Death data = Next/Last birthday, Exposure = Nearest birthday

[Molly]

Hey everyone,

Please could someone just glance over these formulae i have in my notes. They are the substitutions i would use to obtain census data that looks at the same age as the data data. Ive derived them from what i think has been done in the solutions of relevant questions:

for death data=last birthday, exposure data=nearest birthday:
P'_(x)t=1/2 (P_x t +P_(x+1) t)

for death data=next birthday, exposure data=nearest birthday:
P'_(x)t=1/2 (P_(x-1) t +P_(x) t)

Please could someone confirm if these are correct?

Thanks so much,
Molly

 

[Andrew Martin]

Hi Molly

These look correct to me. Note that we get to these by assuming uniform birthdays of the population over the relevant intervals.

Andy

 

[Molly]

Hi Molly

These look correct to me. Note that we get to these by assuming uniform birthdays of the population over the relevant intervals.

Andy

thank you so much andy

 

[lordyamanouchi]

Hi Molly

These look correct to me. Note that we get to these by assuming uniform birthdays of the population over the relevant intervals.

Andy

How does one practice rederiving these for any of the census data to death data mixes so that it can be known?

 

[Andrew Martin]

Hello

My recommendation would be to draw out a timeline of ages. For example:

54.5 ----- 55 ----- 55.5 ----- 56 ----- 56.5 ----- 57

Let's say we have death data for those lives who died age 55 last birthday. Let's say we have exposure data for lives aged x nearest birthday. Then we need to convert the exposure data to age x last birthday. We have exposure data for lives aged 55 nearest birthday, ie those in the interval:

54.5 ----- 55 ----- 55.5 ----- 56 ----- 56.5 ----- 57

We also have exposure data for lives aged 56 nearest birthday, ie those in this interval:

54.5 ----- 55 ----- 55.5 ----- 56 ----- 56.5 ----- 57

What we want is those lives aged 55 last birthday, ie in this interval:

54.5 ----- 55 ----- 55.5 ----- 56 ----- 56.5 ----- 57

If we assume that the individuals in the first two intervals above are evenly spread across the ages, then we can take half of the lives in the first interval and half of the lives in the second interval.

Hope this helps!

Andy