AN ANALYTICAL FRAMEWORK FOR RELATING DOSE, RISK, AND INCIDENCE - AN APPLICATION TO OCCUPATIONAL TUBERCULOSIS INFECTION

An adverse health impact is often treated as a binary variable (respon se vs. no response), in which case the risk of response is defined as a monotonically increasing function R of the dose received D. For a po pulation of size N, specifying the forms of R(D) and of the probabilit y density function (pdf) for D allows determination of the pdf for ris k, and computation of the mean and variance of the distribution of inc idence, where the latter parameters are denoted E[S-N] and Var[S-N], r espectively. The distribution of S-N describes uncertainty in the futu re incidence value. Given variability in dose (and risk) among populat ion members, the distribution of incidence is Poisson-binomial. Howeve r, depending on the value of E[S-N], the distribution of incidence is adequately approximated by a Poisson distribution with parameter mu = E[S-N], or by a normal distribution with mean and variance equal to E[ S-N] and Var[S-N]. The general analytical framework is applied to occu pational infection by Mycobacterium tuberculosis (M. tb). Tuberculosis is transmitted by inhalation of 15 mu m particles carrying viable M. tb bacilli. Infection risk has traditionally been modeled by the expre ssion: R(D) = 1 - exp(-D), where D is the expected number of bacilli t hat deposit in the pulmonary region. This model assumes that the infec tious dose is one bacillus. The beta pdf and the gamma pdf are shown t o be reasonable and especially convenient forms for modeling the distr ibution of the expected cumulative dose across a large healthcare work er cohort. Use of the the analytical framework is illustrated by estim ating the efficacy of different respiratory protective devices in redu cing healthcare worker infection risk.