Logistic vs. linear regression for "inherently continous" variable - comparing probability This is a situation that arises commonly in my area (medicine).

*

*Suppose there is an inherently continuous variable $y$

*Suppose there is some normal range for this variable, say 80 - 120

*Suppose there is a dichotomous categorization of $y$ as "within normal limits", and "outside normal limits" that are commonly used

This sort of setting is exceptionally common.
Now, let's say you wanted to build a prediction model for the patient's categorical status of $y$:
$y_{status} = f(x_1, x_2, ..., x_k)$, where $x_i$ are various measures like age, body weight, smoking status, ...
The usual approach seems to be to use logistic regression. However, it seems you could also predict the blood pressure as a continuous variable, say using a Bayesian approach producing a posterior distirbution, then estimate how much of the posterior is within or beyond the normal limits.
The two approaches yield (at least slightly) different answers, in my experience. Also, I basically never see the latter (Bayesian) approach - which suggests to me there is something fundamentally wrong with this idea. However, I can't understand where the logic is incorrect.
Any guidance on this would be greatly appreciated.

Turning a continuous variable into a binary variable is almost always a bad idea. It has been termed dichotomization. Frank Harrell (@FrankHarrell)explains and gives some examples. Steven Senn gave it the name dichotomania: Dichotomania: an obsessive-compulsive disorder that is badly affecting the quality of analysis of pharmaceutical trials
Basically, the problem is that information is lost when you convert a continuous reading into a binary normal vs. not normal. Worse, it can encourage investigators to try different cutoffs for defining the two groups, and then only publish the results with the cutoff value that gives the results closest to what they were hoping for.
