Time-wise treatment effect / survival analysis

Question

Let's say I have some kind of survival data - i.e. I'm giving a drug that may cause mortality. So I have three patients: A, B and C. All are given the drug at Time t1.

Let's say patient A dies at time t2. Patient B dies at time t3. And Patient C dies at time t100.

Clearly, the likelihood that the drug caused the death of patient A and B is higher than the likelihood that the drug cause patient C's death (i.e. patient C likely died from natural causes whereas patients A and B probably died because of the drug).

Are there any techniques in survival analysis/related fields that allow one to quantify the probability/likelihood that the treatment caused the effect. For example, if I could calculate the probability that the treatment caused the death given that patient was treated at time X and died at time Y.

Thanks!

Answer 1

I think you're going to struggle with any sort of definitive treatment effect, because you lack a comparison group of any sort. You need not necessarily have a control group - there's plenty of methods in the case-crossover literature for using cases as their own controls during unexposed time periods, but if everyone got the drug at t=1, then no one has unexposed time to act as a control.