Actuarial life tables
- Concept
They estimate survival over fixed intervals (for example by year) when the exact date of each event is not known.
What it is
The actuarial method (clinical or Cutler-Ederer life table) groups follow-up into intervals such as years instead of using the exact time of each event. For each interval it calculates the probability of dying among those who started it, counting people withdrawn during the interval as at risk for half of it. It was the standard method before Kaplan-Meier and is still used with many patients or grouped data, as in cancer registries.
Worked example
- Data: 200 patients. Year 1: 20 deaths and 10 withdrawn. Year 2: 15 deaths and 20 withdrawn. Year 3: 10 deaths and 25 withdrawn.
- Year 1: effective at risk = 200 − 10/2 = 195; q = 20/195 = 0.103; p = 0.897.
- Starting year 2: 200 − 20 − 10 = 170. Effective = 170 − 20/2 = 160; q = 15/160 = 0.094; p = 0.906.
- Starting year 3: 170 − 15 − 20 = 135. Effective = 135 − 25/2 = 122.5; q = 10/122.5 = 0.082; p = 0.918.
- Cumulative survival: year 1 = 0.897; year 2 = 0.897 × 0.906 = 0.813; year 3 = 0.813 × 0.918 ≈ 0.747 (without rounding in between).
- Reading: about 75% are estimated to be alive at 3 years (figures rounded to three decimals).
The example’s life table
| Year | Starting | Deaths | Withdrawn | q (dying) | Cumulative survival |
|---|---|---|---|---|---|
| 1 | 200 | 20 | 10 | 0.103 | 0.897 |
| 2 | 170 | 15 | 20 | 0.094 | 0.813 |
| 3 | 135 | 10 | 25 | 0.082 | 0.747 |
Markers
- q
- p
- effective n
Common pitfalls
- Subtracting all withdrawals from the at-risk group (which underestimates survival) instead of half.
- Using very long intervals when the risk changes a lot within them.
- Confusing the clinical life table with the population life table used to calculate life expectancy.
Test yourself
Think of the answer, then tap the question to see it.
How does the actuarial life table differ from the Kaplan-Meier method?
The actuarial method groups time into fixed intervals; Kaplan-Meier calculates survival at the exact time of each event.
How is the effective number at risk in an interval calculated?
Half of those withdrawn during the interval is subtracted from the number who started it.
If 100 start an interval, 20 withdraw and 9 die, what is the probability of dying?
Effective at risk = 100 − 10 = 90; q = 9 / 90 = 0.10.
How is cumulative 3-year survival obtained?
By multiplying the probabilities of surviving years 1, 2 and 3.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Censoring (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012); Empirical model fitting - distribution free (Kaplan-Meier) approach (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012).
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Representative model, for educational purposes only.