Info

We can reorganise the data with age as the time scale and also alSow for the left-truncation necessary to account for subjects entering at different ages. Each member of the dementia cohort provides one observation with the following variables:

(i) entry age, age, in years, at entry in the observation period (that is, age in 1975);

(ii) survival age, age, in years, in their last year of follow-up;

(iii) event status, an indicator variable coded 1 for subjects who developed AD during the observation period and 0 for those who did not;

(iv) any event status, an indicator variable coded 1 for subjects who either developed AD or died during the observation period and 0 for those who did neither.

For example, subject A has entry age — 72 (1975-1903); survival age = 77 (1980-1903); event status = 1; and any event status = 1. This subject contributes 6 years of data at ages 72, 73, 74, 75, 76 and 77. Notice that subject A is considered to contribute an entire year of age 72 follow-up (in 1975) although this subject will not actually be 72 until 3 July 1975. We also consider that subject A becomes demented at age 77 (in 1980) when the age at diagnosis could really be as young as 76j. It is not possible to more accurately assign a time of diagnosis and we choose calendar year to index subjects' ages.

The second subject, subject B, has entry age = 70 (1975-1905); survival age = 73 (1978-1905); event status = 0; any event status = 1, and contributes 4 years, at ages 70, 71, 72 and 73. Subject C has entry age = 70 (1975-1905); survival age = 70 (1975-1905); event status = 1; and any event status = 1. This subject contributes one year at age 70.

We define the following notation to summarize the data structure we will use to perform analyses with age as the time scale:

rA = the number of persons at risk entering age A;

eA = the number of incident events of interest (for example cases of AD) at age A; wA = the weighted number of persons at risk entering age A, computed by assigning a weight of 0.5 observations censored free of the event of interest during age A and a weight of 1 to all other observations (the actuarial method); cA = the number of persons who fail due to either the event of interest, or due to the competing risk (here, death).

In this case the size of the risk set is not a non-decreasing function of time; rather it decreases as subjects fail or are censored, but increases as subjects age into the study period. A summary of data on the three subjects in the example above is as follows:

Age

rA

eA

wA

CA

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