Snipped by me.
I have studied this, or maybe I should say topics tangential to this. I know more about this as it relates to child murderers and serial child murderers than offenders in general. All of this is MOO.
There is a link between substance abuse and violent offending that has been well-established by many studies. One issue is that many of these use self-reporting by inmates so there may be some bias (as they try to find excuses for their crimes) but it appears that many violent criminals (of all kinds) used alcohol or drugs the day that they committed the acts that landed them in custody. And it makes sense because, while studies have not found that people are "driven mad by drugs" and have no choice other than to offend, substance use does lower inhibitions and depress the decision making that leads to proper impulse control. So if you already had a compulsion to offend, by and large the use of substances is not going to help you resist that urge.
Speaking more specifically about those offenders who perpetrate the abduction and murder of children, I will tell you a little about their characteristics. This information comes from a huge study (over 800 cases) of child abduction killers. About one-fourth of people who abducted and killed a child were already on probation or parole for another offense on the day they committed their crime. A large proportion of child abduction killers had a history of prior violent offenses, particularly against children but often against adults as well. Most of these had previous crimes of sex assault or rape against children, but a large number had "regular" kidnap or assault charges with no history of sexual offenses as well.
About one-fourth of the child abduction killers studied have alcohol abuse problems. About one-fifth were judged to have serious drug-related problems. These child killers, as a group, were more likely to experience personal behavior problems than the "average" killer. One-third of them had previously exhibited sexual problems - ten times more likely to exhibit this than a non-child abduction killer. They were slightly more likely to be substance abusers or have diagnosed mental problems than a non-child abduction killer. Offenders who have crimes against children in series are more likely to have sexual, substance abuse, and mental problems than one-off killers of children.
In all respects, the person who abducts and kills a child is more like a serial killer of adults than any other type of criminal in their personal characteristics. Sexual motivation exists for the majority of child abduction/murder crimes.
I'm unaware of anything linking choice of MO to substance abuse but I will make two comments. A weapon is much less likely to be found as a piece of evidence in child abduction murders than other types of crimes. That's because child abduction killers more often kill by human physical agency (strangling, beating, etc.) than by a weapon. Not every case, obviously, but more often. Child abduction murderers are also more likely to use bindings as part of the fantasy of the crime than other types of killers (except serial killers of adults). In fact, use of bindings is the one statistically significant finding that can predict whether investigators are dealing with a serial offender or not. The majority of child abduction murderers use physical force or threats of force to attack their victims (over grooming).
Again, all MOO but for details on the statistics I quoted, again, they can be found here:
Child Abduction Murder Research | Washington State