High prices and stiff competition mean investors must think creatively. : LAST month KKR, a private-equity firm, announced that it would buy Envision Healthcare, one of America’s largest providers of doctors to hospitals. The deal was valued at $9.9bn, including debt. If shareholders agree to the sale, it will be the largest in a string of health-care investments by KKR, including an ambulance service, a company that helps treat children with autism and a maker of medical devices. “Ten years ago only a few private-equity houses had dedicated health-care teams,” says Dmitry Podpolny of McKinsey, a consultancy.