I have a binary predictor, X, in a Cox proportional hazards regression model, and I want to show that it is NOT a significant predictor. In other words, I want to show that there is not a significant difference in the predicted hazards (and, equivalently, predicted survival probabilities) between the 2 classes of X. Mathematically,
- if the estimated hazard ratio is H,
- and if my non-inferiority margin is is H_ni,
then I want the sample size that will adequately show that the test of
H_0: H > H_ni
H_a: H <= H_ni
has a P-value that is less than my significance level, alpha.
The complication for this calculation is the existence of 2 other categorical predictors in my model. They are NOT to be fed as predictors. Instead, I want to STRATIFY the model by these predictors. To clarify what I mean by stratification, please see this document.
Here are my inputs
Each patient has a time to getting the disease or being censored from the study. Let's call it T.
I have a censoring variable that will tell me whether or not an observation was an event or censored at time T. Let's call it C.
My binary covariate of interest is X, and it has 2 values: 0 and 1. I seek to show that the hazard ratio for X = 1 to X = 0 is close to zero. In other words, the hazard functions (and, hence, the survival functions) of these 2 groups are the same.
The maximum hazard ratio that I will consider to be an insignificant difference between those 2 groups is H_ni. If the hazard ratio for X, H is less than or equal to H_ni, then I would conclude that there is no difference between the 2 groups of interest.
Here is the complication: I have 2 other ternary covariates, Y and Z. A colleague said that these 2 covariates predict survival better than X, so I should do this sample-size calculation while stratifying by Y and Z. (I actually don't know why this stratification is needed. If you know why this is helpful, please let me know.) Regardless of whether I understand this or not, I need to run a Cox model that stratifies by these Y and Z.
My questions for you:
A) Can a sample-size calculation be done for this situation? If so, how?
B) How does stratification by Y and Z add value to this model?