  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 \lambda_0(\tau)r(\beta_0^T X_{ij}), where \lambda_0(\tau) is an
unspecified baseline hazard function, r is a relative risk function, \beta_0 is
an unknown covariate vector, and X_{ij} is a covariate vector. When
who-infects-whom is observed, the Cox partial likelihood is a profile
likelihood for \beta maximized over all possible \lambda_0(\tau). When
who-infects-whom is not observed, we use an EM algorithm to maximize the
profile likelihood for \beta 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.
