Table 1 Notation
From: Estimating age conditional probability of developing disease from surveillance data
| Random Variables and Parameters | |
|---|---|
| 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 |
 = rate at t for first cancer given alive and cancer-free
|
| λ o (t) = rate at t for death before cancer given alive |
 = rate at t for death before cancer given alive and cancer-free
|
| λ d (t) = rate at t for death from cancer given alive | |
| λ a (t) = rate at t for death given alive |
 = rate at t for first cancer or death before first cancer given alive and cancer-free
|
|
|
| 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 |
 = 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)
|
| d i = number of cancer deaths | |
| o i = number of other deaths | |