I am trying to simulate the survival data that can fit the model:

$$h(x) = ho(x) exp (a_0*Treatment + a_1*Treatment*x_1 + a_2*Treatment*x_2)$$

Whereas treatment is an binary variable (0 = control treatment, 1 = experimental treatment). $x_1$ and $x_2$ are also binary (0 and 1). $x_1$ and $x_2$ are independent. These 3 variables follow 3 binomial distributions $B(n,pT= 0.5), B(n,p1), B(n,p2)$ relatively.

What I want now is to simulate the data in such a way that $x_1$*Treatment and $x_2$*Treatment are 2 qualitative interaction terms (it means that when $x_1 = 1$, HR(experimental vs. control) < 1 and when $x_1 = 0$, HR(experimental vs.control) > 1. The same for $x_2$).

I know how to simulate survival data (using Weibull distribution and a $\text{linear predictor} = a_0*Treatment + a_1*Treatment*x_1 + a_2*Treatment*x_2)$. However, I don't know how to choose appropriate values for $a_0; a_1; a_2$ for that requirement. Because the a significant interaction coefficient does not ensure that the interaction will be qualitative, I think that it's also about how to choose the values of $p1$ and $p2$;


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