Analysis of Households in Communities
In this chapter, we consider analyses that assume the households or other transmission units are nested in a community. Community-acquired infection serves as a source of initial infection within households as well as possible further cases in the household. Infected household members can infect others in the household. To start, we discuss general aspects of these models. All models in this chapter are variants of the basic models presented in this section. They use different data structures, assumptions, and methods of estimation, but the underlying parameters are similar. The data can be final-value data, time-to-event data, or longitudinal (panel) data.
Each model has two general types of parameters, one for infection from the community, and the other for transmission from an infective to a susceptible within the household. The first is an unconditional parameter, that is, it does not condition on exposure to infection. The second is a conditional parameter. The models can be formulated in discrete time or continuous time. For some data structures, such as data on sexual contacts, contacts can be substituted for time. Models formulated in discrete time have a parameter for the probability of infection from the community per unit time and a parameter for the probability of transmission from an infective to a susceptible within the household per unit time. Continuous-time models have analogous rate parameters. One parameter describes the rate of community-acquired infection, the other the rate of transmission from an infective to a susceptible within a household. Both continuous- and discrete-time parameters can be transformed into the probability of acquiring infection from the community over the period of time of interest, called the community probability of infection, CPI, and the secondary attack rate within the household, SAR.
KeywordsMarkov Chain Monte Carlo Transmission Probability Clearance Time Markov Chain Monte Carlo Method Infectious Period
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