# Validity of using non-time variable in survival analysis

I’ve conducted a time-to-event analysis (accelerated failure time) for a research project, looking at the effect of an intervention on the probability of needing a blood transfusion during surgery. Instead of time however, I’ve used blood loss (in milliliters) as a proxy variable for time to event.

Everything I have read suggests that this is statistically valid (as blood loss increases, eventually everyone will need a transfusion- similar to as time increases everyone will experience disease progression or death, for example). however I can’t find any references where anyone has used an approach like this.

Curious if anyone has heard of this creative use of survival analysis before or could point me to a reference

I’ve determined that CPH assumptions were violated (the hazard of needing a transfusion increases with increasing blood loss, for example) and used an accelerated failure time model. Everything seems to check out

• I'm curious as to why you would do this. One of the big motivations for time to event analysis is that the data are often censored (some of the subjects don't die before the study ends, etc.) You don't seem to have that. So ... why use this models? Sep 22 at 19:22
• In my case some of the patients do not get transfused (eg, the don’t “die”). The reason I like this analysis is because the results are very intuitive to understand and clinically applicable. Sep 22 at 20:01

Parametric "survival" models, like AFT models, are just ways to estimate an underlying probability distribution while taking censoring and truncation of outcome values into account. Technically, a survival function $$S(x)$$ is just the complement of a proper (cumulative) probability distribution function $$F(x)$$; that is, $$S(x) = 1-F(x)$$. The variable $$x$$ doesn't have to represent time. For example, tobit models are used in economics when there are censored outcomes of types other than time (e.g., incomes or expenditures), and they can be implemented by invoking standard survival-analysis methods.
The question is whether cumulative blood loss is a reasonable choice for $$x$$. That depends on your understanding of the subject matter.