ALTAM: Competing decrements share the same population at risk
Two decrement processes cannot both remove the same person twice. Under specified cause-specific constant forces, total survival uses the sum of forces; each cause’s probability integrates its own force against that survival. Do not add independent single-decrement probabilities.
Worked example or practice scenario
Let annual cause-specific forces be .02 and .03. Total one-year decrement probability is 1−e^−.05≈.04877. Cause 1 receives .02/.05 of that probability, about .01951, under these constant-force assumptions.
Try this next
Compare with 1−e^−.02≈.01980 from an isolated single-decrement model. Explain why the competing cause slightly reduces the observed cause-1 probability. Review exactly which assumptions justify converting the rates.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.