A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

Abstract

The most commonly used dose -response models implicitly assume that accumulation of dose is a time-independent process where each pathogen has a fixed risk of initiating infection. Immune particle neutralization of pathogens, however, may create strong time dependence; i.e. temporally clustered pathogens have a better chance of overwhelming the immune particles than pathogen exposures that occur at lower levels for longer periods of time. In environmental transmission systems, we expect different routes of transmission to elicit different dose-timing patterns and thus potentially different realizations of risk. We present a dose -response model that captures time dependence in a manner that incorporates the dynamics of initial immune response. We then demonstrate the parameter estimation of our model in a dose -response survival analysis using empirical time-series data of inhalational anthrax in monkeys in which we find slight dose-timing effects. Future dose-response experiments should include varying the time pattern of exposure in addition to varying the total doses delivered. Ultimately, the dynamic dose-response paradigm presented here will improve modelling of environmental transmission systems where different systems have different time patterns of exposure.

Quantitative Models of the Dose-Response and Time Course of Inhalational Anthrax in Humans

“…For the Brachman data, our model B4 produces an estimated range for the exponential model parameter r , and thus for infectivity at a given dose, that is somewhat higher than the values calculated by Haas [18] (model B1 ) and Mayer et al [35] (model B2 ) for exponential model fits to the same data set (Figure 2). There were several assumptions made by the three studies that contributed to the differing infectivity results among these three models.…”

“…Dashed line = Mayer et al [35] extended exponential model B3 ( α  = 0.90, r  = 1.87×10 −5 ); solid line = Mayer et al [35] exponential model B2 ( r  = 3.95×10 −5 ); dotted line = Haas [18] exponential model B1 ( r  = 2.6×10 −5 ). The Haas curve would shift very close to the Mayer exponential curve if the correct cumulative dose is applied (see Table S5).…”

“…In their procedure for model B2 , Mayer et al [35] independently assumed that the delay between infection take-off and death was 1, 2, 3, or 4 days with equal probability (an assumption not based clearly on data). They then optimized their equivalent to our parameter θ to account for the remaining portion (exposure to infection take-off) of the overall delay between exposure and death, finding an optimal value of θ  = 0.11.…”

“…A model applying one such biological theory is provided by Mayer et al [35], who extended the exponential model to investigate potential effects of immune system dynamics [41]–[43], using an assumption that the immune system is more likely to be overwhelmed when receiving a large dose all at once as compared to receiving the same total exposure in a series of smaller doses over an extended period. I.e., the per-spore infection probability would be higher after a higher single dose, thus producing a dose-response curve that is steeper than the exponential model, which assumes that the size of a single dose does not affect the per-spore infection probability.…”

Herpes simplex virus-2 transmission probability estimates based on quantity of viral shedding

“…Coital events were simulated until infection occurred. The risk for each event was independent and risk did not depend on the time pattern of coital events [37].…”