & Wales, or the entire United Kingdom, for example. If incidence data is taken from the Hospital Episodes Statistics (HES) database the population should be the population of England (use the mid-year estimates for the year in question), as only English data is included in HES.
- For local and regional studies, standardising to the total population of the area studied can yield valuable insights. Such an approach could usefully be applied to, for example, an investigation into health inequalities in mortality rates at ward level.
Selection of strata
In age-banding there need to be some attention paid to granularity (depth of detail). This will generally need to be a compromise between what's reasonably obtainable and what would give optimum calculated results. For most purposes, 5-year age bands are adequate. HES is available pre-analysed in 0-14, 15-60, 60-75, >75 age bands. This is rather crude, though can still be useful for some purposes. If studying female fertility, this banding would be useless, as all fertile ages are included in one band. Studies of teenage pregnancy may need to stratify individual years of age. Access to more detailed HES data is available to NHS organisations via trusted providers, who will produce bespoke analyses on receipt of certain undertakings about data privacy and confidentiality.
Ethnic data are available via HES and associated datasets, and data quality in this area has improved considerably in recent years. Stratification by ethnic group is a possible analysis for patients admitted to hospital. However, this data item is missing from death registrations so cannot be used for mortality studies. Social class is rarely present in any health data, so while it is known to be a major indicator (or determinant) of health, it tends to be a factor only in specially commissioned research studies. However sometimes an indicator of deprivation such as the Index of Multiple Deprivation can be used.
[accessed 20/08/2018]
Indices of fertility
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Crude birth rate |
live births per 1000 per population per year N.B. denominator includes everybody - males, children, post-menopausal women |
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General fertility rate |
live births per 1000 women per year, for women aged 15-44 |
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Age specific fertility rates |
live births per 1000 women per year, in specific age bands N.B. used to take into account different fertility patterns in different age groups |
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Total period fertility rate |
∑ age specific fertility rates, expressed as live births per woman. It is the average number of live born children if current age specific rates are applied over the 30 year period. Enables comparisons over time and across countries. Takes account of differential fertility rates within different age groups and provides a summary measure. |
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Cohort measures of fertility |
birth or marriage cohort followed up until past the age of 44. Occurrence and timing of births and completed family size observed. Used to predict future levels of fertility. Needs to take place over a long time. |
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All indices of fertility refer to births at a specific period of time, most often a single year. |
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Factors that influence trends:
- Economic prosperity
- Employment levels
- Marriage/co-habitation patterns
- Socio/cultural factors such as sexual mores and practices
- Contraceptive availability and usage
Factors affecting physiological reproductive capacity:
- Pelvic Inflammatory Disease for example resulting from Chlamydia and Gonorrhoea
- Decreasing sperm count
Mortality rates
(N.B. rates are often expressed as 'per 1000' as denoted below but not necessarily)
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Crude death rate |
Denominator includes everybody. |
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Age specific death rate |
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Infant mortality rate |
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Neonatal mortality mortality rate |
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Post neonatal mortality rate |
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Early neonatal mortality rate |
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Perinatal mortality rate |
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Stillbirth rate |
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© M Goodyear & N Malhotra 2007, D Lawrence 2018