the best way that those sleepers can be fastened will assure you the best deck.
I would go to all extremes to ensure that they are there for good. I would use the tapcon method if you like that and even cover the bottom part of the sleeper with liquid nails for concrete. To keep the sleepers from cracking with all the tapcom's you might want to use 2x6's instead.
Also, drainage. I would imagine that the patio does drain or fall in one direction. I would definately NOT lay my sleepers perpendicular to the fall or water run off. I would imagine that the fall of the patio is away from the house, so I would run the sleepers perpendicular to the house.