Disaggregate data using a function

Question

Hi

I was wondering if there is a way to disaggregate data using a (logistic?) function. To be specific, I have the data from the UN Population Division with population by age and year (the largest file). From 1950 to 1989 population is aggregate at 80+ years and from 1990 it is aggregate at 100+ years. Is is possible to define ages 80-100 as missing values that we could estimate from the 80+ total (and making sure total population is respected)?

Here is how it looks (male population, US) when comparing 1989 to 1990 (quick chart in Excel). The blue bar should follow the orange ones closely.

Any ideas? Thanks!

Kevin_Anderson · Answer

Hi, camoesjo.

Okay.  Your data are censored, and the level of censoring changed in 1990.

What are you intending to do?  Possible examples could be:

* Extend the pre-1990 data to match the censoring levels of the post-1990 data,
* Model the distributions over time and predict the distribution and censoring of 2025 (for example),
* Calculate and compare actuarial probabilities,
* Many other choices.

JMP has some pretty cool methods for dealing with censored data.  Bill Meeker and Chris Gotwalt gave a cool presentation at the last Discovery conference on fractionally-weighted bootstrapping for censored data.  You should check it out.

camoesjo · Answer

Hi, thanks for the reply. This is how the data looks like in a pivot table in Excel. The first column represents Age, the other represent population by calendar year. Years 1988 and 1989 (and the ones before) should look like 1990 without that subtotal at 80.

Kevin_Anderson · Answer

Hi, camoesjo!

I have several ideas about your data.  Some involve treating the data as if they were censored.

Not really sure exactly what you mean by "disaggregate".  Do you mean you intend to disperse the 1989 excess 80+ data to the 1990 extra years?  Like a prediction? Still censoring at 100+? Based on aging changes in the data year-to-year?

What you intend to do with the results can influence my ideas.  What do you intend to do?