A Leaky Noisy-OR Bayesian Network Applied to Genetic Counseling in Dogs.

Genetic disorders are very frequent in dogs but evaluating individualized risks of their occurrence can be uncertain. Bayesian networks are tools to characterize and analyze such events. The paper illustrates their benefits and challenges in answering two typical questions in genetic counselling: (1) What is the probability of a test-positive animal showing clinical signs of the disease? (2) What is the risk of testing positive for the mutant allele when one parent presents clinical signs? Current limited knowledge on the hereditary mode of transmission of degenerative myelopathy and on the effects of sex, diet, exercise regimen and age on the occurrence of clinical signs concurrent with the finding of the deleterious mutation was retrieved from the scientific literature. Uncertainty on this information was converted into prior Beta distributions and leaky-noisy OR models were used to construct the conditional probability tables necessary to answer the questions. Results showed the network is appropriate to answer objectively and transparently both questions under a variety of scenarios. Once users of the network have agreed with its structure and the values of the priors, computations are straightforward. The network can be updated automatically and can be represented visually so interactive discussion are easy between the veterinarian and his/her interlocutor.

A mathematical model to study resistance and tolerance to infection at the animal and population levels: application to E. coli mastitis.

A mathematical model is proposed that describes the colonization of host tissues by a contagious pathogen and the early nonspecific immune response, the impact of the infection on the performances of the host, and the spread of the infection in the population. The model obeys specific biological characteristics: Susceptible hosts are infected after contact with an infected one. The number of pathogenic units that invade a susceptible host is dependent on the infectious dose provided by the infected host and on the ability of the susceptible host to resist the invasion. After entry in host, pathogenic changes over time are expressed as the difference between the intrinsic logistic growth rate and the Holling type II kill rate provided by the immune response cells. Hosts have different ability to restrict reproduction of the pathogen units. The number of response cells actively recruited to the site of infection depends on the number of the pathogenic units. Response cells are removed after having killed a fixed number of pathogenic units. The effects of the number of pathogenic units on the performances of the host depend upon its levels of tolerance to the deleterious effects of both pathogenic and response cells. Pre-infection costs are associated to tolerance and resistance levels. Estimates of most biological parameters of the model are based on published experimental studies while resistance/tolerance parameters are varied across their allowable ranges. The model reproduces qualitatively realistic outcomes in response to infection: healthy response, recurrent infection, persistent infectious and non-infectious inflammation, and severe immunodeficiency. Evolution across time at the animal and population levels is presented. Effects on animal performances are discussed with respect to changes in resistance/tolerance parameters and selection strategies are suggested.

Effectiveness analysis of resistance and tolerance to infection.

BACKGROUND: Tolerance and resistance provide animals with two distinct strategies to fight infectious pathogens and may exhibit different evolutionary dynamics. However, few studies have investigated these mechanisms in the case of animal diseases under commercial constraints. METHODS: The paper proposes a method to simultaneously describe (1) the dynamics of transmission of a contagious pathogen between animals, (2) the growth and death of the pathogen within infected hosts and (3) the effects on their performances. The effectiveness of increasing individual levels of tolerance and resistance is evaluated by the number of infected animals and the performance at the population level. RESULTS: The model is applied to a particular set of parameters and different combinations of values. Given these imputed values, it is shown that higher levels of individual tolerance should be more effective than increased levels of resistance in commercial populations. As a practical example, a method is proposed to measure levels of animal tolerance to bovine mastitis. CONCLUSIONS: The model provides a general framework and some tools to maximize health and performances of a population under infection. Limits and assumptions of the model are clearly identified so it can be improved for different epidemiological settings.

The analysis of disease biomarker data using a mixed hidden Markov model (Open Access publication).

A mixed hidden Markov model (HMM) was developed for predicting breeding values of a biomarker (here, somatic cell score) and the individual probabilities of health and disease (here, mastitis) based upon the measurements of the biomarker. At a first level, the unobserved disease process (Markov model) was introduced and at a second level, the measurement process was modeled, making the link between the unobserved disease states and the observed biomarker values. This hierarchical formulation allows joint estimation of the parameters of both processes. The flexibility of this approach is illustrated on the simulated data. Firstly, lactation curves for the biomarker were generated based upon published parameters (mean, variance, and probabilities of infection) for cows with known clinical conditions (health or mastitis due to Escherichia coli or Staphylococcus aureus). Next, estimation of the parameters was performed via Gibbs sampling, assuming the health status was unknown. Results from the simulations and mathematics show that the mixed HMM is appropriate to estimate the quantities of interest although the accuracy of the estimates is moderate when the prevalence of the disease is low. The paper ends with some indications for further developments of the methodology.

Genetic management of infectious diseases: a heterogeneous epidemio-genetic model illustrated with S. aureus mastitis.

Given that individuals are genetically heterogeneous in their degree of resistance to infection, a model is proposed to formulate appropriate choices that will limit the spread of an infectious disease. The model is illustrated with data on S. aureus mastitis and is based on parameters characterizing the spread of the disease (contact rate, probability of infection after contact, and rate of recovery after infection), the demography (replacement and culling rates) and the genetic composition (degree of relationship and heritability of the disease trait) of the animal population. To decrease infection pressure, it is possible to apply non-genetic procedures that increase the culling (e.g., culling of chronically infected cows) and recovery (e.g., antibiotic therapy) rates of infected cows. But the contribution of the paper is to show that genetic management of infectious disease is also theoretically possible as a control measure complementary to non-genetic actions. Indeed, the probability for an uninfected individual to become infected after contact with an infected one is partially related to their degree of kinship: the more closely they are related, the more likely they are to share identical genes like those associated to the non-resistance to infection. Different prospective genetic management procedures are proposed to decrease the contact rate between infected and uninfected relatives and keep the number of secondary cases generated by one infected animal below 1.

Javelin diagrams: applications in veterinary medical decision analysis.

This paper introduces javelin diagrams as an innovative way for depicting the results of medical decision analyses. The methods were used to determine whether, and at which values, blood lactate in Belgian White and Blue or maximum tidal volumes in Holstein calves should be measured before deciding to treat or not a calf suffering from the bovine respiratory disease complex. The different alternatives depended upon the probabilities of survival with and without treatment and upon the costs associated with a possible death, the test and the treatment. The chosen alternative was the one with the lowest expected costs. From data collected on the treated calves, the expected costs of measuring lactate (198.01 euro) and tidal volumes (27.38 euro) before deciding to treat or not were lower than the expected costs of directly treating sick Belgian Blue (215.39 euro) and Holstein (51.55 euro) calves, respectively. The treatment should be applied to sick Belgian Blue calves with blood lactate < or = 7.8 mmol/L and to Holstein calves with a maximum tidal volume > or = 1.81 L. At such test values, the treatment expected costs were lower than the expected costs associated with no treatment of calves with other test values. Probabilistic sensitivity analyses showing benefits in treating animals with a positive test (over not treating the animals with a negative test) were mostly invariant to changes in any cost value but were sensitive to uncertainties in probabilities of survival with or without treatment. The javelin diagrams provided a clear visual indication of such results. They depicted how and by how much the benefits were affected by uncertainties in probabilities, they proposed different information values associated with the chosen alternative, and identified directions for further research.