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Let's say I wanted to identify individuals who are taking an excessive amount of the blood clotting drug warfarin relative to their peers. To do this, I'm considering building a regression model that uses patient level data such as sex, age, and health status as factors and their actual drug dosage as the response. After model training, I'd apply the model to new data to generate predicted dosage values and compare those to the actual dosage. Patients who have an actual dosage higher than the predicted dosage would then be flagged as candidates for dose reduction.

Is this a reasonable plan? Essentially I'd be relying on the residuals to identify the patients who should be taking a reduced dosage.

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    $\begingroup$ So you don't know the dosage of all patients? I'm not sure how any physician would not know the actual warfarin dosage. Can you help us understand why you are trying to predict warfin dosage as opposed to simply reading it from the patient's chart? Can you help us understand how the dosages are missing? $\endgroup$
    – StatsStudent
    Commented Feb 21, 2019 at 15:11
  • $\begingroup$ We do know the dosage of all patients. - the goal is to determine when the patient is receiving a dosage higher than what is expected. $\endgroup$
    – T. Shiftlet
    Commented Feb 21, 2019 at 15:28
  • $\begingroup$ So why not simply take average dosages of patients with the same demographics? That would be the expected value. You could then flag any patients with a dosage greater than this amount. It seems like you might be trying to use more statistical machinery and complexity than needed here. $\endgroup$
    – StatsStudent
    Commented Feb 21, 2019 at 15:35
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    $\begingroup$ Warfarin pharmacokinetics are extremely complicated and doses are typically chosen by performing a clotting test such as INR, as doses are adjusted over time to get INR values into the correct range. Are you trying to model INR or warfarin levels? In any event, I trust that you are incorporating information about interacting drugs and dietary components that are known to be related to the clotting effect of administered warfarin. Omitting variables known to be related to INR or warfarin levels can be misleading or dangerous, even statistically. $\endgroup$
    – EdM
    Commented Feb 21, 2019 at 22:13
  • $\begingroup$ +1,Excellent point, @EdM. This just highlights the importance of asking good questions! $\endgroup$
    – StatsStudent
    Commented Feb 22, 2019 at 1:25

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I think you can go for one of these approaches:

  1. cluster your data based on the specified features and then you will be able to identify each group/cluster average, maximum, minimum, ....etc drug dosage. then you can judge any instance by how far it is from it`s cluster mean(far by n-Standard deviations) then decide that the instances that fall 3-sd(Standard deviations) are anomaly and need to be adjusted.

  2. Use Anomaly detection techniques which will help you detect different/extreme behavior in data.

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I think you are right: regression (linear or otherwise) may be the way to go. The only exception would be the case is which dosage is limited to a small amount of fixed values, in which case I would consider classification instead

But remember, you model will only be as good as your data, so make sure you have abundant high quality data for the fitting process.

Also, when flagging candidates for dose reduction, take into account the amount of the difference ("actual"-"expected") and how it compares to the standard deviation among your sample population.

I hope this helped!

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  • $\begingroup$ Thanks! In this case, the dosage can vary considerably and doesn't always fall into discrete amounts - and I have an abundant amount of data. $\endgroup$
    – T. Shiftlet
    Commented Feb 21, 2019 at 15:04

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