I'm trying to investigate several independents on a dataset with time-to-event data for a treatment. I'm measuring time-to-treatment effect (where treatment effect is a binary parameter).
Treatment effect always occurs within the first two month. But for some subjects, the treatment is ineffective altogether. I do have a long follow-up for these subjects. These subjects make up less than 10% of the data.
I want to model both time-to-treatment effect, and amount of subjects never reaching treatment effect.
I can reasonably state that the hazards are proportional, and if a dependent will have a lower hazard of reaching time-to-event, it will have a higher fraction of subjects never reaching the event.
Can I use a Cox proportional hazards model to model this data?
If I use a Cox proportional hazards model, which time do I use for subjects never reaching the event?
Can I just censor patients never reaching treatment effect at 60 days, since they're no longer at risk for experiencing treatment effect, or do I include them for the full length of the follow-up, even though they're no longer at risk?