Four Massachusetts men pleaded guilty yesterday in connection with their participation in a fraudulent scheme carried out through a Massachusetts health insurance company known as HMA Direct.

William O’Brien of West Barnstable pleaded guilty to conspiracy, wire fraud, health care fraud and obtaining customer information from a financial institution by false representation. Mark Celentano of Ipswich pleaded guilty to conspiracy, health care fraud and obstruction of justice. Francis Gaetani, and Ronald Anger, both of Sutton, each pleaded guilty to wire fraud.

HMA Direct offered self-funded insurance plans to small businesses in New England. At the heart of HMA Direct’s business was "carving out" from its clients’ self-funded plans those employees who had significant health risks, and then, through false statements, arranging for those employees to be insured through traditional health insurance providers.

O’Brien and Celentano participated in the carve-out scheme and subsequent lies to health insurance providers. O’Brien also arranged for Gaetani and Anger, who were investors in HMA Direct, to pretend that they were satisfied customers of the company and to provide fake references to prospective clients. In addition, when contacted by federal investigators, Celentano obstructed justice by lying about the role he had played in the HMA Direct carve-out scheme.

For O’Brien, Gaetani and Anger, the maximum sentence under the relevant statutes is 20 years in prison, three years of supervised release and a $250,000 fine. For Celentano, the maximum sentence under the statute is 10 years in prison, three years of supervised release and a $250,000 fine. Sentencing is scheduled for Jan. 14, 2015.

Two other defendants in the scheme, Michael Cassandro of Middleton R.I. and Shelley Lenkutis of Waltham, previously pleaded guilty to related charges. They are scheduled to be sentenced on Dec. 10.