Anyway, moving on to the evidence.......
Your claim was "Actually in cases of missing children in these circumstances, its more likely the parents are involved." So circumstances where the child may have been killed and/or abducted by force rather than where one parent wants the child to be with them over the other and takes them willingly.
US research shows that parents are significantly less likely to be involved in child homicides than the other two categories of stranger and friend/acquaintance.
http://www.atg.wa.gov/ChildAbductionResearch.aspx#.UmPeTRAUaSo
"In 74 percent of the missing children homicide cases studied, the child murder victim was female and the average age was 11 years old.
In 44 percent of the cases studied, the victims and killers were strangers, but in 42 percent of the cases, the victims and killers were friends or acquaintances.
Only about 14 percent of the cases studied involved parents or intimates killing the child."
From the UK (England & Wales) regarding abductions by force under the Child Abduction Act 1984 we see that stranger abductions are double parental ones.
http://www.ceop.police.uk/Documents/ceopdocs/Missing_scopingreport_2011.pdf
"In 2004, a Home Office study of 768 incidents that were recorded as child abductions, 56% (447) involved a stranger and 23% (183) involved a parental dispute."