Is a parent compelled by Halacha to vaccinate her child if it can be statistically proven that, without the vaccine, the likelihood of the child contracting the disease that he is being vaccinated for is still very minimal (mi'ut shaino matzuy)?
R. Ya'akov Emden (מור וקציעה או"ח ס' שכח) suggests that one can only force someone to take medication when there is no counterclaim from the patient or another physician. However, if the patient or the physician feel that the medication, will not work, we can't force him. Furthermore, if he claims that he doesn't want to take the medication because it will cause him more harm than good, we cannot force him to take the medication. However, this only applies to medicines that are taken for internal conditions and the medicine is only based on estimates. Medicines that are taken for external conditions, where the data is readily available, is considered a certainty and one may not oppose the opinion of the physician.
Rabbi Joshua Flug reasons that R' Emden might agree that nowadays, many medicines for internal conditions are also treated like the external because we have means of knowing their effectiveness and it is not based on estimates. He further reasons that unless a vaccine can be proven safe, it cannot be given against the patients will, as the patient can claim he is refusing out of fear that it will harm him.
Since those who wish not to take vaccines frequently say they believe it to be unsafe to take them, and may even have other physicians (even if these are fringe physicians) supporting them, it seems they cannot be forced.