An adverse health impact is often treated as a binary variable (response vs. no response), in which case the risk of response is defined as a monotonically increasing functionRof the dose receivedD.For a population of sizeN, specifying the forms ofR(D)and of the probability density function (pdf) forDallows determination of the pdf for risk, and computation of the mean and variance of the distribution of incidence, where the latter parameters are denotedESN and VarSN, respectively. The distribution ofSNdescribes uncertainty in the future incidence value. Given variability in dose (and risk) among population members, the distribution of incidence is Poisson‐binomial. However, depending on the value ofESN, the distribution of incidence is adequately approximated by a Poisson distribution with parameter μ=ESN, or by a normal distribution with mean and variance equal toESN and VarSN. The general analytical framework is applied to occupational infection byMycobacterium tuberculosis (M. tb).Tuberculosis is transmitted by inhalation of 1–5 μm particles carrying viableM. tbbacilli. Infection risk has traditionally been modeled by the expression:R(D)= 1 – exp(–D), whereDis the expected number of bacilli that deposit in the pulmonary region. This model assumes that the infectious dose is one bacillus. The beta pdf and the gamma pdf are shown to be reasonable and especially convenient forms for modeling the distribution of the expected cumulative dose across a large healthcare worker cohort. Use of the the analytical framework is illustrated by estimating the efficacy of different respiratory protective devices in reducing healthcare worker infec
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