Poisson Regression model in example

Question

I need to fit a model to study the severity of bicycle accidents. The data description is

$X_1$: is the use of helmet, a categorical variable (1=Yes,0=No)

$X_2$:the speed at which he was riding, a categorical variable$(1=10-15 , 2= 15-20, 3= 20-25)$ in mile/hour

$X_3$: the severity of a bicycle accident, is a count with two levels (not severe,severe)

Let the data following

How can I fit a model to study the severity of accident based on the use of helmet and speed?

I was thinking in use a Poisson Regression Model, but in this case we have a two counts data. Can anyone give me suggest?

How can I study the relationship between the severity of accident and use of helmet and severity of accident and speed?

The main problem for me here, is that Severity of accident is a binary random variable , but at same time is a count.

How can I study the association between the severity of accident and use of helmet while fixing (controlling) the variable speed?

How can I study the association between the severity of accident and speed while fixing (controlling) use of helmet?

Answer 1

This can be modeled as a generalised linear model with a binomial response - number of "successes" and number of "failures" - where a success is a not severe accident and a "failure" is a severe accident. In R you could do this with:

glm(cbind(NotSevere, Severe) ~ Helmet + Speed, family = binomial)

The estimates for Helmet and Speed respectively will then provide the associations between each one and the log-odds of accident severity, while holding the other one constant.