No rhyme or reason. Usually as an individual's profile improves, and depending on any marketing efforts or promotions (varies on the card) and to provide additional revenue with a co-branded card, then that's typically when an upgrade offer typically generates.
There is no specific timeframe or score information (although most individuals received them with scores above the ~700 mark). Some get the invitation within a year, others around 12+ months and some after 2 years. .
Or, maybe their marketing group sits around and throws some darts and whichever name or account it lands, then there's your invite 
