Semiparametric Relative-risk Regression for Infectious Disease Data

This paper introduces semiparametric relative-risk regression models for infectious disease data based on contact intervals, where the contact interval from person i to person j is the time between the onset of infectiousness in i and infectious contact from i to j. The hazard of infectious contact from i to j is λ0(τ)r(β T 0Xij), where λ0(τ) is an unspecified baseline hazard function, r is a relative risk function, β0 is an unknown covariate vector, and Xij is a covariate vector. When who-infects-whom is observed, the Cox partial likelihood is a profile likelihood for β maximized over all possible λ0(τ). When whoinfects-whom is not observed, we use an EM algorithm to maximize the profile likelihood for β integrated over all possible combinations of who-infected-whom. This extends the most important class of regression models in survival analysis to infectious disease epidemiology.