I have a data set of N=200 comprised of patients who either received Treatment A (N=50) or Treatment B (N=150). I have treatment toxicity outcomes (binary yes or no) across 4 domains: hematologic, skin, gastrointestinal (GI), or urinary. Patients could have had anywhere from 0 to 4 of the toxicities.

My outcome of interest is # of acute toxicity domains experienced by the patient. So this would be a "count" variable that can take on a value of 0, 1, 2, 3, or 4.

Objective: Determine if Treatment A is associated with fewer acute toxicities compared to Treatment B.

What regression model would you recommend using? I was thinking Poisson regression with robust errors since the dependent variable is a count variable, but I wasn't sure if it would be biased because by definition patients cannot have more than 4 toxicities.

This was the SAS code I was thinking of using:

proc genmod data = my_data;
class treatment id_code /param=glm;
model total_acute_toxicities = treatment confounder_1 confounder_2 /dist=poisson;
repeated subject=id_code; 

Thank you for your advice!

  • 1
    $\begingroup$ I think there could be better approaches. The poisson likelihood is supported on the positive integers, which means your model could predict that patients are likely to get more than 4 comorbidities (e.g. a confidence interval could include numbers larger than 4). I say go for it, but just check that your model gives sane results across all important aspects. $\endgroup$ – Demetri Pananos Dec 27 '19 at 23:35
  • $\begingroup$ Thanks for your comment. My goal with the regression is to determine if Treatment A is associated with fewer total toxicities than Treatment B, rather than to predict the number of toxicities. From a predictive standpoint the model would not make sense because as you said, it could predict for more than 4 toxicities (the maximum). But I'm not sure that it matters for my objective. Regardless, the results of the regression do fit with what I'd expect based on subject matter knowledge and other analyses (contingency tables, logistic regression looking at any toxicity yes/no). $\endgroup$ – JJM Dec 28 '19 at 17:31

Use ordinal logistic regression. This method will preserve the rank ordering of toxicity counts and the maximum of 4 toxicities. The coefficients can be interpreted as the likelihood of increasing (or decreasing) number of toxicities.


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