Hello and thank you for entrusting me to assist you. I can certainly understand your frustration with being accused of something you didn't do. There are times when the best defense is an offense, but to be honest with you this isn't one of them. It is not a crime to accuse someone of something that they didn't do. If the accuser makes the accusation in good faith, it probably isn't actionable in civil court, either. Even if this did give rise to a potential claim for defamation, you would have an affirmative duty to prove that the allegation was false. This will tend to draw a lot of attention to the allegation--far more than would have been the case if you didn't sue. Moreover, a lawsuit for defamation against the patient would not protect you from any adverse employment action by your employer nor would it compel your employer to remove any reference to this incident from your work record. So, from an offensive standpoint, there really isn't anything effective that you can do.
Typically, the best course of action in these circumstances is to adamantly express your innocence and indicate your intent to cooperate fully and completely with any investigation. If this elderly person is senile or potentially prone to lying, that might be something you want to mention to your employer, as well. Basically, you can't do much to make the situation better, but you can do many things to make the situation worse.
I hope that you find this information helpful and am genuinely sorry if it is not what you were hoping to hear. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
If you do not require any further assistance, please be so kind as to provide a positive rating of my service so that I may receive credit for assisting you. Very best wishes moving forward.