Drained stats cannot be restored

In vanilla you can restore stat damage from stats affected by a drain effect, such as drain effects from normal spells and drinks/alcohol and diseases, but in OpenMW (0.46 and the nightlies) you can't (see the comments below for why), Corprus disease is seemingly the exception.

So to test with a disease as an example, open the console and click on the player character, then type any of these commands:

Common disease:

addspell "chills"

Blight disease:

addspell "ash woe blight"

A disease that affects skills:

addspell "crimson_plague"

You can try to restore both attributes and skills at an Imperial Cult Shrine.

(This description has been edited, see below for why)