Survival analysis - follow up duration and sample selection

Question

I'm working on a study that is drawing from another very large study, and proposing a case-cohort design. Briefly, the main cohort consists of ~40,000 individuals, ~1250 of whom had an event over the duration of the study. The intention is to develop a survival model based upon the event time distribution of the dataset.

Regarding selection of cases, the study from which we plan to draw samples extends for ~10 years. Our interest is to focus on the near term events, specifically events occurring in 5 years or less. The question that has come up regarding cases is whether we only use the subset of cases having events within 5 years or if including additional cases beyond that time is beneficial. The target population for use of the model is certainly the under 5-year event group, but it has been argued that we should use all cases regardless of when their event occurred - even well after 5 years - in order to more accurately model the survival curve.

Does inclusion of cases outside the intended use population lead to bias in the model? Would inclusion of those samples beyond our expected time cutoff provide a benefit in a model intended to be used for near term events?

Answer 1

That depends on your model and assumptions.

For example, suppose you are planning on using a Cox-PH model with non-time varying covariates, as is very common. If the proportional hazards assumption is correct, or at least approximately correct, then using data in which events occur within 0-10 years will be unbiased (or at least approximately unbiased) for the change in hazards within 0-5 years and will certainly have less variance than only using the 0-5 years data.

On the other hand, consider the case when the hazards are very much not proportional over the time frame of interest. A classic example of this is chemotherapy; it's very harmful to patients in the short run, but once a patient recovers, they are at much lower risk than patients who never received chemotherapy. Thus, the expected value of the estimated effect of chemotherapy would be very dependent on the time frame considered.

As such, if you think the relation of the risk should be roughly the same over years 0-5 and 5-10, I would recommend using all the data with events from 0-10 years. To inspect this assumption, you could artificially censor your data after 5 years (so if a subject experienced an event at t = 6 years, change this to being censored at 5 years) and check that if the estimated coefficients seem to change much.