Doctors who charge an annual fee to patients in exchange for customized care including house calls are drawing the ire of some health insurance companies, reports the Houston Chronicle.

United Healthcare confirmed it is dropping four local doctors from its network in April because the company disapproves of their so-called "concierge medicine" model. Cigna is also condemning the practice, in which physicians charge an annual retainer of $1,500 to $1,800 for patients who then receive more personal care.

While some medical specialists have chosen to stop dealing with insurance companies entirely, others are trying to couple concierge care with insurance payments. United and Cigna say that's improper. Other major health insurers, including Aetna, Humana and Blue Cross Blue Shield of Texas, consider concierge care just fine so long as patients are clearly informed that the insurers will not reimburse any of the retainer. The Washington Post also writes about the trend toward concierge medicine and notes that more than 1,000 doctors have switched to this mode of practice.