For the Catheter Study, the patients were assessed bimonthly and the measurements about UTIs, catheter blockages, and replacements cover the previous two months. Thus, the patients were under observation the whole time while they were in the study. So, we can study the survival times from the participation of the study until the first UTI, blockage, and replacement, which are defined by their first incident after the intake. Incidents of any of the three at the intake will be included as a covariate.

(a) Estimate the survival functions without adjusting for covariates.

(b) Compare whether there are differences in the survival functions between the two treatment groups.

(c) Fit the proportional hazards and proportional odds models to assess treatment effects while controlling for age, gender, and incident of the same type of event at the intake (main effect only).

(d) Estimate the risk adjusted survival function based on the regression models in

(c) and compare them with the estimate in (a).