# Pairwise accelerated failure time regression models for infectious disease transmission in close-contact groups with external sources of infection

## TL;DR

This paper introduces a pairwise accelerated failure time regression model for infectious disease transmission that accounts for covariates, external infections, and dependent outcomes, improving analysis of transmission data.

## Contribution

The paper develops a novel regression model for infectious disease transmission that handles external sources and dependent outcomes, extending existing pairwise survival analysis methods.

## Key findings

- Model produces valid parameter estimates in simulations.
- Accounting for external infections is crucial for accurate effect estimation.
- Application to influenza data highlights importance of external infection modeling.

## Abstract

Many important questions in infectious disease epidemiology involve the effects of covariates (e.g., age or vaccination status) on infectiousness and susceptibility, which can be measured in studies of transmission in households or other close-contact groups. Because the transmission of disease produces dependent outcomes, these questions are difficult or impossible to address using standard regression models from biostatistics. Pairwise survival analysis handles dependent outcomes by calculating likelihoods in terms of contact interval distributions in ordered pairs of individuals. The contact interval in the ordered pair ij is the time from the onset of infectiousness in i to infectious contact from i to j, where an infectious contact is sufficient to infect j if they are susceptible. Here, we introduce a pairwise accelerated failure time regression model for infectious disease transmission that allows the rate parameter of the contact interval distribution to depend on infectiousness covariates for i, susceptibility covariates for j, and pairwise covariates. This model can simultaneously handle internal infections (caused by transmission between individuals under observation) and external infections (caused by environmental or community sources of infection). In a simulation study, we show that these models produce valid point and interval estimates of parameters governing the contact interval distributions. We also explore the role of epidemiologic study design and the consequences of model misspecification. We use this regression model to analyze household data from Los Angeles County during the 2009 influenza A (H1N1) pandemic, where we find that the ability to account for external sources of infection is critical to estimating the effect of antiviral prophylaxis.