Mortality and experience

The Mortality A/E tile opens the experience analysis an actuary would run on a real portfolio: deaths against the deaths expected on the basis, by age band and sex, with intervals, beside the survival curves and the table itself.

How exposure and expected deaths are counted

Every day, for every resident, the engine adds a day of exposure to their age band and sex, and adds the basis's expected deaths for that day: the table's q at their age, with mortality improvement to date, turned into a daily hazard,

p(day) = 1 − (1 − qₓ)^(1/365.25)

with the first year of life front-loaded so that about 55% of infant deaths fall in the first 28 days. Expected deaths carry no individual risk: they are what the table says for a person of that age and sex. Actual deaths are the deaths that happened, from every cause.

A/E is actual over expected. Above 1, the province dies faster than its basis; below 1, slower.

The cards

Actual vs expected deaths. A/E for everyone, for men and for women, each with its 95% interval, against a line at 1. The full card adds the table by age band (0, 1-4, 5-14, 15-24, …, 75-84, 85+) and sex: exposure in person-years, actual, expected, A/E and its interval.

A/E by age band (both sexes). One bar a band, against 1. A band with no expected deaths yet has no ratio.

Survival curve l(x)/1000: basis vs experience-adjusted. The basis table's survival curve for each sex and, once a sex has three deaths or more, the curve with that sex's q multiplied by its A/E.

Basis qx (log scale). The table the province lives on, per mille, by sex.

Deaths by cause and Deaths by age band. What the province has died of, and at what ages.

The interval

The 95% interval on an A/E is computed as

(A ± 1.96 √A) / E

floored at zero: the normal approximation to a Poisson count of deaths. It is a fair guide once there are a few dozen deaths and a rough one below that; with fewer than about ten deaths, read the interval as "wide". When expected deaths are below 0.1, no ratio is shown.

Reading it honestly

• One province is small. Four hundred people give three or four deaths a year. A/E from one province over a few years moves a long way by chance, which is what the interval says.
• Pool before you fit. To measure the province's mortality properly, pool seeds: pooledExperience() in a script, or Exports › Mortality experience › Pool on the worker pool, or a Monte Carlo run.
• The province need not die on its basis. The basis is what the table says; the province's deaths come from its people's own risks and its illness episodes. On the current version the province's pooled A/E on the default basis is below 1, most of all at older ages: see Calibration and limits for the measured figures.

Fertility, the same way

Births are measured against the fertility basis the same way: every woman's day of exposure adds her age-specific rate to the expected births, and the Fertility tile's births A/E is births over expected births. See Fertility.