# How to model counts of a categorical variable?

I'm interested in assessing the impact of various covariates (age, sex, Charlson comorbidity score, etc.) on the incidence rate of a pulmonary event. However, the event is not binary. Each patient could have one of three values: the first (0) indicating no event, the second (1) indicating a non-severe event, and the third (2) indicating a severe event.

I'm unsure which regression model I should use for these data.

Any insight would be greatly appreciated!

• It sounds like an ordinal regression problem. By the way, you always can combine categories 1 & 2 to make it binary, so I guess that you mean that you don't want to treat this as binary, rather that it isn't..? – Tim Apr 22 at 19:50
• Yeah, I'd prefer it not to be binary. I'm now wondering if I could use a generalized linear model with whichever distribution is appropriate for original regression and the log of each patient's follow-up time as the offset. – cjos0909 Apr 22 at 20:52
• If you are collecting information on follow-up time there is presumably a start date for each patient and a time between start and event, so this seems better to be handled with survival analysis. The two different types of events could be considered competing events, which can be handled by survival analysis. Is there some reason why competing-events survival analysis can't be used here? – EdM Apr 22 at 20:57

$$\Pr(Y \le i|X) = \sigma(\theta_i - X\beta)$$
where $$\sigma$$ is the links function (logit, or probit etc.). For more details, you can check also other questions tagged as .