Quantifying Parameter and Structural Uncertainty of Dynamic Disease Transmission Models Using MCMC: An Application to Rotavirus Vaccination in England and Wales

Cost-effectiveness of monoclonal antibody and maternal immunization against respiratory syncytial virus (RSV) in infants: Evaluation for six European countries

BACKGROUND

Respiratory syncytial virus (RSV) imposes a substantial burden on pediatric hospital capacity in Europe. Promising prophylactic interventions against RSV including monoclonal antibodies (mAb) and maternal immunizations (MI) are close to licensure. Therefore, we aimed to evaluate the cost-effectiveness of potential mAb and MI interventions against RSV in infants, for six European countries.

METHODS

We used a static cohort model to compare costs and health effects of four intervention programs to no program and to each other: year-round MI, year-round mAb, seasonal mAb (October to April), and seasonal mAb plus a catch-up program in October. Input parameters were obtained from national registries and literature. Influential input parameters were identified with the expected value of partial perfect information and extensive scenario analyses (including the impact of interventions on wheezing and asthma).

RESULTS

From the health care payer perspective, and at a price of €50 per dose (mAb and MI), seasonal mAb plus catch-up was cost-saving in Scotland, and cost-effective for willingness-to-pay (WTP) values ≥€20,000 (England, Finland) or €30,000 (Denmark) per quality adjusted life-year (QALY) gained for all scenarios considered, except when using ICD-10 based hospitalization data. For the Netherlands, seasonal mAb was preferred (WTP value: €30,000-€90,000) for most scenarios. For Veneto region (Italy), either seasonal mAb with or without catch-up or MI was preferred, depending on the scenario and WTP value. From a full societal perspective (including leisure time lost), the seasonal mAb plus catch-up program was cost-saving for all countries except the Netherlands.

CONCLUSION

The choice between a MI or mAb program depends on the level and duration of protection, price, availability, and feasibility of such programs, which should be based on the latest available evidence. Future research should focus on measuring accurately age-specific RSV-attributable hospitalizations in very young children.

Quantifying Uncertainty in Mechanistic Models of Infectious Disease

This primer describes the statistical uncertainty in mechanistic models and provides R code to quantify it. We begin with an overview of mechanistic models for infectious disease, and then describe the sources of statistical uncertainty in the context of a case study on SARS-CoV-2. We describe the statistical uncertainty as belonging to three categories: data uncertainty, stochastic uncertainty, and structural uncertainty. We demonstrate how to account for each of these via statistical uncertainty measures and sensitivity analyses broadly, as well as in a specific case study on estimating the basic reproductive number, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${R}_0$\end{document}, for SARS-CoV-2.

The importance of accounting for the uncertainty around the preference-based health-related quality-of-life measures value sets: a systematic review

Preference-based measures of health-related quality-of-life including, but not limited to, the EQ-5D, HUI2 and the SF-6D have been increasingly used in calculations of quality-adjusted life years for cost effectiveness analyses. However, the uncertainty around the measures' value sets is commonly ignored in economic evaluation. There are several types of uncertainties, including methodological, structural, and parameter uncertainties, with the latter being the focus of this review paper. The objective is to highlight the gap in the literature regarding the existence of uncertainty in the value sets, focusing mainly on the EQ-5D and SF-6D. To the best of the authors' knowledge, this is the first systematic review revolving around uncertainty. After searching extensively for studies involving uncertainties in all preference-based measures, the results showed that uncertainty has been approached through different means, while parameter uncertainty has been ignored in most, if not all, cases. These findings suggest that uncertainty should be accounted for when using preference-based measures in economic evaluations. Ignoring this additional information could impact misleadingly on policy decisions.

Quantitative Microbial Risk Assessment and Infectious Disease Transmission Modeling of Waterborne Enteric Pathogens

PURPOSE OF REVIEW

Waterborne enteric pathogens remain a global health threat. Increasingly, quantitative microbial risk assessment (QMRA) and infectious disease transmission modeling (IDTM) are used to assess waterborne pathogen risks and evaluate mitigation. These modeling efforts, however, have largely been conducted independently for different purposes and in different settings. In this review, we examine the settings where each modeling strategy is employed.

RECENT FINDINGS

QMRA research has focused on food contamination and recreational water in high-income countries (HICs) and drinking water and wastewater in low- and middle-income countries (LMICs). IDTM research has focused on large outbreaks (predominately LMICs) and vaccine-preventable diseases (LMICs and HICs). Human ecology determines the niches that pathogens exploit, leading researchers to focus on different risk assessment research strategies in different settings. To enhance risk modeling, QMRA and IDTM approaches should be integrated to include dynamics of pathogens in the environment and pathogen transmission through populations.

Nonidentifiability in Model Calibration and Implications for Medical Decision Making

BACKGROUND

Calibration is the process of estimating parameters of a mathematical model by matching model outputs to calibration targets. In the presence of nonidentifiability, multiple parameter sets solve the calibration problem, which may have important implications for decision making. We evaluate the implications of nonidentifiability on the optimal strategy and provide methods to check for nonidentifiability.

METHODS

We illustrate nonidentifiability by calibrating a 3-state Markov model of cancer relative survival (RS). We performed 2 different calibration exercises: 1) only including RS as a calibration target and 2) adding the ratio between the 2 nondeath states over time as an additional target. We used the Nelder-Mead (NM) algorithm to identify parameter sets that best matched the calibration targets. We used collinearity and likelihood profile analyses to check for nonidentifiability. We then estimated the benefit of a hypothetical treatment in terms of life expectancy gains using different, but equally good-fitting, parameter sets. We also applied collinearity analysis to a realistic model of the natural history of colorectal cancer.

RESULTS

When only RS is used as the calibration target, 2 different parameter sets yield similar maximum likelihood values. The high collinearity index and the bimodal likelihood profile on both parameters demonstrated the presence of nonidentifiability. These different, equally good-fitting parameter sets produce different estimates of the treatment effectiveness (0.67 v. 0.31 years), which could influence the optimal decision. By incorporating the additional target, the model becomes identifiable with a collinearity index of 3.5 and a unimodal likelihood profile.

CONCLUSIONS

In the presence of nonidentifiability, equally likely parameter estimates might yield different conclusions. Checking for the existence of nonidentifiability and its implications should be incorporated into standard model calibration procedures.

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.

The Importance of Model Structure in the Cost-Effectiveness Analysis of Primary Care Interventions for the Management of Hypertension

BACKGROUND

Management of hypertension can lead to significant reductions in blood pressure, thereby reducing the risk of cardiovascular disease. Modeling the course of cardiovascular disease is not without complications, and uncertainty surrounding the structure of a model will almost always arise once a choice of a model structure is defined.

OBJECTIVES

To provide a practical illustration of the impact on the results of cost-effectiveness of changing or adapting model structures in a previously published cost-utility analysis of a primary care intervention for the management of hypertension Targets and Self-Management for the Control of Blood Pressure in Stroke and at Risk Groups (TASMIN-SR).

METHODS

The case study assessed the structural uncertainty arising from model structure and from the exclusion of secondary events. Four alternative model structures were implemented. Long-term cost-effectiveness was estimated and the results compared with those from the TASMIN-SR model.

RESULTS

The main cost-effectiveness results obtained in the TASMIN-SR study did not change with the implementation of alternative model structures. Choice of model type was limited to a cohort Markov model, and because of the lack of epidemiological data, only model 4 captured structural uncertainty arising from the exclusion of secondary events in the case study model.

CONCLUSIONS

The results of this study indicate that the main conclusions drawn from the TASMIN-SR model of cost-effectiveness were robust to changes in model structure and the inclusion of secondary events. Even though one of the models produced results that were different to those of TASMIN-SR, the fact that the main conclusions were identical suggests that a more parsimonious model may have sufficed.

Sustained low rotavirus activity and hospitalisation rates in the post-vaccination era in Belgium, 2007 to 2014

In 2006, Belgium was the first country in the European Union to recommend rotavirus vaccination in the routine infant vaccination schedule and rapidly achieved high vaccine uptake (86-89% in 2007). We used regional and national data sources up to 7 years post-vaccination to study the impact of vaccination on laboratory-confirmed rotavirus cases and rotavirus-related hospitalisations and deaths. We showed that (i) from 2007 until 2013, vaccination coverage remained at 79-88% for a complete course, (ii) in children 0-2 years, rotavirus cases decreased by 79% (95% confidence intervals (CI): 68--89%) in 2008-2014 compared to the pre-vaccination period (1999--2006) and by 50% (95% CI: 14-82%) in the age group ≥ 10 years, (iii) hospitalisations for rotavirus gastroenteritis decreased by 87% (95% CI: 84-90%) in 2008--2012 compared to the pre-vaccination period (2002--2006), (iv) median age of rotavirus cases increased from 12 months to 17 months and (v) the rotavirus seasonal peak was reduced and delayed in all post-vaccination years. The substantial decline in rotavirus gastroenteritis requiring hospitalisations and in rotavirus activity following introduction of rotavirus vaccination is sustained over time and more pronounced in the target age group, but with evidence of herd immunity.

Risk stratification in compartmental epidemic models: Where to draw the line?

Economic evaluations of infectious disease control interventions frequently use dynamic compartmental epidemic models. Such models capture heterogeneity in risk of infection by stratifying the population into discrete risk groups, thus approximating what is typically continuous variation in risk. An important open question is whether and how different risk stratification choices influence model predictions of intervention effects. We develop equivalent Susceptible-Infected-Susceptible (SIS) dynamic transmission models: an unstratified model, a model stratified into a high-risk and low-risk group, and a model with an arbitrary number of risk groups. Absent intervention, the models produce the same overall prevalence of infected individuals in steady state. We consider an intervention that either reduces the contact rate or increases the disease clearance rate. We develop analytical and numerical results characterizing the models and the effects of the intervention. We find that there exist multiple feasible choices of risk stratification, contact distribution, and within- and between-group contact rates for models that stratify risk. We show analytically and empirically that these choices can generate different estimates of intervention effectiveness, and that these differences can be significant enough to alter conclusions from cost-effectiveness analyses and change policy recommendations. We conclude that the choice of how to discretize risk in compartmental epidemic models can influence predicted effectiveness of interventions. Therefore, analysts should examine multiple alternatives and report the range of results.

Did Large-Scale Vaccination Drive Changes in the Circulating Rotavirus Population in Belgium?

Vaccination can place selective pressures on viral populations, leading to changes in the distribution of strains as viruses evolve to escape immunity from the vaccine. Vaccine-driven strain replacement is a major concern after nationwide rotavirus vaccine introductions. However, the distribution of the predominant rotavirus genotypes varies from year to year in the absence of vaccination, making it difficult to determine what changes can be attributed to the vaccines. To gain insight in the underlying dynamics driving changes in the rotavirus population, we fitted a hierarchy of mathematical models to national and local genotype-specific hospitalization data from Belgium, where large-scale vaccination was introduced in 2006. We estimated that natural- and vaccine-derived immunity was strongest against completely homotypic strains and weakest against fully heterotypic strains, with an intermediate immunity amongst partially heterotypic strains. The predominance of G2P[4] infections in Belgium after vaccine introduction can be explained by a combination of natural genotype fluctuations and weaker natural and vaccine-induced immunity against infection with strains heterotypic to the vaccine, in the absence of significant variation in strain-specific vaccine effectiveness against disease. However, the incidence of rotavirus gastroenteritis is predicted to remain low despite vaccine-driven changes in the distribution of genotypes.

Estimating dynamic transmission model parameters for seasonal influenza by fitting to age and season-specific influenza-like illness incidence

Dynamic transmission models are essential to design and evaluate control strategies for airborne infections. Our objective was to develop a dynamic transmission model for seasonal influenza allowing to evaluate the impact of vaccinating specific age groups on the incidence of infection, disease and mortality. Projections based on such models heavily rely on assumed 'input' parameter values. In previous seasonal influenza models, these parameter values were commonly chosen ad hoc, ignoring between-season variability and without formal model validation or sensitivity analyses. We propose to directly estimate the parameters by fitting the model to age-specific influenza-like illness (ILI) incidence data over multiple influenza seasons. We used a weighted least squares (WLS) criterion to assess model fit and applied our method to Belgian ILI data over six influenza seasons. After exploring parameter importance using symbolic regression, we evaluated a set of candidate models of differing complexity according to the number of season-specific parameters. The transmission parameters (average R0, seasonal amplitude and timing of the seasonal peak), waning rates and the scale factor used for WLS optimization, influenced the fit to the observed ILI incidence the most. Our results demonstrate the importance of between-season variability in influenza transmission and our estimates are in line with the classification of influenza seasons according to intensity and vaccine matching.