You can disable the stats service (Analog Stats, Awstats or Webalizer) for a specific user by doing the following:
1) Login to your server via ssh.
2) Edit /var/cpanel/users/username, and add any of the following, as needed:
skipanalog=1
skipawstats=1
skipwebalizer=1
3) Now we’ll restart the cPanel service:
/etc/init.d/cpanel restart