# Data Explanation (AHMD)

## Data Explanation

The Australian Human Mortality Database (AHMD) includes the following types of data:

- live birth counts,
- death counts,
- population size on January 1
^{st}, - population exposed to risk of death,
- death rates,
- life tables, and
- life expectancy at birth.

### Format of the data

- All AHMD data files are tab-delimited text (ASCII) files
- Population size is given for one-year
^{1}and five-year^{2}age groups.^{3} - Deaths are given in the following formats:
^{3}- Lexis triangles (i.e., by age
^{1}, birth cohort, and calendar year) - 1x1 (i.e., by age
^{1}and calendar year) - 5x1 (i.e., by 5-year
^{2}age group and calendar year).

- Lexis triangles (i.e., by age
- Exposure-to-risk, death rates, and life tables are given in similar formats of age and time:
- 1x1 (i.e., by age
^{1}and year) - 1x5 (i.e., by age
^{1}and 5-year time interval) - 1x10 (i.e., by age
^{1}and 10-year time interval) - 5x1 (i.e., by 5-year
^{2}age group and year) - 5x5 (i.e., by 5-year
^{2}age group and 5-year time interval) - 5x10 (i.e., by 5-year
^{2}age group and 10-year time interval).

- 1x1 (i.e., by age

^{1} One-year age groups (or "by age") means 0, 1, 2, ..., 109, 110+.^{2} Five-year age groups means 0, 1-4, 5-9, 10-14,..., 105-109, 110+. Age groups are defined in terms of completed age, so "5-9" extends from exact age 5 to just before the 10^{th}birthday.^{3} Some of these numbers are estimates (not actual counts), and therefore may be expressed as non-integers.

The following columns are included in each life table:

Year | Year or range of years |

Age | Age group for n-year interval from exact age x to just before exact age x+n, where n=1, 4, 5, or ∞ (open age interval) |

m(x) | Life table death rates between exact ages x and x+n |

q(x) | Probability of death between exact ages x and x+n |

a(x) | Average number of person-years lived between exact ages x and x+n |

l(x) | Number of survivors at exact age x, assuming l(0) = 100,000 |

d(x) | Number of deaths between exact ages x and x+n |

L(x) | Number of person-years lived between exact ages x and x+n |

T(x) | Number of person-years remaining after exact age x |

e(x) | Life expectancy at exact age x (in years) |

See the Methods Protocol (pg. 34-44) available on the Human Mortality Database’s web site for more details about life table calculations.

### Important Notes

- Deaths, population estimates, death rates, and life tables are provided by single years of age up to 109, with an open age interval for 110+. However, these data are sometimes the product of aggregate raw data (e.g., open age intervals at 100 years old and over), which have been split into single years of age using the methods described in the Methods Protocol.
- For all life tables, the central death rate m(x) is used to compute probabilities of death q(x). By definition, the values of m(x) below age 80 are equal to the observed population death rate M(x). At older ages, however, the number of deaths and the exposure-to-risk eventually become quite small, and thus observed death rates display considerable random variation. Therefore, the values for M(x) at ages 80 and older are smoothed and then used to compute q(x) above a certain age (based on the number of observed deaths). This procedure helps to avoid certain difficulties in life table calculations at older ages that may be caused by:
- extremely high death rates resulting from exposure being smaller than the number of deaths,
- death rates of zero resulting from no deaths at an age where exposure is non-zero, and
- undefined death rates at all ages where exposure is zero.

**NOTE**: The text above has been adapted from the Human Mortality Database web site (www.mortality.org).