For the sake of completeness, I will now present a couple of Bass models I derived for the administrative prevalence of autism at the US level, based on data from the Department of Education, otherwise known as IDEA data. The following is a graph of the 6-17 IDEA prevalence along with Bass model hind-casting and forecasting all the way to 2030.
Model # 2 (the red line) is the one I prefer in this case. (I'll explain why shortly.) It predicts that prevalence will eventually level off at almost 1.1%. This is completely plausible, not only because that's roughly the new consensus prevalence of ASD, but also because Minnesota is already there.
I also find it to be a fascinating prediction of the model. If you recall, a Bass model predicts a maximum prevalence of about 0.65% (at most 0.7%) for children 6 to 9 in California DDS. This absolutely makes sense. California DDS is not like IDEA. DDS does not find every autistic person to be eligible for services, and not all developmentally disabled Californians pursue eligibility with DDS. So, in my view, a Bass model makes predictions that are remarkably consistent with our current reality.
If the models are correct, by 2013 IDEA prevalence should just have surpassed 80 in 10,000. Additionally, a leveling-off trend should not be completely evident yet. It may be slightly noticeable. Meanwhile, in the California report of Q4 2013 (and let's hope they produce data equivalent to that of reports currently available) a leveling-off trend should already be evident in the 6-9 cohort.
For formulas and variable names, see the California post. Parameters of both models are, again, estimated by means of genetic programming. For model # 1 I simply tried to fit the 1993-2007 prevalence series without any modifications. The resulting parameters were:
p = 4.808·10-8
q = 0.22
t0 = 1938.809 (year)
m = 118.32 (per 10,000 population)
Model # 2 is based on the observation that IDEA practically did not have an autism category prior to 1993. However, once the category was introduced, many children would've been put in the category all at once. It's like introducing a product into the market that already has a number of owners. So I performed the calculation by reducing the prevalence in all report years by 3.864, which is the 1993 prevalence. Hence, t0 should be equal to 1993. The parameters actually derived by the code I wrote were:
p = 0.0072
q = 0.222
t0 = 1993.03 (year)
m = 105.992 (per 10,000 population)
Note: In this case, model results must be added to 3.864 to obtain the projected prevalence.
The rationale of the derivation of Model # 2 makes sense to me, and that's why I prefer it. However, there's not a huge difference between the models.
I forgot to mention that the correlation coefficient R for both models was approximately the same: 0.99993. This is exceedingly good, and better than the fit for CalDDS.