Bacillus anthracis. Summary Data

Transcription

1 Bacillus anthracis Overview: Bacillus anthracis and Anthrax Bacillus anthracis is a rod shaped gram negative bacterium which is the causative of a multi-symptom disease anthrax. There are three main types of anthrax; cutaneous, inhalational and gastrointestinal. Cutaneous anthrax is the most common form of naturally occurred anthrax. This type of the disease although possibly debilitating and scaring to the host, is not typically fatal especially where there is modern healthcare available. Gastrointestinal anthrax is a very rare form of the disease. This form of anthrax is typically encountered for those people who are immune compromised or are exposed to an overwhelming load of pathogens. This form of the disease is potentially lethal due to the development of a systemic infection from the internal infection. Inhalational anthrax is the most lethal form of the disease and the preferred form of anthrax in bioterror scenarios. Inhalation of the spores introduces them to the lower regions of the lungs (alveoli, or air sacs) where oxygen and carbon dioxide are exchanged with the blood. At this location the pathogenesis of B. anthracis occurs where eventually after intracellular transport can result in septicemia and death (Dixon et al., 2000; Majno and Jaris, 2004). There are three main strains of B. anthracis. The Ames strain is well known particularly from the 2001 anthrax postal attack. The Vollum strain is a weaponized form which is more infectious compared to the Ames strain. There is also an attenuated vaccine strain, this being the Sterne strain. The main datasets gathered for B. anthracis are for the Vollum strain. Summary Data In Altboum et al (2002) female Hartley guinea pigs were first rendered unconscious then dosed intranasally with B. anthracis spores. Mortality was monitored for and the lethality rate was recorded, it is this mortality rate that is being modeled with respect to dose. Therefore this dose response model is for a lethal response to inhaled spores. The isolate preparation was not described thoroughly, however the overall dose was estimated in the paper in units of spores inhaled. In Druett et al (1953) both rhesus macaques and guinea pigs were exposed to an aerosol of spores, while conscious. The macaques and guinea pigs were monitored for mortality, thus allowing for a dose response model estimating the probability of death from aerosol exposure to spores. 15

2 Experi ment Numb er Summary of data for Bacillus anthracis Reference 87 * Druett et al., (1953) Altboum 84 et al, (2002) Altboum 85 et al, (2002) Druett et 86 al., (1953) Host Type Guinea pig Guinea Pig Guinea Pig Rhesus macaques Pathogen Strain Route # of Doses Dose Units Resp onse Best Fit Model Optimized Parameter(s) Vollum Inhalation 4 Spore Death Exponential k = 1.65 E-05 Vollum Intranasal 6 Spores Death ATCC 6605 Beta- α = 5.49E -01 N 50 = 2.85 Intranasal 6 Spores Death Exponential k = 7.11 E-06 Vollum Inhalation 9 Spores Death Exponential k = 7.16 E-06 LD * It is recommended that experiment 87 be used as the best dose response model for use. Despite the host animal being less representative of humans than one like rhesus macaques, the optimized model had the best fit based on the minimized deviance and likelihood ratio test performed. Also the exposure route was inhalation which is a better representation of an actual release scenario, and the strain being Vollum which is a better option than an attenuated strain, thus being able to simulate an attack scenario better. Criteria for choosing dose response models We prefer dose response models with the following criteria, in rough order of importance: 1. Statistically acceptable fit (fail to reject goodness of fit, p > 0.05) 2. Human subjects, or animal models that mimic human pathophysiology well 3. Infection as the response, rather than disease, symptoms, or death 4. Exposure route similar/identical to the exposure route of natural infection 5. Pathogen strain is similar to strains causing natural infection 6. Pooled model using data from 2 or more experiments, provided the data sets are statistically similar (fail to reject that datasets are from the same distribution, p > 0.05) 7. Low ID 50 /LD 50 (to obtain a conservative risk estimate) We generally recommend a single dose response model, and we justify the decision in terms of the above criteria. This decision is somewhat subjective, since dose response datasets seldom meet all of these criteria. If all available models are unsatisfactory, we choose a single model to recommend with reservations. Our recommended model will seldom (if ever) be the best model for all applications. The user should carefully choose the model that is most appropriate for their particular problem. 16

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4 Optimized Models and Fitting Analyses Optimization Output for experiment 87 Guinea pig/vollum Strain model data Dose Dead Survived Total Druett et al., (1953) Goodness of Fit and Model Selection Model Deviance DF Exponenti al Beta E-04 2 χ ,1 p- value χ ,m-k p-value Exponential is preferred to beta-; cannot reject good fit for exponential. Parameter Optimized parameters for the exponential model, from bootstrap iterations MLE Estimate Percentiles 0.5% 2.5% 5% 95% 97.5% 99.5% k 1.65E E E E E E E-05 ID50/LD50/ETC* *Not a true parameter of the exponential model, but included to facilitate comparison with other models. Parameter histogram for exponential model (uncertainty of the parameter) Exponential model plot, with confidence bounds around optimized model 18

5 Optimization Output for experiment 84 Guinea pig/vollum Strain model data Dose Dead Survived Total 20,000, ,000, , , , Altboum et al., (2002) Goodness of Fit and Model Selection Model Deviance DF Exponenti al Beta χ ,1 p- value E -07 χ ,m-k p-value E Beta- fits better than exponential; cannot reject good fit for beta-. Parameter Optimized parameters for the beta- model, from bootstrap iterations MLE Estimate Percentiles 0.5% 2.5% 5% 95% 97.5% 99.5% α 5.49E E E E E E E+03 N E+05 Parameter scatter plot for beta model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters. beta model plot, with confidence bounds around optimized model 19

6 Optimization Output for experiment 85 Guinea pig/atcc 6605 Strain model data Dose Dead Survived Total 3,000, , , , Altboum et al., (2002) Goodness of Fit and Model Selection Model Deviance DF Exponenti al Beta χ ,1 p- value χ ,m-k p-value Exponential is preferred to beta-; cannot reject good fit for exponential. Optimized parameters for the exponential model, from bootstrap iterations Parameter MLE Estimate Percentiles 0.5% 2.5% 5% 95% 97.5% 99.5% k 7.11E E E E E E E-05 ID50/LD50/ETC* E E E+05 *Not a true parameter of the exponential model, but included to facilitate comparison with other models. Parameter histogram for exponential model (uncertainty of the parameter) Exponential model plot, with confidence bounds around optimized model 20

7 Optimization Output for experiment 86 Rhesus Macaques/Vollum Strain model data Dose Dead Survived Total Druett et al., (1953) Goodness of Fit and Model Selection Model Deviance DF Exponenti al Beta E-04 7 χ ,1 p- value χ ,m-k p-value Exponential is preferred to beta-; cannot reject good fit for exponential. Parameter Optimized parameters for the exponential model, from bootstrap iterations MLE Estimate Percentiles 0.5% 2.5% 5% 95% 97.5% 99.5% k 7.16E E E E E E E-05 ID50/LD50/ETC* E E E+05 *Not a parameter of the exponential model; however, it facilitates comparison with other models. Parameter histogram for exponential model (uncertainty of the parameter) Exponential model plot, with confidence bounds around optimized model 21

8 Advanced Dose Response Model An advanced dose response model was developed for Bacillus anthracis, where the physiology of the host as well as the pathogenesis of inhaled spores, was modeled and integrated into the does response models. Both the beta and exponential models were modified. First the fate and transport of inhaled spores was modeled in a stochastic system (Markov chain), which was then coupled with a deterministic model of the pathogenesis of inhaled spores. This first (stochastic) model used independently allows for an estimation of a correction factor for correcting exposed dose to delivered dose. The left figure shows the linear correction factor for human respiratory systems, which remains linear when the same model is adapted to guinea pig or rhesus macaque respiratory systems. The pathogenesis model simulates the survival, germination, and eventual growth of B. anthracis rods. Therefore the coupled models allow for an estimation of the pathogen burden, since the coupled model accounts for fate and transport as well as the pathogenesis. Again as can be seen in the right figure, this is a linear correction as well. These correction factors can be incorporated into the dose response models by multiplying the dose by the chosen correction factor; η dd for delivered dose and η pb for pathogen burden (equations 1 and 2 for the exponential model and 3 and 4 for the beta ). The η dd allows for a drop in the number of spores, since there are some being entrapped along the path through the respiratory system, with a value for η dd of for humans. Conversely the pathogen burden accounts for; fate and transport survival and growth of the bacilli in the body therefore, this correction factor allows for an increase between exposed dose and pathogen burden, thus η pb is for humans. Linear correction factor to estimate delivered dose from exposed dose Linear correction factor to estimate pathogen burden from exposed dose Equation 1 Equation 2 Equation 3 Equation 4 22

9 References Altboum Z., Gozes, Y., Barnea, A., Pass, A., White, M., Kobiler, D. (2002) Postexposure prophylaxis against anthrax: Evaluation of various treatment regimes in intranasally infected guinea pigs Infection and Immunity 70(1): Druett, H.A., Henderson, D.W., Packman, L., Peacock, S. (1953) Studies on respiratory infection. I. The influence of particle size on respiratory infection with anthrax spores Journal of Hygiene 51: