A hierarchical Bayesian model to predict the duration of immunity to Haemophilus influenzae type b

Elucidating the difference in the kinetics of antibody titres of infants in Belgium and Vietnam

Serological results obtained in a single laboratory from twin-studies on maternal immunisation, in Vietnam and Belgium offer the opportunity to compare antibody kinetics in infants before and after infant vaccination in the presence of vaccine-induced maternal antibodies. Nonlinear mixed-effects models (NLMMs) making use of a hypothesised dynamic evolution that captures the change in antibody titres over time, were employed to model anti-PT and anti-Prn antibody dynamics. Our proposed modelling approach provided useful insight into understanding the differences in the infants' antibody kinetics in both countries since NLMMs offer the possibility of pooling all data in one analysis and incorporate relevant covariates of interest. In both controlled cohort studies, pregnant women were vaccinated with a tetanus, diphtheria, acellular pertussis (Tdap) vaccine (Boostrix®, Belgium; Adacel®, Vietnam), and children were followed before and after primary vaccination, and before and after booster vaccination (Infanrix hexa®). From our models, both anti-PRN and anti-PT antibody titres at birth of Vietnamese infants were significantly lower than those of Belgian infants born to vaccinated women groups. Even though the antibody titres in the cord at birth of Belgian infants were also higher than those of Vietnamese infants born to the control women groups, the difference was not significant. The significant difference between infants born to vaccinated women in the two countries was likely due to the use of different vaccine brands in pregnant women and the different vaccination histories of women in these two countries. Our analyses also suggested that the blunting effect was present during the primary immunisation but went away afterward for anti-PT data. In contrast, for anti-PRN antibodies, the blunting effect persisted after the primary vaccination and possibly went away after the booster dose. Countries should be aware of the regional situation in view of recommending maternal immunization.

A dynamic Bayesian Markov model for health economic evaluations of interventions in infectious disease

BACKGROUND

Health economic evaluations of interventions in infectious disease are commonly based on the predictions of ordinary differential equation (ODE) systems or Markov models (MMs). Standard MMs are static, whereas ODE systems are usually dynamic and account for herd immunity which is crucial to prevent overestimation of infection prevalence. Complex ODE systems including distributions on model parameters are computationally intensive. Thus, mainly ODE-based models including fixed parameter values are presented in the literature. These do not account for parameter uncertainty. As a consequence, probabilistic sensitivity analysis (PSA), a crucial component of health economic evaluations, cannot be conducted straightforwardly.

METHODS

We present a dynamic MM under a Bayesian framework. We extend a static MM by incorporating the force of infection into the state allocation algorithm. The corresponding output is based on dynamic changes in prevalence and thus accounts for herd immunity. In contrast to deterministic ODE-based models, PSA can be conducted straightforwardly. We introduce a case study of a fictional sexually transmitted infection and compare our dynamic Bayesian MM to a deterministic and a Bayesian ODE system. The models are calibrated to simulated time series data.

RESULTS

By means of the case study, we show that our methodology produces outcome which is comparable to the "gold standard" of the Bayesian ODE system.

CONCLUSIONS

In contrast to ODE systems in the literature, the dynamic MM includes distributions on all model parameters at manageable computational effort (including calibration). The run time of the Bayesian ODE system is 15 times longer.

Dynamics of naturally acquired antibody against Haemophilus influenzae type a capsular polysaccharide in a Canadian Aboriginal population

Severe infections caused by Haemophilus influenzae type a (Hia) have reached alarming rates in some Canadian Aboriginal communities. We sought to estimate the frequency of exposure to this pathogen and timelines for boosting protective antibodies.

We developed a model of secondary antigenic challenge (natural exposure), and used data for anti-Hia antibodies in serum samples of healthy and immunocompromised adults in a population of Northwestern Ontario, Canada. We parameterized the model with available estimates from previous studies for the decay rate of antibody and its protective levels against both Hia carriage and invasive disease. Simulations were initialized using antibody concentrations from data. We investigated both the duration of immunity without secondary antigenic challenge and the average time between subsequent exposures to Hia.

When there was no new natural exposure, serum antibody concentrations in healthy Aboriginal individuals decreased below the level (1 μg/ml) assumed for protection against invasive Hia disease 3 years after primary exposure. This period was shorter (about 2 years) for Aboriginal individuals suffering from chronic renal failure. We estimated that a new antigenic challenge occurs once in 5 and 2 years for healthy and immunocompromised Aboriginal individuals, respectively. More frequent natural exposure was required to maintain protective antibody levels for non-Aboriginal individuals compared to Aboriginal individuals.

The findings suggest that frequent boosting of natural immunity is required to maintain the anti-Hia antibody levels protecting against invasive Hia disease, particularly in individuals with underlying medical conditions. This information has important implications for immunization when an anti-Hia vaccine becomes available.

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Frequent natural exposure to Hia is required to maintain protective immunity.

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Epigenetic factors may affect formation of natural immunity in Aboriginal people.

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Further data pertaining to immunological correlates of Hia are needed.

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Modeling can inform timelines of boosting immunity and vaccination policies.

Understanding and Governing Public Health Risks by Modeling

Increase in the use and development of computational tools to govern public health risks invites us to study their benefits and limitations. To analyze how risk is perceived and expressed through these tools is relevant to risk theory. This chapter clarifies the different concepts of risk, contrasting especially the mathematically expressed ones with culturally informed notions, which address a broader view on risk. I will suggest that a fruitful way to contextualize computational tools, such mathematical models in risk assessment is “analytics of risk,” which ties together the technological, epistemological, and political dimensions of the process of governance of risk. I will clarify the development of mathematical modeling techniques through their use in infectious disease epidemiology. Epidemiological modeling functions as a form of “risk calculation,” which provides predictions of the infectious outbreak in question. These calculations help direct and design preventive actions toward the health outcomes of populations. This chapter analyzes two cases in which modeling methods are used for explanation-based and scenario-building predictions in order to anticipate the risks of infections caused by Haemophilus influenzae type b bacteria and A(H1N1) pandemic influenza virus. I will address an interesting tension that arises when model-based estimates exemplify the population-level reasoning of public health risks but has restricted capacity to address risks on individual level. Analyzing this tension will lead to a fuller account to understand the benefits and limitations of computational tools in the governance of public health risks.

Never mind the length, feel the quality: the impact of long-term epidemiological data sets on theory, application and policy

Infectious diseases have been a prime testing ground for ecological theory. However, the ecological perspective is increasingly recognized as essential in epidemiology. Long-term, spatially resolved reliable data on disease incidence and the ability to test them using mechanistic models have been critical in this cross-fertilization. Here, we review some of the key intellectual developments in epidemiology facilitated by long-term data. We identify research frontiers at the interface of ecology and epidemiology and their associated data needs.

Seven items were identified for inclusion when reporting a Bayesian analysis of a clinical study

OBJECTIVE

(1) To generate a list of items that experts consider most important when reporting a Bayesian analysis of a clinical study, (2) to report on the extent to which we found these items in the literature, and (3) to identify factors related to the number of items in a report.

STUDY DESIGN AND SETTING

Based on opinions from 23 international experts, we determined the items considered most important when publishing a Bayesian analysis. We then performed a literature search to identify articles in which a Bayesian analysis was performed and determined the extent to which we found these items in each report. Finally, we examined the relationship between the number of items in a report and journal- and article-specific attributes.

RESULTS

Our final set of seven items described the prior distribution (specification, justification, and sensitivity analysis), analysis (statistical model and analytic technique), and presentation of results (central tendency and variance). There was >99% probability that more items were reported in studies with a noncontrolled study design and in journals with a methodological focus, lower impact factor, and absence of a word count limit.

CONCLUSION

We developed a set of seven items that experts believe to be most important when reporting a Bayesian analysis.

Long-term persistence of immunity after immunisation with Haemophilus influenzae type b conjugate vaccine

Although Haemophilus influenzae type b (Hib) conjugate vaccines, after licensure in 1987, are now recommended for world-wide use, the duration of protective immunity afforded by them is not known. We therefore assessed the immunogenity at 9-10 years of age in 37 children who had received the first Hib conjugate, PRP-D, in infancy (the Hib-conjugate group) and were now given a dose of Hib polysaccharide (PS) as a test vaccine. The anti-Hib PS antibodies (Hib-ab) were measured before and after this test vaccination, and the values compared to those in 37 control children who had not previously received any Hib vaccine and in 13 children who had received Hib PS vaccine in infancy (the Hib-PS group). Prior to the test vaccination, the Hib-ab concentrations in the Hib-conjugate group were 3.6-fold higher than in the control group. After the test vaccination, the Hib-conjugate group had higher total Hib-ab concentrations, higher proportion of IgG and higher avidity of Hib-ab than the control or the Hib-PS group, suggesting persisting immunological memory in a Hib-c group. A mathematical model, including memory, predicted accurately the Hib-ab concentrations, which are maintained through anamnestic responses to intervening stimuli (Hib or cross-reacting bacteria).

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

Cryptosporidium dose-response studies: variation between hosts

The issue of variation is highly important in dose-response analysis: variation among genetically related pathogens infecting the same host, but also variation among hosts, in susceptibility to infection by the same pathogen. This latter issue is addressed here for the protozoan parasite Cryptosporidium parvum, the causative agent for many outbreaks of water-borne gastrointestinal illness. In human feeding studies, infectivity has been shown to be low in subjects with high preexisting anti-Cryptosporidium IgG-levels. Here we adapt the hit theory model of microbial infection to incorporate covariables, characterizing the immune status of the susceptible host. The probability of any single oocyst in the inoculum to cause infection appears to depend on preexisting IgG-levels. This does not necessarily imply direct protection by the humoral immune system; high IgG-levels may reflect a recent episode of infection/illness, and be an epi-phenomenon associated with other protective responses. The IgG-dependence of the dose-response relation can be easily applied in quantitative risk analysis. The distribution of anti-Cryptosporidium IgG levels in the general population is accessible by analyzing serum banks, which are maintained in many Western countries. Using such an approach provides first insights into the variation of susceptibility to infection in the general population.

Bayesian inference on protective antibody levels using case-control data

In the study of immune responses to infectious pathogens, the minimum protective antibody concentration (MPAC) is a quantity of great interest. We use case-control data to estimate the posterior distribution of the conditional risk of disease given a lower bound on antibody concentration in an at-risk subject. The concentration bound beyond which there is high credibility that infection risk is zero or nearly so is a candidate for the MPAC. A very simple Gibbs sampling procedure that permits inference on the risk of disease given antibody level is presented. In problems involving small numbers of patients, the procedure is shown to have favorable accuracy and robustness to choice/misspecification of priors. Frequentist evaluation indicates good coverage probabilities of credibility intervals for antibody-dependent risk, and rules for estimation of the MPAC are illustrated with epidemiological data.

Back-calculating the age-specific incidence of recurrent subclinical Haemophilus influenzae type b infection

We consider the estimation of an age-specific incidence rate of a subclinical Haemophilus influenzae type b (Hib) infection from data recording the ages of children with a clinical Hib infection (Hib disease). The model is based on the assumption that the probability of being immune to clinical infection is determined by the time of the previous immunization caused by a subclinical infection, and by the distribution of the duration of immunity. We use a non-parametric Bayesian intensity model to arrive at smooth estimates of incidence rates. The estimated age-specific incidence rate of subclinical Hib infection is almost constant which indicates that the observed age-specific pattern of clinical Hib infection incidence is mainly due to immunity by either maternally derived antibodies or by immunizing subclinical infections. The estimated rate is relatively high, corresponding to one immunizing subclinical infection in less than two years.