How can I create nonexistent subdirectories recursively using Bash?

I am creating a quick backup script that will dump some databases into a nice/neat directory structure and I realized that I need to test to make sure that the directories exist before I create them. The code I have works, but is there a better way to do it?

[ -d "$BACKUP_DIR" ] || mkdir "$BACKUP_DIR"
[ -d "$BACKUP_DIR/$client" ] || mkdir "$BACKUP_DIR/$client"
[ -d "$BACKUP_DIR/$client/$year" ] || mkdir "$BACKUP_DIR/$client/$year"
[ -d "$BACKUP_DIR/$client/$year/$month" ] || mkdir "$BACKUP_DIR/$client/$year/$month"
[ -d "$BACKUP_DIR/$client/$year/$month/$day" ] || mkdir "$BACKUP_DIR/$client/$year/$month/$day"

You can use the -p parameter, which is documented as:

-p, --parents

no error if existing, make parent directories as needed

So:

mkdir -p "$BACKUP_DIR/$client/$year/$month/$day"

mkdir -p "$BACKUP_DIR/$client/$year/$month/$day"