# Dirichlet multinomial for adverse event data

I am trying to see which distribution will best fit the data I am working on. The dataset is as following:

Site          Nausea      headache        Abdominal Distension
1              17              5                   10
2              12              8                   7
.....


So each site has the total # adverse events for each type/category and have equal # patients per site, say 60. If I were to analyse the data for multiple outcomes per site, the number of events per category given the category response rates can be assumed to be independently distributed. They can be modeled by a multinomial distribution with parameters $n=60$ and category response rates $p_{i1}, \ldots , p_{iC}$.The variability in the vectors of response counts is often higher than can be accommodated by the multinomial distribution. Therefore, individual variation in category response rates can be modeled by a Dirichlet distribution.

Just wondering if I am thinking through this correctly. If so, could someone share some thoughts on how this could be done in R?

## 2 Answers

I'm trying to understand why this wouldn't just be addressed by a chi-square test for general independence ( with df=(r-1)*(c-1) ) using chisq.test in R. I do not see any complicating bits of extra information that need to be accounted for. I suppose you could test for a more restricted null if you just wanted to ask the question: are there systematic differences in the distribution of event proportions across the 60 sites. That would reduce the df to (60-1) which might improve power. I do not see an obvious advantage for introducing the Dirichlet distribution if you do not have an analysis platform in mind that takes that naturally as a starting point.

The more general approach might be to use a GLM model although this will require that you use the original data rather than the aggregated date you offered.:

row.by.col.mdl <- glm(counts ~ Site+Type, data=df, family="poisson")


The fact that you were going to use a Dirichlet distribution mean that there could not have been case where more than one adverse event was recorded per subject, right?

• Thanks for the advice. Let me try and restate the question I am trying to answer- Which model better estimates the random effect of sites on multiple binomial outcomes in clinical trial setting? If we used any of the fixed effects model we would be ignoring the fact that the site has a random effect, right? May 13, 2013 at 4:14
• Not to my understanding. If you model the sites as "random" you are essentially giving up on estimation of distribution of the site-results. At the very least you are saying that you really do not believe that the site-effect warrants any assumptions about the nature of its parent distribution. My understanding is that the fixed effects are what return useful estimates. I have raised the fact that this is (very) confusing terminology with persons more expert than I and have gotten general agreement.
– DWin
May 13, 2013 at 22:24

This is not multinomial data, however, since a given individual from a site may have more than 1 possible adverse event or none at all. That's problematic since AEs are often very highly correlated such as "aedema" and "injection site reaction". A multinomial model for outcomes is not appropriate here.

Secondly, clinical trials are extremely averse to using Bayesian modeling. My experience has been so, anyway. I don't understand why averaging frequencies across sites does not provide a sufficient summary of AE rates in your sample.