I am attempting to model the probability of death while controlling for a number of other variables. I began to do this with standard logistic regression, but I've come across a number of articles that use Poisson regression to model mortality rates. My independent variable is death (0/1). Is Poisson regression preferred to Logistic Regression when modelling something like death or vice versa? If so why?
Partially answered in comments:
It depends on the data setup and research question. Since your interest is in the probability of death and your independent variable is 0/1, logistic regression is suitable here. The other articles might have been counting the incidents of death. Then their response variable would be count data. – Greenparker
Another point is that researchers sometimes use Poisson regression with an offset of log(population size) even when modelling "rate" or probability (and not total number). For outcomes with low probabilities, the results will be very similar (the link functions [logit and log], as well as the variance functions [$np(1-p)$ and $\mu$], are very similar when the probability is close to 0).
Logistic regression still makes more sense as a model of the system (Poisson regression in principle would allow for rates > 1). I don't honestly know whether Poisson regression is preferred in some fields because it has (or used to have) computational advantages, or because it might have slightly better finite-sample properties (the latter is complete speculation).