A sequential threshold cure model for genetic analysis of time-to-event data

Genetic analysis of resistance in Mekong striped catfish (Pangasianodon hypophthalmus) to bacillary necrosis caused by Edwardsiella ictaluri

The aim of this study was to analyse four cohabitation challenge-test experiments with Mekong striped catfish (Pangasianodon hypophthalmus) against the bacterium Edwardsiella ictaluri. The data were genetically analysed per experiment by three models: 1) a cross-sectional linear model; 2) a cross-sectional threshold model; and 3) a linear survival model, at both 50% mortality (for models 1 and 2) and at the end of the test (for all three models). In two of the experiments (3 and 4) that were carried out in two replicated tanks, the predicted family effects (sum of sire, dam and common environmental effects) in each tank were correlated with the family survival in the other replicated tank (cross-validation). The heritability estimates of resistance to E. ictaluri infection were ≤ 0.012 with the survival model, and up to 0.135 - 0.220 (50% survival) and 0.085 and 0.174 (endpoint survival) for the cross-sectional linear and threshold models, respectively. The challenge test should aim for an endpoint survival that ceases naturally at 50%. Then, genetic analysis should be carried out for survival at the endpoint (reflecting susceptibility) with a simple cross-sectional linear model.

The economic value of R0 for selective breeding against microparasitic diseases

Background

Microparasitic diseases are caused by bacteria and viruses. Genetic improvement of resistance to microparasitic diseases in breeding programs is desirable and should aim at reducing the basic reproduction ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0. Recently, we developed a method to derive the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 for macroparasitic diseases. In epidemiological models for microparasitic diseases, an animal’s disease status is treated as infected or not infected, resulting in a definition of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 that differs from that for macroparasitic diseases. Here, we extend the method for the derivation of the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 to microparasitic diseases.

Methods

When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0} \le 1$$\end{document}R0≤1, the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 is zero because the disease is very rare. When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0. is higher than 1, genetic improvement of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 can reduce expenditures on vaccination if vaccination induces herd immunity, or it can reduce production losses due to disease. When vaccination is used to achieve herd immunity, expenditures are proportional to the critical vaccination coverage, which decreases with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0. The effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 on losses is considered separately for epidemic and endemic disease. Losses for epidemic diseases are proportional to the probability and size of major epidemics. Losses for endemic diseases are proportional to the infected fraction of the population at the endemic equilibrium.

Results

When genetic improvement reduces expenditures on vaccination, expenditures decrease with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 at an increasing rate. When genetic improvement reduces losses in epidemic or endemic diseases, losses decrease with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 at an increasing rate. Hence, in all cases, the economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 increases as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 decreases towards 1.

Discussion

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 and its economic value are more informative for potential benefits of genetic improvement than heritability estimates for survival after a disease challenge. In livestock, the potential for genetic improvement is small for epidemic microparasitic diseases, where disease control measures limit possibilities for phenotyping. This is not an issue in aquaculture, where controlled challenge tests are performed in dedicated facilities. If genetic evaluations include infectivity, genetic gain in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 can be accelerated but this would require different testing designs.

Conclusions

When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0} \le 1$$\end{document}R0≤1, its economic value is zero. The economic value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 is highest at low values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0 and approaches zero at high values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}R0.

The genetic analysis of tolerance to infections: a review

Tolerance to infections is defined as the ability of a host to limit the impact of a given pathogen burden on host performance. Uncoupling resistance and tolerance is a challenge, and there is a need to be able to separate them using specific trait recording or statistical methods. We present three statistical methods that can be used to investigate genetics of tolerance-related traits. Firstly, using random regressions, tolerance can be analyzed as a reaction norm slope in which host performance (y-axis) is regressed against an increasing pathogen burden (x-axis). Genetic variance in tolerance slopes is the genetic variance for tolerance. Variation in tolerance can induce genotype re-ranking and changes in genetic and phenotypic variation in host performance along the pathogen burden trajectory, contributing to environment-dependent genetic responses to selection. Such genotype-by-environment interactions can be quantified by combining random regressions and covariance functions. To apply random regressions, pathogen burden of individuals needs to be recorded. Secondly, when pathogen burden is not recorded, the cure model for time-until-death data allows separating two traits, susceptibility and endurance. Susceptibility is whether or not an individual was susceptible to an infection, whereas endurance denotes how long time it took until the infection killed a susceptible animal (influenced by tolerance). Thirdly, the normal mixture model can be used to classify continuously distributed host performance, such as growth rate, into different sub-classes (e.g., non-infected and infected), which allows estimation of host performance reduction specific to infected individuals. Moreover, genetics of host performance can be analyzed separately in healthy and affected animals, even in the absence of pathogen burden and survival data. These methods provide novel tools to increase our understanding on the impact of parasites, pathogens, and production diseases on host traits.

Bias, accuracy, and impact of indirect genetic effects in infectious diseases

Selection for improved host response to infectious disease offers a desirable alternative to chemical treatment but has proven difficult in practice, due to low heritability estimates of disease traits. Disease data from field studies is often binary, indicating whether an individual has become infected or not following exposure to an infectious disease. Numerous studies have shown that from this data one can infer genetic variation in individuals’ underlying susceptibility. In a previous study, we showed that with an indirect genetic effect (IGE) model it is possible to capture some genetic variation in infectivity, if present, as well as in susceptibility. Infectivity is the propensity of transmitting infection upon contact with a susceptible individual. It is an important factor determining the severity of an epidemic. However, there are severe shortcomings with the Standard IGE models as they do not accommodate the dynamic nature of disease data. Here we adjust the Standard IGE model to (1) make expression of infectivity dependent on the individuals’ disease status (Case Model) and (2) to include timing of infection (Case-ordered Model). The models are evaluated by comparing impact of selection, bias, and accuracy of each model using simulated binary disease data. These were generated for populations with known variation in susceptibility and infectivity thus allowing comparisons between estimated and true breeding values. Overall the Case Model provided better estimates for host genetic susceptibility and infectivity compared to the Standard Model in terms of bias, impact, and accuracy. Furthermore, these estimates were strongly influenced by epidemiological characteristics. However, surprisingly, the Case-Ordered model performed considerably worse than the Standard and the Case Models, pointing toward limitations in incorporating disease dynamics into conventional variance component estimation methodology and software used in animal breeding.

Genetics of ascites resistance and tolerance in chicken: a random regression approach

Resistance and tolerance are two complementary mechanisms to reduce the detrimental effects of parasites, pathogens, and production diseases on host performance. Using body weight and ascites data on domesticated chicken Gallus gallus domesticus, we demonstrate the use of random regression animal model and covariance functions to estimate genetic parameters for ascites resistance and tolerance and illustrate the way individual variation in resistance and tolerance induce both genotype re-ranking and changes in variation of host performance along increasing ascites severity. Tolerance to ascites displayed significant genetic variance, with the estimated breeding values of tolerance slope ranging from strongly negative (very sensitive genotype) to weakly negative (less sensitive). Resistance to ascites had heritability of 0.34. Both traits are hence expected to respond to selection. The two complementary defense strategies, tolerance and resistance, were genetically independent. Ascites induced changes to the correlations between ascites resistance and body weight, with the genetic correlations being weak when birds were ascites-free but moderately negative when both healthy and affected birds were present. This likely results because ascites reduces growth, and thus high ascites incidence is genetically related to low adult body weight. Although ascites induced elevated phenotypic and genetic variances in body weight of affected birds, heritability displayed negligible changes across healthy and affected birds. Ascites induced moderate genotype re-ranking in body weight, with the genetic correlation of healthy birds with mildly affected birds being unity but with severely affected birds 0.45. This study demonstrates a novel approach for exploring genetics of defense traits and their impact on genotype-by-environment interactions.

Quantitative genetics of Taura syndrome resistance in Pacific white shrimp (Penaeus vannamei): a cure model approach

Background

In aquaculture breeding, resistance against infectious diseases is commonly assessed as time until death under exposure to a pathogen. For some diseases, a fraction of the individuals may appear as "cured" (non-susceptible), and the resulting survival time may thus be a result of two confounded underlying traits, i.e., endurance (individual hazard) and susceptibility (whether at risk or not), which may be accounted for by fitting a cure survival model. We applied a cure model to survival data of Pacific white shrimp (Penaeus vannamei) challenged with the Taura syndrome virus, which is one of the major pathogens of Panaeid shrimp species.

Methods

In total, 15,261 individuals of 513 full-sib families from three generations were challenge-tested in 21 separate tests (tanks). All challenge-tests were run until mortality naturally ceased. Time-until-event data were analyzed with a mixed cure survival model using Gibbs sampling, treating susceptibility and endurance as separate genetic traits.

Results

Overall mortality at the end of test was 28%, while 38% of the population was considered susceptible to the disease. The estimated underlying heritability was high for susceptibility (0.41 ± 0.07), but low for endurance (0.07 ± 0.03). Furthermore, endurance and susceptibility were distinct genetic traits (r_g = 0.22 ± 0.25). Estimated breeding values for endurance and susceptibility were only moderately correlated (0.50), while estimated breeding values from classical models for analysis of challenge-test survival (ignoring the cured fraction) were closely correlated with estimated breeding values for susceptibility, but less correlated with estimated breeding values for endurance.

Conclusions

For Taura syndrome resistance, endurance and susceptibility are apparently distinct genetic traits. However, genetic evaluation of susceptibility based on the cure model showed clear associations with standard genetic evaluations that ignore the cure fraction for these data. Using the current testing design, genetic variation in observed survival time and absolute survival at the end of test were most likely dominated by genetic variation in susceptibility. If the aim is to reduce susceptibility, earlier termination of the challenge-test or back-truncation of the follow-up period should be avoided, as this may shift focus of selection towards endurance rather than susceptibility.