Table 1 Notation
From: Estimating age conditional probability of developing disease from surveillance data
Random Variables and Parameters | |
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T = age at death | T* = age at first cancer or death before cancer |
J = type of death | J* = type of event |
(J = d) = death from cancer | (J* = c) = first cancer |
(J = o) = death from other causes | (J* = o) = death before first cancer |
λ c (t) = rate at t for first cancer given alive |
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λ o (t) = rate at t for death before cancer given alive |
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λ d (t) = rate at t for death from cancer given alive | |
λ a (t) = rate at t for death given alive |
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Observations | |
Within the age interval, [a i , a i +1), and within the calendar interval of interest we observe... | |
c i = number of first cancer incident cases |
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d i = number of cancer deaths | |
o i = number of other deaths | |
= rate at t for first cancer given alive and cancer-free
= rate at t for death before cancer given alive and cancer-free
= rate at t for first cancer or death before first cancer given alive and cancer-free
= estimate of person-years alive associated with j = c, d, o (DevCan uses the sum of mid-year populations during the calendar interval of interest)