I see that sometimes, more so in the games you're losing, your death count is not too hot. Now sometimes this is just cause you are, say, Syndra mid and the enemy has fed Yasuo and Malphite and there's just no chance. But I think perfecting positioning could be something to work on (I need to as well). Especially with a champ like Anivia, your #1 goal is to not die. You have one of the best kits for stalling, catching, and controlling teamfights. If you die, it'll take longer to get to that point (Anivia needs bank), and can't contribute as much as your kit offers.
I'm guilty of bad positioning sometimes as well. But with Anivia it's so crucial as she's very immobile. Don't take dangerous shortcuts, make sure (unless very confident and fed), that you have protection when roaming around (especially with assassins making a strong comeback - yay -_- ).
Hopefully, this helps. Just remember, from a fellow Anivia main and lover: farm, don't die, and stay safe. Your kit will take it from there :) And feel free to add me and queue up with me if you want. You have an attitude I would definitely want to have on a team I'm playing on.