But again, there is a problem of sample size. Dr. Anderson’s model found that patients who never took their prescribed Truvada had a 3 percent chance of contracting H.I.V. in a given year, which is a little lower than what was observed among patients taking a placebo. But that estimate comes with a range of confidence; perhaps the true figure is as low as 2 percent or as high as 7 percent. If the true figure is on the high end, then subjects who chose not to take their pills really did have greater independent risk of contracting H.I.V., in line with Dr. Buchbinder’s concern.

Then there is the issue of the model itself, what statisticians call a regression analysis. It fits a curve to the outcomes for participants in iPrEx, including many infections among people not taking Truvada, a handful among people taking it sporadically, and none among people who appear to have taken it daily. This approach effectively forces the estimate into a box: Infection risk must approach zero as frequency of Truvada dosing increases, because none of the high-adherence subjects became infected. If rare circumstances make infections possible among people with high blood levels of the drug (and two such infections were observed in a study of heterosexual couples, called Partners PrEP), that chance won’t be reflected in the model.

All of which is to say, while there are good reasons to find the 99 percent estimate plausible, the model is not so bulletproof as to say the figure was “shown in a major study.” Tim Horn, H.I.V. Project Director at the H.I.V. think-tank Treatment Action Group, said in an email, “Though it is possible that efficacy can approach 99 percent — language in the lay literature seems to be growing increasingly casual as to what this really means — the data supporting this currently exist in a vacuum.”

As such, Mr. Horn prefers to point to direct study findings, such as the 92 percent figure. Dr. Buchbinder uses qualitative descriptions, such as saying PrEP is “highly effective” and can “drastically” reduce infection risk if taken daily.

Dr. Anthony Fauci, who has headed the National Institute of Allergy and Infectious Diseases since 1984 and was one of the leading researchers involved in developing antiretroviral therapy for H.I.V., has perhaps found the best way to split the difference. Dr. Fauci told me PrEP is “highly efficacious, in my mind easily over 90 percent if you adhere rigidly to it,” without specifically citing the 99 percent figure. He was quick to add, in line with the guidelines from all the United States government agencies encouraging the use of Truvada as a preventive measure, that it’s meant to augment the protection provided by condoms, not to replace them.

From a policy perspective, the difference between 92 percent and 99 percent is not necessarily very important: Either way, PrEP looks to be a highly useful tool for reducing the spread of H.I.V. Any reduction in the 90-percent range looks extremely impressive when you consider a C.D.C. study from last year finding that gay men who said they “always” used condoms were only 70 percent less likely to contract H.I.V. than those who said they never used them. With perfect use, condoms (like PrEP) may approach 100 percent effectiveness, but in the real world, people often use them improperly, or do not use them through the entirety of intercourse, or “forget” to use them despite an intent to do so. The failure of condoms as a prevention strategy is one reason Gov. Andrew Cuomo has made PrEP one of three planks in his strategy to end the H.I.V. epidemic in New York.