# Logistic Regression with Individual Level Data

In a study there are 300 patients in total, 100 suffering from each of three diseases (D = 1, 2, or 3). The 100 patients with each disease are further divided randomly into four equally sized groups that received different doses of the same drug (dose = 20, 30, 40, 50) respectively. Initially the binary data (dead or alive) is grouped by 25 since there are 12 covariate patterns. An appropriate analysis is therefore a logistic regression model since the number of deaths per group follows a binomial distribution.

Now suppose that I also have the weight of each patient and I wish to extend the model to allow weight to influence the odds of mortality, and that weight is continuous with no two patients having the same weight. What is an appropriate generalised linear model for this purpose?

Instead of having $$log(odds)= \alpha+\beta x_{dose}+\gamma x_{disease}$$, you will have another variable for weight:
$$log(odds)=\alpha+\beta x_{dose}+\gamma x_{disease}+\nu x_{weight}$$