"It is more important for me to be here with my family," said Clarke. "(There) are more important issues to be dealt with at the moment than swinging a golf club."
Clarke's wife, Heather, checked into a hospital last month during the BMW Championship and her husband has not competed since.
Clarke, ranked No. 15 in the world, is being replaced in the 156-player field by Conrad Ray, who is the golf coach at Stanford University and finished as the first alternate at this week's sectional qualifying event at Tarzana, Calif.
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