stratification or two-way interaction with multilevel categorical variable

Question

I have a data with around 1600 patients from an observational study, around 230 events. 800 have a disease, and the rest do not. My main question is the effect of therapy in a multivariable adjusted cox regression model (17 covariates) only in patients with the disease as the literature shows no prognostical benefits in the healthy group. The variable therapy has 4 levels: 1. no therapy; 2. medication A or B; 3. medication A and B; 4. medication A, B and C. Is it justified to stratify the data in this case into healthy and sick and do the cox regression only in the sick group? I guess a much larger sample is needed to detect a significant interaction of disease and multilevel categorical variable.

Answer 1

That decision has more to do with your understanding of the subject matter and the goal of your study. If you aren't interested in evaluating the association between therapy and outcome in the healthy group, there's no need to include the group in the modeling at all.

Omitting the healthy group will presumably, however, decrease the number of events that you will analyze and put you more at risk of overfitting with 17 unpenalized covariates. A model formally stratified by healthy/sick would incorporate all events and allow for different baseline survival for the 2 groups, but you would still have to include an interaction between therapy and the strata if you suspect that therapy has different implications for the 2 groups.

Including the healthy group in the model with an interaction between healthy/sick strata and the 4-level therapy variable only adds 3 coefficients to the model, if you don't also need to evaluate interactions of healthy/sick with the other covariates. Based on the usual rule-of-thumb of 10-20 events pre coefficient in the model, it might make sense to build a stratified model with that therapy interaction if you have on the order of 45 events in the healthy group. Or you could model all cases together without stratification, if you included coefficients for healthy/sick and its interactions with therapy.

I suspect that the study will be more informative if you model all the related data together in some way unless you absolutely know that therapy has no association with outcome in the healthy group. To avoid overfitting due to the increased number of coefficients, you might want to consider methods for unsupervised data reduction as described in Section 4.7 of Frank Harrell's course notes to cut down on the number of covariates, or to use a ridge-regression penalty on the covariates that you need to adjust for but that aren't of primary interest.