Cox PH question

[diegoro...@gmail.com]

Hello, 

I am trying to build a cox PH model that considers 3 aspects: 

- Time dependent covariates

- Spatial random effects for the geostatical data

- Temporal effect

I have some time to event, across an area of interest (spatial) and the measures are taken every year in the same location (temporal) 

Does it make sense for the function inla.surv() if I include two Flailrty terms, one for space and one for time. something like: 

inla.surv(time, event) ~  L + # time dependent covariate

f(spatial.field, model=spde)+ # spatial random effect

f(year, model = "ar1") # temporal correlation

Thank you for your help, any other comments will be helpful. 

:) 

[Denis Rustand]

Hi,

Time dependent covariates can be handled through the decomposition of the folllow-up into intervals for the Poisson approximation of the Cox model in INLA. The ar1 you show will likely conflict with the baseline hazard, do you mean you want a population average time trend (i.e., baseline hazard)? Or a spatio-temporal random effect where each location has its own time trend? I'm not sure about the latter as it might also conflict with baseline hazard somehow, so it might require some extra work to have proper constraints and avoid identifiability issues...

Maybe this will have some answers: 10.1016/j.ejor.2025.07.060

Denis Rustand

[diegoro...@gmail.com]

Hello, 

Thank you for your answer. 

my idea right now is to have the spatio-temporal where each location has its own time trend. and Indeed, I understand how can this can be challenging and interfere with the base line hazard function. 

I will take a look at the literature, maybe I can start thinking about how to include the constrains to avoid identifiability.

:)