No.
In Massachusetts, any statements, writings, or benevolent gestures relating to the suffering of patients involved in an unexpected outcome are inadmissible as evidence of liability. Even so, some types of apologies are better than others. An apology that includes such words as I am so sorry that my treatment caused you harm is inappropriate.
A sincere expression of regret following a poor outcome or upsetting experience, such as I am sorry this happened coupled with a discussion about future treatment options can demonstrate an empathetic and caring attitude. Apologies can help to mitigate any anger the patient may feel, and communicate that you will work with the patient to improve the outcome.