, and pairwise covariates. When who-infects-whom is observed, we derive a profile likelihood maximized over all possible baseline hazard functions that is similar to the Cox partial likelihood. When who-infects-whom is not observed, we derive an EM algorithm to maximize the profile likelihood 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. These methods can be implemented in standard statistical software, and they will be able to address important scientific questions about emerging infectious diseases with greater clarity, flexibility, and rigor than current statistical methods allow.