Comparing "Age of emergence" or "Age of onset" in a statistical model

Question

Say I have a set of participants and I follow them for a year to see when they first produce two behaviors, A and B. I'm interested in whether there is a relationship between the onset of these two behaviours. My overall question is: is it appropriate to conduct a regression analysis predicted the age-of-onset of behaviour B using the age-of-onset of behaviour A? Or to run a correlation between ages of onset (A) and ages of onset (B)?

I'm aware that generally, if you're interested in the appearance of some event, it is best practice to use a Cox regression to deal with censoring issues (since the event may not occur). However, there are a few reasons I don't want to here (just bare with me on this!):

1. I know every age of onset for every participant.
2. I'm not interested in the time-to-event per se, just whether the onset of behaviour A is related to the onset of behavior B- specifically, do those who tend to produce behaviour A earlier tend to produce behaviour B earlier?

I suppose I could have time-varying covariates here for each participant in a Cox regression. But surely just running a simple regression with ages-of-onset is simpler and still addresses my main question?

Is there any reason this is problematic, other than generally for a study you wouldn't know every age of onset? I'm unsure as I can't find any discussion of this anywhere online. Conceptually I can't see any issues, but I would appreciate guidance on this.

Answer 1

Survival modeling has advantages when time-to-event from some well defined starting time is of interest, particularly when you have censored data. You don't seem to have censored data with respect to "age of onset" of either behavior ("I know every age of onset for every participant") so the answer depends on the nature of your data with respect to event timing.

If the onset of Behavior A always precedes that of Behavior B, a simple survival model (Cox or otherwise) could use onset of Behavior A as the time = 0 reference for each individual, include age of onset of Behavior A as a covariate (potentially among other covariates), and determine whether the interval between ages-of-onsets is associated with "age of onset" of Behavior A. Those results could then be interpreted in the way you desire. For example, if there is no association between age-of-onset of Behavior A and that interval to onset of Behavior B, you then could infer that later age-at-onset of Behavior A means later age-at-onset of Behavior B.

If the behaviors can start in different orders, you could consider a a multi-state model, with each behavior onset modeled as a separate type of event and birth date (or other fixed age) as time = 0. That could provide interesting ways to evaluate whether the prior occurrence of one event alters the time course to the other event. See the vignettes for the R survival package as an introduction to ways to model different types of events in a single model. But if all you are interested in is the association between the two ages-at-events, that approach might be overkill.

Think carefully about precisely what hypothesis you wish to test, and choose accordingly.