Frustrated with a changing health care system that has resulted in longer workdays and less time with patients, a growing number of doctors in California and across the nation are turning to a new type of practice—concierge medicine. The model is simple: Doctors charge their patients an annual fee and in turn give them more time and attention. Rising costs and shrinking insurance reimbursements have prompted doctors to search for innovative ways to keep their solo practices afloat. Concierge medicine, practiced by more than 5,000 physicians nationwide, provides them with extra income and allows them to limit their patient rolls.