Reply #6: How is it that studies that compare dissimilar groups of people

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yet draw conclusions based on that comparison are valid?

Researchers draw conclusions from studying dissimilar groups all the time.

"As compared with the controls, the victims more often lived alone or rented their residence. Also, case households more commonly contained an illicit-drug user, a person with prior arrests, or someone who had been hit or hurt in a fight in the home. After controlling for these characteristics, we found that keeping a gun in the home was strongly and independently associated with an increased risk of homicide (adjusted odds ratio, 2.7; 95 percent confidence interval, 1.6 to 4.4). Virtually all of this risk involved homicide by a family member or intimate acquaintance."

Why is it that no other researcher outside of a small circle of academics have reproduce any of the studies?

It might have something to do with the fact that conducting a study of this magnitude requires a lot of funding, and: "Kellermann’s findings have been linked to the June, 1996 Republican-led decision of the U.S. House Appropriations Committee to strip US$2.6 million from the budget of the National Center for Injury Prevention and Control at the U.S. Centers for Disease Control – the exact amount previously set aside for NCIPC/CDC research into the causes and effects of firearm-related death and injury."

Wayne LaPierre and the NRA successfully used money and intimidation to stifle any research which might portray (even if accurately) risks associated with handgun ownership. Do you want to tell the truth or have a career?

Why is it that when these same researchers repeat a study, they can't find the same level of 'risk'?

You're in the wrong venue; you should be working in a laboratory. No consecutive studies in public health ever show the same levels of risk and they don't attempt to. The point is to draw broad conclusions from many smaller independent ones, and Kellerman's 1993 study was a decisive confirmation of the 1986 one:

"These results confirmed the 1986 finding that, in the net, a firearm in the home represents a greater risk overall than the protection it may offer against intruders, either indirectly or by discouraging potential assaults. Kellermann noted that the study demonstrates the pervasiveness of domestic assault, as compared to better publicized crimes such as home invasion, but continued to stress the role of handguns in increasing the lethality of such assaults."

http://en.wikipedia.org/wiki/Arthur_Kellermann

Regarding the NRA and their manic attempt to quash anti-gun research: "The final appropriation language included the following statement: “none of the funds made available for injury control at the Centers for Disease Control and Prevention may be used to advocate or promote gun control”. These words appear in every CDC grant announcement to this day." A question for you: if handgun ownership was so safe, why wouldn't the NRA welcome a study which vindicates it?