Unveiling time in dose-response models to infer host susceptibility to pathogens

Abstract

The biological effects of interventions to control infectious diseases typically depend on the intensity of pathogen challenge. As much as the levels of natural pathogen circulation vary over time and geographical location, the development of invariant efficacy measures is of major importance, even if only indirectly inferrable. Here a method is introduced to assess host susceptibility to pathogens, and applied to a detailed dataset generated by challenging groups of insect hosts (Drosophila melanogaster) with a range of pathogen (Drosophila C Virus) doses and recording survival over time. The experiment was replicated for flies carrying the Wolbachia symbiont, which is known to reduce host susceptibility to viral infections. The entire dataset is fitted by a novel quantitative framework that significantly extends classical methods for microbial risk assessment and provides accurate distributions of symbiont-induced protection. More generally, our data-driven modeling procedure provides novel insights for study design and analyses to assess interventions.

Figure 1. Survival curves for Wolb⁻ (A) and Wolb⁺ (B) groups of D. melanogaster.

Dots represent experimental data. Dark blue curves show the model fit to the survival of control flies. Shaded areas represents 95% CI (credible intervals).

Figure 2. Dose-response curves and susceptibility distributions inferred from mortality measurements 30 and 50 days post-challenge.

Dose-responses models adopted here are the standard formulations (1–3). A,D, Curves represent the fitted dose-response model to mortality on selected day post-challenge (dots), for Wolb⁻ (black) and Wolb⁺ (blue). Shaded areas represent the 95% CI. B,E, Distribution of susceptibility to infection in Wolb⁺. The posterior median distribution is the curve and the shaded area is the 95% CI. C,F, Posterior samples of the Beta-distribution shape parameters describing Wolb⁺ susceptibility in blue. Red dot mark the median of the respective distributions. The homogeneous model was adopted for Wolb⁻.

Figure 3. Schematic illustration of the proposed experimental design and inference procedure.

Figure 4. Fit of time-dependent dose-response model to survival curves.

Black and blue dots are the observed proportions surviving over time for Wolb⁻ and Wolb⁺ groups, respectively. The curve is the fitted mean posterior survival over time and the shaded area is the 95% CI. Fifty flies per group were pricked with: A, buffer solution (shown for comparison but not used on this analysis); and B, ; C, ; D, ; E, ; F, ; G, ; H, TCID₅₀ DCV.

Figure 5. Dose-response curves and susceptibility distributions inferred from survival curves.

A, Curves represent the estimated dose-response relationships from fitting the model described in Methods to survival over time, for Wolb⁻ (black) and Wolb⁺ (blue). Shaded areas represent the 95% CI. B, Distribution of susceptibility to infection in Wolb⁺. The posterior median distribution is the curve and the shaded area is the 95% CI. C, Posterior samples of the Beta-distribution shape parameters describing Wolb⁺ susceptibility in blue. Red dot marks the median of distribution.

Figure 6. Selection of optimal days to collect mortality measurements for traditional dose-response models.

The red line traces a score for how well mortality at any given day represents infection estimated by the time-dependent model (refer to axis on the right). The score is given by , where Δ denotes the number of doses in the dataset, () represents the proportion infected in the Wolb⁻ (Wolb⁺) group subject to DCV dose j, and () the observed mortality proportion over time in the Wolb⁻ (Wolb⁺) group subject to DCV dose j. Gray vertical lines mark the optimal day to measure mortality for dose-response models (day 30, dash-dotted line) and the limits of the acceptable range (days 17 and 46). Dashed lines represent the Gamma distributions that describe old-age mortality, and black (blue) full curves refer to the Gamma distributions that describe infection-induced mortality in Wolb⁻ (Wolb⁺) (refer to axis on the left). Curves are the mean posterior probabilities and shaded areas represent the 95% CI.