Hi all,
I've been reading up on parametric survival analysis, especially on accelerated failure time models, and I am having trouble wrapping my head around the family of distributions.
I am aware that there are the exponential/weibull/log-normal/log-logistic distributions. But what I can't seem to find a clear and consistent answer on is which of the following is the one that is actually assumed to follow one of those distributions? Is it the survival time T, the log survival time ln(T), the hazard function h(t), the survival function S(t), or the residuals ε?
Thanks in advance.
Please see if this resource is useful to you:
https://www.theanalysisfactor.com/parametric-or-semi-parametric-models-in-survival-analysis/
Dear Shaun,
It would be T itself - as is, or transformed as per your interest. For example, ln T would be something that you model. The survival function would be the exponential/weibull/etc... The hazard function has a shape derived from this survival function but is not the function itself. Residuals are something else entirely, they tell how well you have empirically described the data using your assumptions about S(t). The distributions of residuals can be discussed in their own right, but this is not part of the initial choice of S(t), it is part of the discussion of how your choice of model has described your data.
Hope this helps.
Dear Shaun,
Yes, if you have enough data then the empirical density estimates will be very helpful. If you know enough about the process(es) by which T was generated this may be enough on its own. In other cases one might make decisions by comparing various models.
Take care,
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