Semiparametric Relative-risk Regression for Infectious Disease Data

TL;DR

This paper develops semiparametric regression models for infectious disease contact data, allowing for flexible baseline hazards and covariate effects, and introduces an EM algorithm for unobserved transmission pathways.

Contribution

It extends survival analysis regression models to infectious disease data, accommodating unknown transmission links with an EM algorithm.

Findings

Provides a new modeling framework for infectious contact intervals.

Derives an EM algorithm for unobserved who-infected-whom scenarios.

Connects survival analysis techniques with infectious disease epidemiology.

Abstract

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.