Can we get to the bottom of canine anal gland impaction?

Has anyone researched this topic? I am constantly taking all three of my small dogs to the vet to have their anal glands expressed. I didn't have this problem until I adopted a cat and noticed the dogs eating out of the cat litter box. Problem:  Anal sac disease is very common in dogs. The sacs frequently become impacted (plugged) usually due to inflammation of the ducts. The secretion within the impacted sacs will thicken and the sacs will become swollen and distended. It is then painful for your dog to pass feces. Point to consider: Dr. Brittany Cartlidge, AtlasVet DC, stated in a Washingtonian article dated February 11, 2015, "Theoretically, a dog could also get sick if they ate a large amount of cat litter since it absorbs moisture and could cause constipation or an obstruction".  Hypothesis: Dogs who eat cat feces mixed with cat litter are more prone to anal gland impactions. It seems reasonable to assume that a dog's anal gland may be particularly sensitive to the passage of some or all cat litters. The active ingredients in clumping litters may make things worse. Validating Hypothesis: Survey one hundred pet owners who have both dogs and cats vs one hundred exclusive dog owners, a possible answer might be found.