Critics have argued that the doctors have a financial incentive in sending patients to their own facilities, even when those patients might be better off having their surgery in regular hospitals.

But the Texas case, and others like it, have invited new scrutiny from regulators and members of Congress about these hospitals’ ability to care for patients who suffer complications after their operations.

While some of these hospitals are large sophisticated operations, like those hospitals specializing in cardiac care, others are much more modest. For example, small surgical hospitals may not have separate emergency facilities or, as in the Texas case, a doctor on site at all times during a patient’s recovery.

A similar case involved an 88-year-old woman two years ago at a small doctor-owned hospital in Portland, Ore., where the nurses called 911 after she was given too much pain medicine following spine surgery. She, too, later died.

As the number of doctor-owned surgical hospitals grows, federal and state officials now acknowledge that the government rules may be too vague about the emergency abilities a hospital must have in place. Regulators are particularly concerned about the very small hospitals that focus on only a few kinds of surgery but perform operations that frequently require an overnight stay. While Medicare’s rules currently say a hospital must “meet the emergency needs of patients in accordance with acceptable standards of practice,” the details are left largely to the hospital’s discretion. Federal and state officials say they are now reviewing the guidelines to toughen the rules and make them more specific.