Order, Supreme Court, New York County (Joan B. Lobis, J.), entered May 16, 2013, which denied plaintiffs’ motion for leave to amend the pleadings to add a new party defendant and to file an amended summons and second amended complaint after the statute of limitations had run, unanimously affirmed, without costs.

In this medical malpractice action, plaintiffs allege that the defendant doctors, employed by or affiliated with defendant New York-Presbyterian Hospital, were negligent in performing a laparoscopic cholecystectomy procedure and providing aftercare. After the statute of limitations had run, plaintiffs sought leave to amend the complaint to add a claim against another physician, a surgeon affiliated with the hospital, who made two notes in the injured plaintiffs medical chart after she underwent the procedure.

While leave to amend the pleadings is ordinarily freely given (CPLR 3025 [b]), the court providently exercised its discretion in denying plaintiffs leave to amend for a second time to add a new party defendant, since the proposed amended pleading clearly lacks merit (see Eighth Ave. Garage Corp. v H.K.L. Realty Corp., 60 AD3d 404, 405 [1st Dept 2009], lv dismissed 12 NY3d 880 [2009]). Since the statute of limitations has run as to the proposed medical malpractice claim against the proposed additional defendant, plaintiffs bore the burden of demonstrating the applicability of the relation-back doctrine (Cintron v Lynn, 306 AD2d 118, 119-120 [1st Dept 2003]; CPLR 203 [c]).

Plaintiffs argue that the hospital may be vicariously liable for treatment negligently rendered by the proposed defendant, even[*616] if he was not an employee of the hospital, because the injured plaintiff sought “treatment from the hospital, not from a particular physician” (Shafran v St. Vincent’s Hosp. & Med. Ctr., 264 AD2d 553, 558 [1st Dept 1999]). However, that rationale for imposition of vicarious liability against the hospital is an insufficient basis for finding that the proposed defendant is so “united in interest” with the hospital that he can be charged with notice of the commencement of the action for purposes of the relation-back doctrine (Anderson v Montefiore Med. Ctr., 41 AD3d 105, 107-108 [1st Dept 2007]). Even if the proposed additional defendant could be charged with such notice, plaintiffs failed to provide any basis for finding that the proposed defendant “knew or should have known” that the action would have been brought against him too, but for a mistake by the plaintiffs as to the identity of the proper parties (see Soto v Bronx-Lebanon Hosp. Ctr., 93 AD3d 481 [1st Dept 2012]; Alvarado v Beth Israel Med. Ctr., 60 AD3d 981 [2d Dept 2009]; Cintron v Lynn, 306 AD2d at 119-120). To the contrary, under the circumstances, when plaintiffs first moved to add two other physicians as party defendants, and then allowed the statute to elapse without bringing suit against him, he could have concluded that there was no intent to sue him “at all ‘and that the matter has been laid to rest as far as he is concerned’ ” (Buran v Coupal, 87 NY2d 173, 181 [1995]). Concur — Tom, J.E, Friedman, Saxe, Richter and Clark, JJ.