Analysis of survival data using binomial GLM with offset

We are interested in determining whether there's an association between frequency of screening visits and cancer outcomes and whether that differs by race. We have Medicare data to analyze this. Typically, the knee jerk reflex for modeling survival times is that of Cox proportional hazards models, but the problem is that we're directly interested in modeling the effect due to time, since this influences the number of screening visits that a person would be eligible for.

The outcome is binary: whether or not a person died at the end of a study interval. Study intervals technical differ from subject to subject. At most, we have 5 years worth of screening data, where eligible in subjects, though some subjects are censored because they enroll in other health care plans and we can't determine what their further COAs are for screening, diagnosis, or treatment).

In my mind, these data are cross sectional, not prospective, since we use visit data from the future to infer about proportions that are homogeneous in the past. Yet, subjects differ in weight between one another due to the length of available follow-up.

I'm struggling to write a correct linear model for these data and propose a valid analysis plan for them. How does one write a linear model with an offset?

• If the outcome is binary, you don't want Cox - Cox is for cases where the outcome is time and is censored. But do you have one observation per person or multiple observation? If the latter (which I think it is) you need to account for that, perhaps with a nonlinear mixed model. But I think you need to clarify what data you have and what you want to find out. – Peter Flom - Reinstate Monica Apr 1 '13 at 18:58
• Technically, there are multiple observations including the date of visits and the date of death if available. Cox models were proposed since some subjects were not eligible for the full duration of follow-up and because the endpoint could be conceived of as time-to-event. I am uncomfortable to use rates extrapolated retrospectively to infer a prospective outcome. I can see the use of mixed modeling with the number of annual visits and indicators of death that aggregate up to the person level. – AdamO Apr 1 '13 at 19:07
• I think that the limitation of the mixed model is that it doesn't explicitly model the effect from year to year and that it only depends upon outcome. For instance, I may have a good number of follow-up visits after mainline treatment for cancer one year, and then I pass away next year. I would like to explicitly model the influence of those previous years' visits on next year's cancer risk. Mixed models would only borrow the information from the outcome, i.e. that I didn't die last year. – AdamO Apr 1 '13 at 19:20
• Do you know the time of diagnosis and the number of screening also before the study period started? – Benjamin Christoffersen Nov 1 '17 at 21:42