Survival models in rstanarm

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I thought I was missing something because it was hard to invert due to the splines, but maybe not since you are using exponential_rng in your example code. To draw an exponential random number with an upper bound ub without rejection sampling, you could use the following (untested) code:

real exponential_ub_rng(real beta, real ub) {
    real p = exponential_cdf(ub, beta);  // cdf for bounds
    real u = uniform_rng(0, p);
    return (-log1m(u) / beta);  // inverse cdf for value
  }

The beta here matches the Stan manual parameterization and would be exp(intercept+X_uncensored[i,]*betas) in your notation.

This is somewhat tangential, though. You are presupposing that the same individuals will be censored (or not censored) in any replicated data, and I don’t see why that would be the case. Is it possible that when people are suggesting you take the minimum, they mean to suggest you apply artificial censoring at T^*? That is what I do. However, it requires knowing a potential censoring time for each individual. For example, if the study ends on Dec 31 and I know they entered the study on June 3, I know exactly when they would have been censored, even if I observe the event to occur in August (and thus do not directly observe the censoring “event” time). Alternately, you may know that everyone will be followed up for a maximum of 90 days. For some censoring mechanisms, this knowledge is not possible, unfortunately.

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