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An Analytical Framework for Relating Dose, Risk, and Incidence: An Application to Occupational Tuberculosis Infection

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  • Mark Nicas

Abstract

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 function R of the dose received D. For a population of size N, specifying the forms of R(D) and of the probability density function (pdf) for D allows determination of the pdf for risk, and computation of the mean and variance of the distribution of incidence, where the latter parameters are denoted E[SN] and Var[SN], respectively. The distribution of SN describes 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 of E[SN], the distribution of incidence is adequately approximated by a Poisson distribution with parameter μ=E[SN], or by a normal distribution with mean and variance equal to E[SN] and Var[SN]. The general analytical framework is applied to occupational infection by Mycobacterium tuberculosis (M. tb). Tuberculosis is transmitted by inhalation of 1–5 μm particles carrying viable M. tb bacilli. Infection risk has traditionally been modeled by the expression: R(D)= 1 – exp(–D), where D is 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 infection risk.

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  • Mark Nicas, 1996. "An Analytical Framework for Relating Dose, Risk, and Incidence: An Application to Occupational Tuberculosis Infection," Risk Analysis, John Wiley & Sons, vol. 16(4), pages 527-538, August.
    • Handle: RePEc:wly:riskan:v:16:y:1996:i:4:p:527-538
    DOI: 10.1111/j.1539-6924.1996.tb01098.x
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    References listed on IDEAS

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    1. Kenneth T. Bogen & Robert C. Spear, 1987. "Integrating Uncertainty and Interindividual Variability in Environmental Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 7(4), pages 427-436, December.
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    1. Ralf R. Küsel & Ian K. Craig & Anton C. Stoltz, 2019. "Modeling the Airborne Infection Risk of Tuberculosis for a Research Facility in eMalahleni, South Africa," Risk Analysis, John Wiley & Sons, vol. 39(3), pages 630-646, March.
    2. Rachael M. Jones & Yoshifumi Masago & Timothy Bartrand & Charles N. Haas & Mark Nicas & Joan B. Rose, 2009. "Characterizing the Risk of Infection from Mycobacterium tuberculosis in Commercial Passenger Aircraft Using Quantitative Microbial Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 29(3), pages 355-365, March.
    3. Qi Zhen & Anxiao Zhang & Qiong Huang & Jing Li & Yiming Du & Qi Zhang, 2022. "Overview of the Role of Spatial Factors in Indoor SARS-CoV-2 Transmission: A Space-Based Framework for Assessing the Multi-Route Infection Risk," IJERPH, MDPI, vol. 19(17), pages 1-38, September.
    4. Charles N. Haas, 2002. "On the Risk of Mortality to Primates Exposed to Anthrax Spores," Risk Analysis, John Wiley & Sons, vol. 22(2), pages 189-193, April.
    5. Szu‐Chieh Chen & Chung‐Min Liao & Sih‐Syuan Li & Shu‐Han You, 2011. "A Probabilistic Transmission Model to Assess Infection Risk from Mycobacterium Tuberculosis in Commercial Passenger Trains," Risk Analysis, John Wiley & Sons, vol. 31(6), pages 930-939, June.
    6. Mark Nicas & Edmund Seto, 1997. "A Simulation Model for Occupational Tuberculosis Transmission," Risk Analysis, John Wiley & Sons, vol. 17(5), pages 609-616, October.

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