From the allip example: Any wisdom-draining effects from creatures of madness instead deal a dice level higher, doubled.
Automatic wisdom drain effects that offer no SR or AC (these are few and far between) instead give an indefinite insanity (see the above disorder). These effects are rare, like the Aelfborn or Far Look [DragMag330p27].
Effects that give saves but are assumed to eventually cause the insanity spell instead force up to half of the DC in automatic sanity damage, with 1d2 to 1d6 to 2d6 to 1d10 to 3d6 to 2d10+1 to d% sanity loss upon failing the sanity check (compare Table: Sanity Loss from Creatures & the Severe Shocks table). The Far Realm [MotP212] is the basis for this. Since its about as bad as seeing Orcus or something.
Effects that force saves to avoid wisdom damage (that only hurt the sane) instead force sanity checks or take sanity damage up to the DC. See DragMag330p23's Cerebrotic Marrow, a type of corruption that gives only gives wisdom damage to the Sane who sleep within the effects of a blot/connection to the Far Realms.
Sleep Deprivation is another wisdom-damaging insanity effect that should instead deal sanity damage. As per Elder Evils page 9:
A living creature can go without sleep for a number of days equal to its Constitution modifier (minimum one). Thereafter it is fatigued, remaining in this state for a number of days equal to its Constitution modifier (again, minimum one); if it would become fatigued during that time, it is exhausted instead. Each day after that period, the creature takes 1 point of Wisdom damage. If the total Wisdom damage exceeds its Hit Dice, the creature is affected as if by an insanity spell.
This is quite a brutal and quick effect compared to sanity damage's more subtle and linear one, but they both end up in the same place. If using this sanity variant, it should deal 1d6 sanity damage each day after the first rather than the wisdom damage that has a HD threshold only after being exhausted. The fatigue and exhaustion make sense and should stay. Bonus fluff points is that if the reason a character is being sleep deprived is a choice, rather than an unwilling effect, then it is excluded from the maximum sanity damage per session cap. See the maelphalent [FF120] creature for a reason a PC would chose to sleep deprive herself, even when knowing the threat of insanity.