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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?

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The conditional distribution remains binomial, just with an additional predictor. Feel free to continue using logistic regression.

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

$$log(odds)=\alpha+\beta x_{dose}+\gamma x_{disease}+\nu x_{weight}$$

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  • $\begingroup$ Thanks for the answer. So does it not matter that I can no longer group the patients since weight is continuous? For example, if I now fit this in Stata, instead of having 12 observations as before (12 covariate patterns), I now have 300 observations. What implications does this have? Is this example where multilevel logistic analysis should be used (sorry I have heard about multilevel but don't actually know much about it)? $\endgroup$ Jun 10 '20 at 13:43
  • $\begingroup$ @DavidYoung No need for a multilevel model. The inclusion of the covariate only changes how one might go about assessing the fit of the model. Including a continuous covariate or using binary outcomes rather than binomial outcomes is fine. $\endgroup$ Jun 10 '20 at 14:01

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