I'm trying to model the risk of a binary event following surgery (event=admitted for observation, y/n), and my main predictor is a three-level 'treatment' administered during the procedure (Tx_A, Tx_B, Tx_A&B).
It's observational data, and I'd like to somehow account for something like "surgeon preference" (since surgeons differ both in their tendencies to admit patients and in their tendencies to administer certain treatments).
Sample: Apx. n=1,000 patients from ~10 different surgeons, with ~5% experiencing the event.
Question: What's the best way to account for surgeon preferences (or group patients by surgeon), aside from including indicators for each surgeon as main effects? Thank you!
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One way to proceed would be to code the surgeons as random effects in a mixed model rather than as fixed main effects.
The simplest inclusion of a random effect for surgeons would allow their intercepts to differ. In your case with a logistic regression for admission, this means that each surgeon has a different probability of admitting patients, all else equal. The single random effect captures the variability in that characteristic among the surgeons without treating them as fixed main effects. Insofar as the effects of the treatments themselves on admission probability don't depend on the surgeons (except for the surgeons' overall tendencies to admit) then that could be OK.
In principle you could have more complicated mixed models that allow for random slopes (the relationship of each treatment type to admission also depends on the surgeon), but I'm not sure that you have enough data to do that reliably. To avoid overfitting you typically need 10-20 events per predictor that you are evaluating. You're already at that limit with your 3 treatment types and a single random effect for surgeon admission probabilities, given that you have only 50 events.
The lme4 package in R provides this functionality.
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$\begingroup$ Isn't including surgeons as a fixed effect equivalent to adding a random intercept for surgeons? Obviously, the fixed effect is a much messier model with all the dummy variables but I've been wondering about this question. Anecdotally, all my models seem equivalent when specifying as dummy-variable fixed vs random intercept. $\endgroup$ Commented Oct 11, 2018 at 22:19
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2$\begingroup$ @AaronSpringer the fixed and random-effect models can produce similar results for other coefficients but they aren't equivalent. With fixed effects you use up one degree of freedom for each surgeon beyond the first, leading to potential overfitting with only 50 events. Using a random effect for surgeons' intercepts only adds one extra term to the model and is generally more efficient if the assumptions hold. $\endgroup$– EdMCommented Oct 11, 2018 at 22:47
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$\begingroup$ Thank you! Yes, I'm trying to avoid overfitting, but need to adjust for comorbidities as well, since patients getting Tx A tend to be overall less healthy individuals (e.g. more heart issues) and often can't receive Tx B due to contraindications. This seems to be a bigger confounder than surgeon whims, although it's hard to say with so few 'events' for each surgeon. Do you know of any resources that could help me code surgeons as a fixed effect in SAS?? I'm unfortunately not very good with R, and have not done much with fixed effects in SAS either... $\endgroup$– SgolenboCommented Oct 12, 2018 at 19:51
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