I am trying to perform an analysis involving the use of gestational age and incidence of preterm birth as the independent variable. I've decided that using survival analysis methods would be helpful. So I am creating kaplan-meier curves presenting the stratified survival probabilities for many of my covariates of interest, as well as performing multivariate analysis using the cox proportional hazards models. However I am coming upon an issue where many of my variables, especially my main covariates of interest, are violating the proportional hazards assumption.
I know that I can undertake a number of different methods in the situation of failing to meet that assumption, such as including a time:covariate interaction term or by performing a stratified cox analysis. I have also read over pages such as this one:
providing suggestions on alternative survival methods to use in cases where the above corrections may not be appropriate.
However, I am wondering whether the use of preterm birth as an outcome in a cox model was flawed to begin with. My time is gestational age in weeks, and the event is experiencing a preterm birth. As such the event is completely a function of time since those with a gestational age <37 weeks are considered preterm birth.
Violating the proportional hazards assumption means that the hazard ratio is not proportional across time. Given the nature of the outcome, would it be the case then that after approaching a gestational age of 36, it doesn't matter how high or low my intervention/covariates are and that their effect on the outcome will be zilch? Would having preterm birth as the outcome in a cox model inevitably cause a violation of the cox proportional hazards assumption? Or am I misunderstanding the assumption and my outcome here?
