Every day the scorecards went up, where they could be seen by all of the hospital’s emergency room doctors. Physicians hitting the target to admit at least half of the patients over 65 years old who entered the emergency department were color-coded green. The names of doctors who were close were yellow. Failing physicians were red. The scorecards, according to one whistle-blower lawsuit, were just one of the many ways that Health Management Associates, a for-profit hospital chain based in Naples, Fla., kept tabs on an internal strategy that regulators and others say was intended to increase admissions, regardless of...