I have a large set of data for 37 different clinical units (all oncology) in their respective 37 hospitals. There are two specific outcome variables that I need to analyse:

First, drug usage for specific drugs types and classes (aggregated drugs) that are expressed as a rate – DDD (Defined Daily Doses) per 100 patient days. There are individual patient drug use figures for this set.

Question1: Which regression approach should I take? From what I can gather I can use a Poisson regression model. IF there is overdispersion in the outcome I could resort to a negative binomial model.

Second: I have antibiotic resistance data that is expressed as proportion in the range 0 – 1.These are not available as individual patient data points but aggregated to each of the 37 hospitals.

Question 2: Again, which approach? From what I have read I can use a logistic regression model. I have been advised by another statistician to initiall use a logit model and then use a probit model and compare goodness of fit for each model.

Does this sound like a reasonable approach? Is there a specific text that you could direct me to in order to upgrade my basic regression modelling skills. I will be using R for the analysis.

• Logit and probit models are usually so close that it will likely do no good to apply both. Use just one of them along with appropriate goodness-of-fit tests to detect and diagnose possible mis-specifications. (The coefficients in logit models usually have simpler interpretations.) – whuber Aug 23 '12 at 13:09

I agree with Erik in most respects. However I do think that in the first case that you are trying to predict a rate parameter from a point process and so Poisson or negative binomial regression would be appropriate. Most texts on regression deal primrily with linear regression. Some also include topics on nonlinear regression. But in your case you are interested in learning about special topics like logistic regression, probit models and Poisson and Negative Binomial regression which are best covered in specialized books such as: Negative Binomial Regression by Hilbe

Probit Analysis by Finney

Applied Logistic Regression by Hosmer and Lemeshow

I will supply some cautious answers and some further suggestions.

For question 1 I would probably use a binomial model instead of a Poisson model. This is under an assumption tha a patient gets a DDD on a certain day or not, so that the the outcome variable is betweeen 0 and 100.

But I would urge a lot of caution here. One problem is that daily medication is not independent on a day level at all. I would really look carefully at the distribution here and go from there. Try to think carefully about interdependence of your data and the underlying processes. Look at the data. Plot the data. I would also use a hierachical model to properly model the differences on the hospital model and the differences on the patient level.

Generally a good reading suggestion for this would Data Analysis using Regression and Multilevel/Hierachical Models from Gelman & Hill.

Your approach to question 2 seems workable. You could improve it a lot if you know over what amount of data each hospital has aggregated and model this in a bayesian hierachical model. The additional amount of learning required might not be practicable to you. Section 5.5. of Bayesian Data Analysis (2nd Edition) from Gelman et al would be a good ressource for this.

• Thanks @erik, I had a look at the Gelman book and will explore the hierarchical approach. – John Aug 23 '12 at 22:10