Age, period, cohort models. Trying to simplify the complex.

Now I know my APC….

Separating the linear effects of age, period (year) and cohort (birth year) on a health outcome is, in one sense, impossible, as all three are interdependent. Age is period minus cohort. Despite this, debates about whether these effects can be estimated simultaneous are endless. Much of the debate is highly statistical but it seems to me that a step back might be helpful.


For a while I have thought that drawing a causal diagram would help. Prompted by Judea Pearl’s excellent book, I now have. One key message of the book for me is that diagrams are useful for such seemingly intractable statistical problems. This is not the first-time causal diagrams have been used in age, period, cohort modelling. In these instances, age, period and cohort are shown as interdependent with two-way relationships. For me, this ignores the temporality of their relationship. At least in my thinking, cohort and period are causes of age. It seems wrong to say age causes year or birth year, so age is not a cause of period or cohort. Year of birth is the cause of birth cohort, but year does not continue to be a cause of your birth cohort so I haven’t drawn an arrow between them. This diagram is not to deny they can be used to determine each other, rather it is my assumptions about causal relations. You may think I am wrong, the beauty is you can draw your own.

Table 2 fallacy?

My conclusion from the figure is that age, period, cohort thinking suffers from the Table 2 fallacy. Put simply there are different types of effect an exposure can have, and people end up comparing apples and oranges. For example, if we model cohort against the outcome and do not control for age, that is the total effect of cohort. If we control for age, then we have the direct effect that does not run through age. If you simultaneously model age, period and cohort, you compare the total effect of age, and the direct effects of period and cohort. The total effect of age comes from controlling for cohort and period. The total effect of cohort and the total effect of period do not require control for age or each other. Well at least in my diagram.


I am probably wrong here, and nothing I have written solves the deterministic relationship and the modelling problems. But the very act of drawing causal assumptions is important I believe to progress this field. Moreover, clarity about the exposure these effects represent would also be good but that’s a discussion for another time.