The missing dogs are actresses
Many of the important women characters in the movie are associated in some way to acting, dogs, or vampires. Not vampire monsters like in fiction movies, but they have a lot of vampire references and symbolism associated with them. Many of these women are all three. The movie has a lot of odd symbolisms throughout. Dogs, vampires, and acting are the symbols used to portray a specific group of women in this story. Included in this set of women are Sarah, Troy, the Rising Stars, and the 'actress' character in the beginning of the movie.
These women will be referenced as 'ADVW' for 'actress dog vampire women'.
The primary motivation of the ADVW this seems to be money. The primary indication of this is is the scene where Sarah is eating Sevence after eating her dog. What other reason is there to portray Sarah as eating Sevence other than to say Sarah's motivation is to consume Sevence? If the dream were about Sam killing Sarah, the dream would have been about Sam killing Sarah and not Sarah eating Sevence and her dog. The ADVW do acting because of the money associated with acting, when they're not acting they're doing something else to get money including prostitution such as the Rising Stars, they associate with various social groups because of money including the Songwriter social groups, the 'ascension' entombment thing is about money, the vampire song has some lines about money in it, the movie that Sarah and Sam watch at the start is about money, etc. There are only three other major women characters in the movie who are not like this and who are also are not associated with dogs, vampires, or acting: The Bird Lady, the Owl Woman, and Millicent. The Songwriter, who is associated with the actresses and the musicians in the movie and is sort of the final boss of the movie, is another character motivated by money who is 'trying to make a living'.
Sam's motivations are unclear because the movie starts somewhere after the missing dogs 'rash' has begun. The other reason Sam's motivations are unclear is that the Dog Killer story is about a man upset at a dog because of his acting career, but Sam makes no indication he's into acting at all the entire movie or that he has abandoned an acting career or something like this. Another indication that puts Sam's motivations into question is that some people in the movie die while Sam is off doing something else, implying that 'The Dog Killer' is more than one person.
Dog Reasons
Both times dog biscuits are mentioned, a group of one man and three women are 'entombed'. Sarah's group and Troy's group.
The dog biscuits are about money for these ADVW. Biscuits are made of dough, another word for money. Biscuits are also often used to get dogs to do something, and throughout the movie the ADVW are shown being taken advantage of in their pursuit of money. Money for dogs.
Every character that barks in the movie is either one of these women or is associated with them.
Millicent says 'anybody who would kill a dog wouldn't think twice about killing a person' to which Sam replies 'not sure that's true' which could mean a lot of things but I think he means that he doesn't see the dog women as people but as dogs, or vampires.
After Sam meets Sarah and passes out at his apartment with the gum on his hand, he wakes up to a movie playing which details what happens to dogs after their owner doesn't show up for a while. This is in reference to how Sarah, a dog woman, is dead or will die at some point in the future its not really clear if she's already dead.
The Comic Man says 'there's been this rash of lost and found signs for dogs, humans, musical instruments' but there is no detail about any musical instruments that are missing or humans that are missing in the movie only dogs. And what is the supposed motivation of Sam? Finding missing Sarah.
The missing dog signs have some odd details that don't make sense and really sound more like human details, such as a missing dog poster that says '15 years old', or a dog named 'cookie' which has a definition of 'attractive woman' or 'person', or a dog named 'spade' which is derogatory word for black person.
The women who 'ascend' go missing, just like the dogs.
Sam is never indicated in any way harming dogs the entire movie. Dogs do not show hostility towards Sam either, but the women who act like dogs do show hostility towards Sam.
The same street intersection where Sam spots Troy getting into a car is the same street intersection that Sam spots an actress audition and street grafitti on another nearby street intersection of 'Beware the Dog Killer'. The actresses comment about the sulfur smell that Sam has.
There are pretty significant similarities between Sam and The Dog Killer, but there is no direct connections between them. Which implies the Dog Killer story is told in the movie for some other reason than literal dogs.
Vampire Reasons
Dogs are also known as canines. The characteristic physical trait of vampires is large canines.
There is a 'Vamp' sign in the first scene of the movie behind the 'Beware the Dog Killer' grafitti.
There is some woman talking about vampires at the Purgatory party.The Jesus and The Brides of Dracula band. This group is introduced at the start of the movie along with the Dog Killer grafitti. Throughout the movie there are many other groups of three women, including many who are dog women.
Sam wears a 'Zola la Vampira' shirt when he encounters the Homeless King.
There is a dracula poster in Sam's apartment.
The lake where Sam acquires the mcguffin to bring down the final vampire group in the movie is called 'Silver Lake'.
The song 'Turning Teeth' has many components which sound like vampires. The first line says it all IMO, 'turning like teeth' or transforming someone's teeth into vampire canines similar to the vampire that bites that person.
Both Sarah and Troy, who are depicted with the dog references, also have scenes with the Turning Teeth song in it.
There are various things which connect the vampire women throughout the story, but the primary one is that they are in groups of three throughout the movie.
Many of the women which have the vampirism characterization make some kind of comment or indication that they smell something bad when they're around Sam. Sam is shown in the movie to have been hit with skunk spray, and it is implied that this is the smell the women are talking about. Skunk spray smells like sulfer. Garlic, which also has a strong scent that lingers and is detailed in various stories to repel vampires, also smells like sulfer. Both the 'actress' at the start of the movie and Sarah make an indication they smell something bad around Sam before Sam is hit with Skunk spray. Sam's smell many times causes these people who comment about the smell to leave, similar to garlic repelling a vampire.
Dog Women Are Vampires
There are many groups of three women throughout the movie. The first group of three women the movie states is the Brides of Dracula music group. Women associated with dogs in the movie belong to some group of three women.
Actress Women Are Vampires
The smell is about sulfer. The actresses throughout the movie smell the sulfur. The only person who isnt an actress that smelled the sulfer was the homeless king.
Dog Women Are Actresses
Sarah's death involved dog biscuits. Troy's death involved dog biscuits. Sam was associated with both deaths, who is also associated with The Dog Killer.
Conclusion
The actresses who are dog women and are also portrayed as vampires are part of some group that Sam and the people associated with him cause to go 'missing'. Some of the women who have only one or two of the three characteristics of the ADVW do not go missing such as the Rising Stars. The reason for this happening isn't detailed from what I can tell and the movie starts when this has been happening for some time, about two years I think.