Pairwise Accelerated Failure Time Regression Models for Infectious Disease Transmission in Close-Contact Groups With External Sources of Infection

Abstract

Many important questions in infectious disease epidemiology involve associations between covariates (e.g., age or vaccination status) and infectiousness or susceptibility. Because disease transmission 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 individual-level infectiousness covariates for $i$ , individual-level susceptibility covariates for $j$ , and pair-level covariates (e.g., type of relationship). 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). We show that this model produces consistent and asymptotically normal parameter estimates. In a simulation study, we evaluate bias and confidence interval coverage probabilities, explore the role of epidemiologic study design, and investigate the effects 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 increases the statistical power to estimate the effect of antiviral prophylaxis.

Keywords: accelerated failure time model; infectious disease epidemiology; secondary attack risk; survival analysis.

FIGURE 1

Notation for the stochastic SEIR model natural history (top) and infectious contact process (bottom) [29]. Here, we have${\tau }_{ij}^{\ast }={\tau }_{ij}$ because${\tau }_{ij}\le {\iota }_i$. Otherwise, we would have${\tau }_{ij}^{\ast }=\infty$ and$t_{ij}=\infty$ so infectious contact from$i$ to$j$ never occurs.

FIGURE 2

The bias${\widehat{\beta }}_{\text{sus}}-{\beta }_{\text{sus}}$ versus the true${\beta }_{\text{sus}}$ for correctly‐specified exponential pairwise AFT models fit to simulated data under all four study designs. Gray dots represent analyses where who‐infected whom was observed, and black dots represent analyses where who‐infected‐whom was not observed. In each plot, the dashed locally‐weighted polynomial regression (LOWESS) line represents the smoothed mean of the gray dots, and the solid LOWESS line represents the smoothed mean of the black dots [56]. The dashed lines are sometimes obscured by the solid lines.

FIGURE 3

The bias${\widehat{\beta }}_{\inf }-{\beta }_{\inf }$ versus the true${\beta }_{\inf }$ for correctly‐specified exponential pairwise AFT models fit to simulated data under all four study designs. Gray dots represent analyses where who‐infected whom was observed, and black dots represent analyses where who‐infected‐whom was not observed. In each plot, the dashed LOWESS line represents the smoothed mean of the gray dots and the solid LOWESS line represents the smoothed mean of the black dots [56]. The dashed lines are sometimes obscured by the solid lines.

FIGURE 4

The bias${\widehat{\beta }}_{\text{sus}}-{\beta }_{\text{sus}}$ versus the true${\beta }_{\text{sus}}$ for pairwise AFT models under the contact tracing with delayed entry study design. In the top two panels, the simulated data was generated using exponential internal contact intervals, so the log‐logistic model is misspecified but the Weibull model is correctly specified. In the bottom two panels, the simulated data was generated using log‐logistic internal contact intervals, so the exponential and Weibull models are both misspecified. Gray dots represent analyses where who‐infected whom was observed, and black dots represent analyses where who‐infected‐whom was not observed. In each plot, the dashed LOWESS line represents the smoothed mean of the gray dots and the solid LOWESS line represents the smoothed mean of the black dots [56]. The dashed lines are sometimes obscured by the solid lines.

FIGURE 5

The bias${\widehat{\beta }}_{\inf }-{\beta }_{\inf }$ versus the true${\beta }_{\inf }$ for pairwise AFT models under the contact tracing with delayed entry study design. In the top two panels, the simulated data was generated using exponential internal contact intervals, so the log‐logistic model is misspecified but the Weibull model is correctly specified. In the bottom two panels, the simulated data was generated using log‐logistic internal contact intervals, so the exponential and Weibull models are both misspecified. Gray dots represent analyses where who‐infected whom was observed, and black dots represent analyses where who‐infected‐whom was not observed. In each plot, the dashed LOWESS line represents the smoothed mean of the gray dots and the solid LOWESS line represents the smoothed mean of the black dots [56]. The dashed lines are sometimes obscured by the solid lines.