You should scour the Compose file docs.
Most docker run commands have a compose equivalent, and they should all be listed there.
The background flag -d goes after run or up.
The tty flag -t and interactive flag -i are not required as docker-compose run does this by default. You can add tty to individual containers in the compose file with -t, but you cannot use interactive mode since you may start multiple containers at once and you can’t interact with them all.
In regard to your situation the command you’re using should be working. If you add -d after the run command it will run in the background. But I recommend using up instead of run, as it will simply start all containers in the file rather than you having to specify hdinsight.