Moreover, it is also interesting to specify a time prior to which disease is present with certainty (the active period of treatment) and after which disease is present with some probability such as equation 3. This time is called the time to cure, noted by Tc.
Then following [MZ96], a probability of recovering from cancer given currently elapsed survival time can be attributed to each individual of the cancer registry database.
In this paper, time- and age-specific total prevalence refers to all persons in a given population diagnosed in the past with cancer and alive on a determined date. The time- and age-specific L-year partial prevalence at time t, age z , including all persons who have developed the disease in the age interval [z,z - L), n (z, L), is therefore formulated as follows
P (a subject at age z is diseased, diagnosed in [z,z - L)) n (z,L) = -—-—-:---:---• (4)
P (a subject at age z is alive at time t)
The notion of time-, age-specific non recovery L-year partial prevalence, nNR (t, z, L), that is defined as, on a determined date, the proportion of people alive who have been diagnosed with the disease, have not been cured and have developed the disease in the age interval [z, z - L). This prevalence at time t and age z is therefore formulated as follows nNR (z,L)= (5)
P (a subject at age z is diseased and non cured, diagnosed in [z, z - L)) P (a subject at age z is alive at time t)
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