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I have some patient data where I want to model (regress) the severity score of their condition. The scores are in a domain [0, 1], where 1 indicates a hard case.

If a person is sick I may assume a beta distribution (unimodal, some skewness). As my data also includes healthy patients (severity=0) that are yet undetected, the joint distribution over all patients can not be assumed to be beta distributed. There is an additional spike on 0.

I am therefore unclear what distribution I should choose for my model. Is a simple logistic regression faithful to the problem?

On a second thought this may also be described as a hierarchical model with a latent binomial that decides if a patient is healthy or not. If the patient is healthy the distribution over severity scores is a deterministic 0. If the patient is sick the distribution follows some beta I may infer. Is this a preferable approach?

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