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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?

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    $\begingroup$ 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. $\endgroup$ – Greenparker Mar 26 '16 at 12:20
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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

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  • $\begingroup$ I'd add another factoid: the articles that use Poisson are probably counting the number of deaths where the observation is something like a hospital, a county, or some other group (and they would have standardized the exposure, e.g. deaths per 1,000 discharges or person-years). If the original poster has individuals as the unit of observation, then Poisson can't be appropriate (unless we're in some world where you can die multiple times). $\endgroup$ – Weiwen Ng Mar 28 '19 at 22:10
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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).

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