we did the double whammy of:
running a home programme, and keeping data (this was when dd1 was about 3, so it was on easy-to-test stuff like numbers/letters recognition; increasing vocab etc - standard pre-school stuff, to prove she was actually able to learn)
then we put her into LA approved (and ultimately paid for) ASD pre school provision. where she floundered, and failed. after a year there, they could not demonstrate that she knew the stuff we had taught her the preceding year, let alone anythign new.
then back into ABA, and the obvious leap forward was striking, and could not be argued against.
this was all on concrete things, rather than the more difficult to track (not impossible, but certainly more subjective) emotions/anxiety etc - dd1 absolutely had sensory issues and a LOT of anxiety, but we concentrated on things we could absolutely prove, and that the LA (and their provision) could not demonstrate at all.
interestingly, the ABA structure - with tiny steps, and errorless learning (an approach that has always been essential for dd1 as her confidence is so low) went a long way to reducing her anxiety without any specific targetting of it - once dd1 was more comfortable ,it reduced of it's own accord.
once she was secure in her first ABA school, we added in the desensitisation programmes for a couple fo things that were really making life difficult, like the animal phobia, and also a water issue she had.
her current (ABA) school are now working furhter on the water/fluids issue, and desensitising her to the feel of eg liquids on her lips (she cannot drink from a cup becuase she cannot bear anything on her lips at all - she would rather stop drinking, and has done so in the past)
thw whole premise is to find her comfort zone (wherever that may be - eg when she first went riding, she would not get out of the car. this was fine, and taken as the place she was to work from, iyswim) and then add in steps in tiny little stages - taking her to the edge of her comfort zone, but never far enough to tip her into panic. a little discomfort (and I really, really mean tiny little bit) is good, as it means she is having to deal with it, and can begin to tease out her emotions, and talk it thorugh etc. so in the riding example, the first goal was to get her able to go in the car to the stables, and sit happily, without being worried about anything. once achieved, they went ot the stables, stayed in the car ad opened the window a bit, so she could hear and smell etc.
then the door open.
then the door open and her tutor got out and came to stand by her, chatting.
then the door open and chatting to one of the RDA people.
all the while watching the horses from afar, talking about them etc.
then the slow process of getting her out of the car - slowly, slowly, no expectation of even going near the horses. the whole target and expectation at that point was the next tiny little step. even if she achieved the next step really easily, there was no 'oh, brilliant, let's rush throught he next bit too' - jsut lots of praise for work well done, and then back to school.
it did take months (with one weekly visit), but it was all done at her pace, and she was taught (by going through the process, rather than explicitly) how to self-calm when she was gettign a little bit uncomfortable. because she was secure in the knowledge that it would nver get too uncomfortable, as she trusted ehr tutors implicitly. and so she knew she would never be aske dot do somethign she couldn't deal with, iyswim.