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I'm working on a project where the objective is to determine whether there are factors that distinguish an emergency department (ED) encounter from a high-frequency patient (8 or more encounters per year) from all other encounters. My data is at the ED encounter level and contains data that is both specific to the encounter, which can vary at every encounter, and data specific to the patient, which usually does not vary with the encounter. Naturally, since some patients are high frequency patients, the data is imbalanced; some patients have more rows of data than others. Out of 40,000 encounters from a single year, the highest frequency user has 80 rows.

I've read a few papers on the subject and based on what I've seen, my initial thought is to use a simple logistic regression, where the binary outcome variable is whether any given ED encounter was from a high frequency patient. I feel as though I should be worried about patient-level data from high frequency patients biasing the coefficients because they are over-represented in the data in terms of rows per patient. On the other hand these are the patients I want to know about so is this really a valid concern? I've also thought about a mixed model, with a random intercept for each patient, but this won't work because the outcome doesn't vary within patients. They're either high frequency or not.

A few other notes:

  • I'm not terribly interested in modeling the number of encounters.
  • The goal of the model is to explain, more than to predict, and model coefficients should not be difficult to communicate to a lay audience with simple conversion (such as log odds to odds).
  • I'm working in R

What's the best modeling approach here? Are my concerns about bias valid?

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  • $\begingroup$ In the mixed model surely the outcome is not the patient status but the characteristic of that encounter? $\endgroup$
    – mdewey
    Commented Oct 16, 2022 at 15:39
  • $\begingroup$ The outcome is whether the encounter was from a high-frequency patient. I've ruled out mixed model with patient random intercepts due to zero variation in the outcome within a patient. $\endgroup$
    – Dan
    Commented Oct 16, 2022 at 20:33
  • $\begingroup$ The first sentence in your question seems to me to clearly state that your scientific question is about encounters. $\endgroup$
    – mdewey
    Commented Oct 17, 2022 at 9:09

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I think your approach is appropriate. A logistic model predicting high freq. vs non-high is probably the best option. You'll have easily interpretable results. I'd like to know if the data of an individual changes much over the 80 encounters/year? if not, then collapsing and individual to a single row with 1 or 0 for high or non-high seems right. If the data changes, e.g. there's a different weight per visit, you might wanna rethink the method.

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    $\begingroup$ patient-level data such as age, sex, residency doesn't change frequently, but details about the encounter, such as time of day, diagnosis, and method of arrival can certainly change within the same patient, so I wouldn't want to collapse to the patient level and lose that information. $\endgroup$
    – Dan
    Commented Oct 16, 2022 at 20:31
  • $\begingroup$ @Dan. So now comes the tricky part. If I understand you correctly, some factors don't change in a year (age, sex) but others (blood pressure) will change and this change is a key part of your study. Is there a way of capturing these variables (blood pressure, heart rate) as changes over a year (Xt - Xt-1) ? If you can get each patient to have only one observation in your dataset, your problems are solved. If this reduction is not possible, you'll have to look at a panel model. $\endgroup$
    – ATee
    Commented Oct 17, 2022 at 13:14
  • $\begingroup$ unfortunately an annual change variable won't work because most of the encounter level variables are categorical (method of arrival, presence/absence of particular diagnosis, nursing shift). I've seen one study attempt to get this information aggregated to patient level by reducing the categorical data to dummy variables and then calculating % of encounters...but I'm interested in what kind of panel model you have in mind. Some patients will have just a single obs, others will have >20. $\endgroup$
    – Dan
    Commented Oct 17, 2022 at 14:31

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