0
$\begingroup$

I use the Cox PH model in an ecology study in order to estimate the risk of "migration departure" of a bird species according to different variables. In this way I can put forward the factors influencing the migration departure. I have different variables, some are independent of time (sex, age...) and others are dependent on time (temperature, day length, wind speed).

I understood well how to code and how to use the Cox model in R, but I have a problem when I interpret the results.

Indeed, several variables give me incoherent results (they are even the expected inverse results). This is particularly the case with the variables 'day length' and 'temperature'. The birds start migrating as soon as spring arrives and with the increase of the day length and the temperature. But, here, my coefficients are negative. The particularity of these two variables is to be very strongly correlated with time (the more the time of experience increases, the more the value of the variable increases).

I wonder then if I have not missed something in the design of the model that would prevent the use of time correlated variables in a Cox model? Is it possible to code variables correlated to time?

I apologize if my English is not comprehensive, please do not hesitate to ask me for clarification.

Improve this question
$\endgroup$
2
  • $\begingroup$ Welcome to CV, Sara Gomez! Depending on your study duration and season, day length may have a nonlinear relationship with migration departure (e.g., there are 8 hour days twice a year for many latitudes, and migration departure may only be more likely with longer day lengths when daylight hours are increasing (i.e. moving towards the summer solstice). $\endgroup$
    – Alexis
    Commented Jun 2, 2021 at 20:42
  • $\begingroup$ Your variables are called internal time-dependent covariates and can be handled with a Cox model that explicitly treats them as time-dependent (i.e., you can't just put them in the model as if they were baseline covariates). You need to use for example the interval start, stop time notation. See this vignette for useful information: cran.r-project.org/web/packages/survival/vignettes/timedep.pdf $\endgroup$
    – Frank Harrell
    Commented Jun 3, 2021 at 12:26

1 Answer 1

Reset to default
0
$\begingroup$

First, make sure that you are treating your predictor variables properly as time-varying covariates, as Frank Harrell recommended in a comment and as explained in detail in the vignette to which he linked. Also consider the possibility of nonlinear associations of predictors with outcome, as in the comment from Alexis.

If you are modeling properly, what's going on might have to do with the nature of multiple regression itself. Each coefficient in a multiple regression represents the association of a predictor with outcome when all of the other predictors are held constant. Depending on the other predictors in your model, a negative coefficient for temperature might just mean that a higher temperature makes migration less likely when all the other predictors have the same values. That's not incompatible with temperature gradually rising as a function of time overall; the coefficient represents how much of a difference temperature itself makes when everything else is the same. When there are multiple correlated predictors, as you have, an apparently anomalous negative coefficient might just represent an implicit correction for too high an estimated positive coefficient for a correlated variable.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.