In a nutshell...
There's loads of information arguing for both sides, as well as anecdotal stories in support of both sides - Some people argue that the MMR vaccine directly causes autism. While some say that it is the combination of having so many things vaccinated at the same time that causes the child harm (disproved here). There are anecdotes of children hitting their developmental milestones and then suddenly deteriorate after receiving the MMR. There are also others who say they noticed the signs of autism in their children from before they were vaccinated, and some anti-vac turned pro-vac folks who had to deal with their children falling seriously ill from measles.
How did this concern come about?
In 1998, a study was published in British medical journal The Lancet connecting the MMR vaccine with autism. It was based on a sample size of 12 children. This study was eventually discredited and the researcher has been struck off as a doctor. There have been other studies that have been done that have been referred to as indicating a correlation between the MMR/measles virus and autism.
On the other hand...
Studies have also been done and cited to disprove a correlation. And studies that compared the stats of autism levels before and after the introduction of the MMR vaccine do not show any correlation either. Other studies show that there are subtle signs of autism noticeable from before the child turns 1. They also point to the fact that the timing of giving the MMR coincides with the usual onset of symptoms of autism.
My take on the issue
I think the current research has not proven a causal link between the vaccine and autism, and I don't think the vaccine causes autism. But the study done by Singh seems to suggest that there are genetic differences between those diagnosed with autism and those without, and maybe it is possible that the MMR vaccine accelerates the symptoms of autism, but not cause it.
From personal experience, we vaccinated Josiah & Joanie according to schedule and both are fine. And we will do the same for Joash as well. The only issue we had was this strange chicken pox mixed with measles rash that Josiah had after he took the MMR + Chicken Pox vaccination (Chicken Pox is optional). So when it came to Joanie's turn, we opted not to combine the chicken pox shot with the MMR.
Don't forget to get the chicken pox vaccine separately though. We had a bit of a scare when I had shingles in late 2012 as Joanie hadn't received her chicken pox vaccine yet. And at just 2 yrs old, it would have been tough keeping her from scratching and scarring herself...:/ Needless to say, we vaccinated her once we were sure she wasn't infected by me.
a mix between chicken pox and measles after the mmrv.
What is compulsory in Singapore?
In accordance with the fourth schedule of the Infectious Diseases Act in Singapore, a child is to be vaccinated against Diphtheria and Measles. These are compulsory by law.
But if we look at the back of our kids' health booklets, we'll notice that the National Childhood Immunisation Programme includes a lot more than that. Check out the immunisation chart based on age here.
If you want to check your child's immunisation records, you can check www.nir.hpb.gov.sg (login via Singpass)
If you're interested to read up more on this subject, check out these links (or just google)