The number needed not to treat to harm (NNNTTTH) is the number of patients whom you have to not treat with something beneficial in order to cause one harm from your omission. It is numerically equivalent to the number needed to treat (NNT), but it reframes the decision from action to omission and from benefit to harm. Ignoring bleeding altogether (because making relative utilities for bleeding and stroke is a fraught endeavor), you could ask yourself "how many patients can I withhold stroke prophylaxis from for one year before I statistically cause (or allow to happen, if you are prone to omission bias) a stroke?" For most patients, withholding stroke prophylaxis has a NNNTTTH of about 25-30 per year (check the corresponding NNT from CHADS2 for a more "precise" estimate). Reframing the question into "how much am I asking the patient to pay, in terms of statistical likelihood of stroke, to avoid anticoagulation and the particular side effects that cause me concern in his case?" can often provide some reassurance for the clinician and the patient alike.
Twice recently I have used the NNNTTTH heuristic to reassure patients who could not afford or no longer wanted to take Advair. Using data from the TORCH trial (which admittedly oversimplifies the issue), and assuming P=0.052~=0.049 and there is a statistically significant survival benefit, I can tell the patients that the NNNTTTH is 38 for mortality with Advair. According to some interpretations of NNT (that I don't necessarily agree with but my reservations don't preclude its use for estimation), this means that I can fail to treat 37 patients with Advair before one has a premature death. Or as I stated to my patient "if I give 38 patients Advair, 37 of them receive no benefit and one does." My patient, who has less than a year to live and who called me to complain of the high cost of Advair and to inquire about alternatives, was incredulous: "Then why have I been paying $400 a month for it? Why have they been telling me to take it?" he queried.
The answer is that dichotomizing medical decisions into "works" and "doesn't work" without regard to how much it works or how much it costs is not good shared decision making. Ignoring size of effect makes it impossible to balance risks and benefits for good medical decision making in individual cases.
It is good policy, as a general rule, to give all patients therapies which, on the population level will maximize outcomes (the therapeutic paradox and the related prevention paradox notwithstanding). But when side effects, costs, complexity, or limited lifespan enter the fray, reframing the calculus to the NNNTTTH heuristic and asking yourself how many times you can not give something and get away with it, and whether that number is acceptable to you and your patient, is a worthy exercise.