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October 6, 1993

Risk Calculations for HIV Transmission From Infected Health Care Workers

JAMA. 1993;270(13):1543-1544. doi:10.1001/jama.1993.03510130049017

To the Editor.  —I applaud the efforts of the authors in the three articles showing no transmission of HIV infection from health care workers to their patients.1-3 These add to the assurance that the risk is not large. I share the opinion that the actual risk of transmission is vanishingly low when universal precautions are observed.These articles point out the difficulty and high cost of determining the incidence of rare events. Unfortunately, in all three, the calculation of maximum probability based on their numerator of zero was incorrect.The question can be stated as follows: What is the minimum rate that would result in zero cases in n tries less than α (usually P=.05) percent of the time? The binomial distribution should be used, as suggested by von Reyn et al.3 In the special case of zero of n, this simplifies to the following: