I'm working on a study that is drawing from another very large study, and proposing a case-cohort design in order to reduce the overall number of samples we use (primarily due to cost of sample analysis). Briefly, the main cohort consists of ~40,000 individuals, ~1250 of whom had an event over the duration of the study. The plan is to use all 1250 event samples (cases) and select a random sample from the non-event samples (controls). The intent is to perform survival analysis (Cox Proportional Hazards or Accelerated Failure Time) to generate a probability of event within a given time period.
The question that has come up is the number of controls to choose. To me, a 1:1 balance is OK, but perhaps even better if we had more than one control per case. It was suggested, however, that this was unnecessary due to the cases being the samples which are affecting the calculation of event times. There was even a suggestion of 2 cases per 1 control.
I'm not sure how the optimization process operates and haven't found much description of the overall role of non-event controls in survival analysis, but it seems odd to me that there might be a suggestion of fewer that 1 control per case. I would assume that the controls are quite important to establish the distributions of the co-variates used in the model, and the more information we have about those distribution in controls, the better we can determine how cases differ.
What is an appropriate sample size for such a study - rules of thumb, of course, and how do the non-event samples affect the procedure? Are they of limited value as suggested or is my perception of their importance correct?