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# Calculating Sample Size for Equivalence Test in Cox Proportional Hazards Regression With Stratification

Dear Community,

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, I want to show that the regression coefficient for this predictor 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

1) Each patient has a time to getting the disease or being censored from the study.  Let's call it T.

2) 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.

3) My binary covariate of interest is X, and it has 2 values: 0 and 1.  I seek to show that the hazard functions (and, hence, the survival functions) of these 2 groups are the same.

4) The maximum hazard ratio that I will consider to be an insignificant difference between those 2 groups is H.  If the hazard ratio for X is less than or equal to H, then I would conclude that there is no difference between the 2 groups of interest.

5) 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?

Thanks for your help.

Eric

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