Is npregress useful for Age-Period-Cohort (APC) models?

[Anders Alexandersson]

I am learning about the new -npregress- command in Stata 15 for nonparametric regression, and wonder: is it useful for Age-Period-Cohort (APC) models? When and when not?

A classic example of an APC model is Frost (1940) who noted that changes in observed mortality rates could be attributed not only to aging effects but also period and cohort effects. Two user-written Stata commands exist for APC models, -apcfit- and -apcspline-, see

net sj 12-1 st0245
net sj 10-4 st0211

Because of the direct linear relationship between the terms, A = P - C, the model needs to be constrained. My understanding is that both -apcfit- and -apcspline- use a special form of a generalized additive (GAM) model. However, many alternative APC models exist such as mixed model or hierarchical APC (e.g., Bell and Jones 2017) and nonparametric bounding strategies (Fosse and Winship 2016). Intuitively, nonparametric regression seems very useful for APC models because it makes no assumptions about the functional form of the relationship between the outcome and the covariates. A relevant Stata blog is at http://blog.stata.com/2017/06/27/non...ssion-but-not/ . The blog and the manual for -npregress- do not refer to APC models. Below, -npregress- results are very similar to -apcfit- and -apcspline-. The example is modified from the SJ article for -acpspline- on pages 53-54:

use colorectal, clear

apcspline cases age year if sex==1, exposure(population)
predict fit2

apcfit if sex==1 & case!=., cases(cases) period(year) age(age) ///
    poprisktime(population) cohort(cohort)
predict fitapc

npregress kernel cases year age if sex==1, vce(bootstrap)
predict fitnpregress

(output omitted)

su fi* if case<. & sex==1
. su fi* if case<. & sex==1

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
        fit2 |        594    886.3923    1057.698   .0264056   3572.244
      fitapc |        594    886.3923        1057   .0457746   3532.978
fitnpregress |        594    885.5453    1050.219  -.0005832   3557.695

Based on the summary results, it seems that -npregress- can be very useful for APC models. Any thoughts or additional references are most welcomed.


References:
Bell, Andrew and Jones, Kelvyn. 2017. The hierarchical age-period-cohort model: Why does it find the results that it finds. Quality and Quantity (February), 1-17.

Fosse, Ethan and Winship, Christopher. 2016 (draft). Nonparametric Bounds of Age-Period-Cohort Effects.
http://q-aps.princeton.edu/sites/def...unds_draft.pdf

Frost, W. H. 1940. The age selection of mortality from tuberculosis in successive decades. Milbank Memorial Fund Quarterly, 18(1), 61–66.

[Ariel Karlinsky]

Hi Anders,

This is a very interesting post and I'm also currently studying the subject. Did you reach any interesting conclusions?

[Anders Alexandersson]

Ariel, no I did not but I never worked on npregress or on APC models more since then which fully explains why. Go for it!

I want to study the relationship one day, but I have focused on other more critical assignments for my staff position ever since my original posting. At least two new books on APC models are available, which might be useful:

Fu, Wenjiang . 2018. A Practical Guide to Age-Period-Cohort Analysis: The Identification Problem and Beyond. CRC.
Rau, Roland, and Christina Bohk-Ewald, et al. 2018. Visualizing Mortality Dynamics in the Lexis Diagram. Springer.