Comparison of a static cohort model and dynamic transmission model for respiratory syncytial virus intervention programs for infants in England and Wales.

BACKGROUND: A recent study comparing results of multiple cost-effectiveness analyses (CEAs) in a hypothetical population found that monoclonal antibody (mAb) immunoprophylaxis for respiratory syncytial virus (RSV) in infants averted fewer medically attended cases when estimated using dynamic transmission models (DTMs) versus static cohort models (SCMs). We aimed to investigate whether model calibration or parameterization could be the primary driver of inconsistencies between SCM and DTM predictions. METHODS: A recently published DTM evaluating the CEA of infant mAb immunoprophylaxis in England and Wales (EW) was selected as the reference model. We adapted our previously published SCM for US infants to EW by utilizing the same data sources used by the DTM. Both models parameterized mAb efficacy from a randomized clinical trial (RCT) that estimated an average efficacy of 74.5% against all medically attended RSV episodes and 62.1% against RSV hospitalizations. To align model assumptions, we modified the SCM to incorporate waning efficacy. Since the estimated indirect effects from the DTM were small (i.e., approximately 100-fold smaller in magnitude than direct effects), we hypothesized that alignment of model parameters should result in alignment of model predictions. Outputs for model comparison comprised averted hospitalizations and averted GP visits, estimated for seasonal (S) and seasonal-with-catchup (SC) immunization strategies. RESULTS: When we aligned the SCM intervention parameters to DTM intervention parameters, significantly more averted hospitalizations were predicted by the SCM (S: 32.3%; SC: 51.3%) than the DTM (S: 17.8%; SC: 28.6%). The SCM most closely replicated the DTM results when the initial efficacy of the mAb intervention was 62.1%, leading to an average efficacy of 39.3%. Under this parameterization the SCM predicted 17.4% (S) and 27.7% (SC) averted hospitalizations. Results were similar for averted GP visits. CONCLUSIONS: Parameterization of the RSV mAb intervention efficacy is a plausible primary driver of differences between SCM versus DTM model predictions.

Cost­Effectiveness Risk­Aversion Curves: Comparison of Risk-Adjusted Performance Measures and Expected-Utility Approaches.

Accounting for risk attitudes in medical decision making under uncertainty has attracted little research. A recent proposal recommended using the results of a cost-effectiveness analysis to construct a cost-effectiveness risk-aversion curve (CERAC) to inform risk-averse decision makers choosing among healthcare programs with uncertain costs and effects. The CERAC is based on a risk-adjusted performance measure widely used in financial economics called the Sortino ratio. This paper evaluates the CERAC based on the Sortino ratio, derives its various properties, discusses the implications of using it to inform decision making under uncertainty, and compares it with the expected-utility approach. Analytic formulae for the CERAC, relating it to the means and standard deviations of costs and effects of a healthcare program, are derived for both approaches. Compared with the expected-utility approach, the CERAC based on the Sortino ratio implicitly assumes that the decision maker is highly risk averse.

Vaccination and herd immunity thresholds in heterogeneous populations.

It has been suggested, without rigorous mathematical analysis, that the classical vaccine-induced herd immunity threshold (HIT) assuming a homogeneous population can be substantially higher than the minimum HIT obtained when considering population heterogeneities. We investigated this claim by developing, and rigorously analyzing, a vaccination model that incorporates various forms of heterogeneity and compared it with a model that considers a homogeneous population. By employing a two-group vaccination model in heterogeneous populations, we theoretically established conditions under which heterogeneity leads to different HIT values, depending on the relative values of the contact rates for each group, the type of mixing between the groups, the relative vaccine efficacy, and the relative population size of each group. For example, under biased random mixing assumption and when vaccinating a given group results in disproportionate prevention of higher transmission per capita, we show that it is optimal to vaccinate that group before vaccinating the other groups. We also found situations, under biased assortative mixing assumption, where it is optimal to vaccinate more than one group. We show that regardless of the form of mixing between the groups, the HIT values assuming a heterogeneous population are always lower than the HIT values obtained from a corresponding model with a homogeneous population. Using realistic numerical examples and parametrization (e.g., assuming assortative mixing together with vaccine efficacy of 95% and the value of the basic reproduction number, [Formula: see text], of the model set at [Formula: see text] 2.5), we demonstrate that the HIT value generated from a model that considers population heterogeneity (e.g., biased assortative mixing) is significantly lower (40%) compared with a HIT value of 63% obtained if the model uses homogeneous population.

Cost-effectiveness of routine catch-up hepatitis a vaccination in the United States: Dynamic transmission modeling study.

BACKGROUND: Despite routine vaccination of children against hepatitis A (HepA), a large segment of the United States population remains unvaccinated, imposing a risk of hepatitis A virus (HAV) to adolescents and adults. In July of 2020, the Advisory Committee on Immunization Practices recommended that all children and adolescents aged 2-18 years who have not previously received a HepA vaccine be vaccinated. We evaluated the public health impact and cost-effectiveness of this HepA catch-up vaccination strategy. METHODS: We used a dynamic transmission model to compare adding a HepA catch-up vaccination of persons age 2-18 years to a routine vaccination of children 12-23 months of age with routine vaccination only in the United States. The model included various health compartments: maternal antibodies, susceptible, exposed, asymptomatic infectious, symptomatic infectious (outpatient, hospitalized, liver transplant, post- liver transplant, death), recovered, and vaccinated with and without immunity. Using a 3% annual discount rate, we estimated the incremental cost per quality-adjusted life year (QALY) gained from a societal perspective over a 100-year time horizon. All costs were converted into 2020 US dollars. FINDINGS: Compared with the routine vaccination policy at 12-23 months of age over 100 years, the catch-up program for unvaccinated children and adolescents aged 2-18 years, prevented 70,072 additional symptomatic infections, 51,391 outpatient visits, 16,575 hospitalizations, and 413 deaths. The catch-up vaccination strategy was cost-saving when compared with the routine vaccination strategy. In scenario analysis allowing administering a second dose to partially vaccinated children, the cost-effectiveness of was not favorable at a higher vaccination coverage ($196,701/QALY at 5% and $476,241/QALY at 50%). INTERPRETATION: HepA catch-up vaccination in the United States is expected to reduce HepA morbidity and mortality and save cost. The catch-up program would be optimized when focusing on unvaccinated children and adolescents and maximizing their first dose coverage.

Mathematical assessment of the impact of cohort vaccination on pneumococcal carriage and serotype replacement.

Although pneumococcal vaccines are quite effective in reducing disease burden, factors such as imperfect vaccine efficacy and serotype replacement present an important challenge against realizing direct and herd protection benefits of the vaccines. In this study, a novel mathematical model is designed and used to describe the dynamics of two Streptococcus pneumoniae (SP) serotypes, in response to the introduction of a cohort vaccination program which targets one of the two serotypes. The model is fitted to a pediatric SP carriage prevalence data from Atlanta, GA. The model, which is rigorously analysed to investigate the existence and asymptotic stability properties of the associated equilibria (in addition to exploring conditions for competitive exclusion), is simulated to assess the impact of vaccination under different levels of serotype-specific competition and illustrate the phenomenon of serotype replacement. The calibrated model is used to forecast the carriage prevalence in the pediatric cohort over 30 years.

A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations.

The novel coronavirus (COVID-19) pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world. It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic. Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic. This study presents a primer for formulating, analysing and simulating mathematical models for understanding the dynamics of COVID-19. Specifically, we introduce simple compartmental, Kermack-McKendrick-type epidemic models with homogeneously- and heterogeneously-mixed populations, an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine. We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model. A brief overview of other kinds of models that have been used to study the dynamics of COVID-19, such as agent-based, network and statistical models, is also presented. Possible extensions of the basic model, as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics, are suggested.

Public health impact and cost effectiveness of routine and catch-up vaccination of girls and women with a nine-valent HPV vaccine in Japan: a model-based study.

BACKGROUND: Combined with cancer screening programs, vaccination against human papillomavirus (HPV) can significantly reduce the high health and economic burden of HPV-related disease in Japan. The objective of this study was to assess the health impact and cost effectiveness of routine and catch-up vaccination of girls and women aged 11-26 years with a 4-valent (4vHPV) or 9-valent HPV (9vHPV) vaccine in Japan compared with no vaccination. METHODS: We used a mathematical model adapted to the population and healthcare settings in Japan. We compared no vaccination and routine vaccination of 12-16-year old girls with 1) 4vHPV vaccine, 2) 9vHPV vaccine, and 3) 9vHPV vaccine in addition to a temporary catch-up vaccination of 17-26 years old girls and women with 9vHPV. We estimated the expected number of disease cases and deaths, discounted (at 2% per year) future costs (in 2020 ¥) and discounted quality-adjusted life years (QALY), and incremental cost effectiveness ratios (ICER) of each strategy over a time horizon of 100 years. To test the robustness of the conclusions, we conducted scenario and sensitivity analyses. RESULTS: Over 100 years, compared with no vaccination, 9vHPV vaccination was projected to reduce the incidence of 9vHPV-related cervical cancer by 86% (from 15.24 new cases per 100,000 women in 2021 to 2.02 in 2121). A greater number of cervical cancer cases (484,248) and cancer-related deaths (50,102) were avoided through the described catch-up vaccination program. Routine HPV vaccination with 4vHPV or 9vHPV vaccine prevented 5,521,000 cases of anogenital warts among women and men. Around 23,520 and 21,400 diagnosed non-cervical cancers are prevented by catch-up vaccination among women and men, respectively. Compared with no vaccination, the ICER of 4vHPV vaccination was ¥975,364/QALY. Compared to 4vHPV, 9vHPV + Catch-up had an ICER of ¥1,534,493/QALY. CONCLUSIONS: A vaccination program with a 9-valent vaccine targeting 12 to 16 year-old girls together with a temporary catchup program will avert significant numbers of cases of HPV-related diseases among both men and women. Furthermore, such a program was the most cost effective among the vaccination strategies we considered, with an ICER well below a threshold of ¥5000,000/QALY.

Correction to: Public health impact and cost effectiveness of routine childhood vaccination for hepatitis a in Jordan: a dynamic model approach.

Following publication of the original article1, the authors noted the following.

Alternative Conversion Methods for Transition Probabilities in State-Transition Models: Validity and Impact on Comparative Effectiveness and Cost-Effectiveness.

Background. In state-transition models (STMs), decision problems are conceptualized using health states and transitions among those health states after predefined time cycles. The naive, commonly applied method (C) for cycle length conversion transforms all transition probabilities separately. In STMs with more than 2 health states, this method is not accurate. Therefore, we aim to describe and compare the performance of method C with that of alternative matrix transformation methods. Design. We compare 2 alternative matrix transformation methods (Eigenvalue method [E], Schure-Padé method [SP]) to method C applied in an STM of 3 different treatment strategies for women with breast cancer. We convert the given annual transition matrix into a monthly-cycle matrix and evaluate induced transformation errors for the transition matrices and the long-term outcomes: life years, quality-adjusted life-years, costs and incremental cost-effectiveness ratios, and the performance related to the decisions. In addition, we applied these transformation methods to randomly generated annual transition matrices with 4, 7, 10, and 20 health states. Results. In theory, there is no generally applicable correct transformation method. Based on our simulations, SP resulted in the smallest transformation-induced discrepancies for generated annual transition matrices for 2 treatment strategies. E showed slightly smaller discrepancies than SP in the strategy, where one of the direct transitions between health states was excluded. For long-term outcomes, the largest discrepancy occurred for estimated costs applying method C. For higher dimensional models, E performs best. Conclusions. In our modeling examples, matrix transformations (E, SP) perform better than transforming all transition probabilities separately (C). Transition probabilities based on alternative conversion methods should therefore be applied in sensitivity analyses.

Projected impact of elbasvir/grazoprevir in patients with hepatitis C virus genotype 1 and chronic kidney disease in Vietnam.

BACKGROUND: Hepatitis C virus (HCV) infection is an important cause of morbidity and mortality in patients with chronic kidney disease (CKD). The objective of this study was to predict the impact of EBR/GZR on the incidence of liver and kidney related complications compared with no treatment (NoTx) and pegylated interferon plus ribavirin (pegIFN/RBV) in patients with CKD stage 4/5 in Vietnam. METHODS: We developed a mathematical model of the natural history of chronic HCV, CKD, and liver disease. Efficacy of EBR/GZR and pegIFN/RBV were derived from the C-SURFER trial and a meta-analysis, respectively. We calculated lifetime cumulative morbidity and mortality rates, including incidence of decompensated cirrhosis (DC), hepatocellular carcinoma (HCC), and life expectancy. RESULTS: Estimated lifetime incidence of DC was significantly reduced in patients receiving EBR/GZR (3.47%) compared to NoTx (18.14%) and pegIFN/RBV (9.01%). Estimated incidence of HCC was 1.02%, 21.64%, and 8.90%, and 1.02% in patients receiving EBR/GZR, NoTx, and pegIFN/RBV. EBR/GZR was estimated to extend life expectancy by 4.2 and 2.0 years compared with NoTx and pegIFN/RBV. CONCLUSIONS: Our model predicted that EBR/GZR will significantly reduce the incidence of liver-related complications and prolong life in patients with chronic HCV GT1 infection and CKD compared with NoTx or pegIFN/RBV.

Public health impact and cost effectiveness of routine childhood vaccination for hepatitis a in Jordan: a dynamic model approach.

BACKGROUND: As the socioeconomic conditions in Jordan have improved over recent decades the disease and economic burden of Hepatitis A has increased. The purpose of this study is to assess the potential health and economic impact of a two-dose hepatitis A vaccine program covering one-year old children in Jordan. METHODS: We adapted an age-structured population model of hepatitis A transmission dynamics to project the epidemiologic and economic impact of vaccinating one-year old children for 50 years in Jordan. The epidemiologic model was calibrated using local data on hepatitis A in Jordan. These data included seroprevalence and incidence data from the Jordan Ministry of Health as well as hospitalization data from King Abdullah University Hospital in Irbid, Jordan. We assumed 90% of all children would be vaccinated with the two-dose regimen by two years of age. The economic evaluation adopted a societal perspective and measured benefits using the quality-adjusted life-year (QALY). RESULTS: The modeled vaccination program reduced the incidence of hepatitis A in Jordan by 99%, 50 years after its introduction. The model projected 4.26 million avoided hepatitis A infections, 1.42 million outpatient visits, 22,475 hospitalizations, 508 fulminant cases, 95 liver transplants, and 76 deaths over a 50 year time horizon. In addition, we found, over a 50 year time horizon, the vaccination program would gain 37,502 QALYs and save over $42.6 million in total costs. The vaccination program became cost-saving within 6 years of its introduction and was highly cost-effective during the first 5 years. CONCLUSION: A vaccination program covering one-year old children is projected to be a cost-saving intervention that will significantly reduce the public health and economic burden of hepatitis A in Jordan.

Cost-Utility of Elbasvir/Grazoprevir in Patients with Chronic Hepatitis C Genotype 1 Infection.

OBJECTIVE: To evaluate the cost-utility of treatment with elbasvir/grazoprevir (EBR/GZR) regimens compared with ledipasvir/sofosbuvir (LDV/SOF), ombitasvir/paritaprevir/ritonavir + dasabuvir ± ribavirin (3D ± RBV), and sofosbuvir/velpatasvir (SOF/VEL) in patients with chronic hepatitis C genotype (GT) 1 infection. METHODS: A Markov cohort state-transition model was constructed to evaluate the cost-utility of EBR/GZR ± RBV over a lifetime time horizon from the payer perspective. The target population was patients infected with chronic hepatitis C GT1 subtypes a or b (GT1a or GT1b), stratified by treatment history (treatment-naive [TN] or treatment-experienced), presence of cirrhosis, baseline hepatitis C virus RNA (< or ≥6 million IU/mL), and presence of NS5A resistance-associated variants. The primary outcome was incremental cost-utility ratio for EBR/GZR ± RBV versus available oral direct-acting antiviral agents. One-way and probabilistic sensitivity analyses were performed to test the robustness of the model. RESULTS: EBR/GZR ± RBV was economically dominant versus LDV/SOF in all patient populations. EBR/GZR ± RBV was also less costly than SOF/VEL and 3D ± RBV, but produced fewer quality-adjusted life-years in select populations. In the remaining populations, EBR/GZR ± RBV was economically dominant. One-way sensitivity analyses showed varying sustained virologic response rates across EBR/GZR ± RBV regimens, commonly impacted model conclusions when lower bound values were inserted, and at the upper bound resulted in dominance over SOF/VEL in GT1a cirrhotic and GT1b TN noncirrhotic patients. Results of the probabilistic sensitivity analysis showed that EBR/GZR ± RBV was cost-effective in more than 99% of iterations in GT1a and GT1b noncirrhotic patients and more than 69% of iterations in GT1b cirrhotic patients. CONCLUSIONS: Compared with other oral direct-acting antiviral agents, EBR/GZR ± RBV was the economically dominant regimen for treating GT1a noncirrhotic and GT1b TN cirrhotic patients, and was cost saving in all other populations.

Verification of Decision-Analytic Models for Health Economic Evaluations: An Overview.

Decision-analytic models for cost-effectiveness analysis are developed in a variety of software packages where the accuracy of the computer code is seldom verified. Although modeling guidelines recommend using state-of-the-art quality assurance and control methods for software engineering to verify models, the fields of pharmacoeconomics and health technology assessment (HTA) have yet to establish and adopt guidance on how to verify health and economic models. The objective of this paper is to introduce to our field the variety of methods the software engineering field uses to verify that software performs as expected. We identify how many of these methods can be incorporated in the development process of decision-analytic models in order to reduce errors and increase transparency. Given the breadth of methods used in software engineering, we recommend a more in-depth initiative to be undertaken (e.g., by an ISPOR-SMDM Task Force) to define the best practices for model verification in our field and to accelerate adoption. Establishing a general guidance for verifying models will benefit the pharmacoeconomics and HTA communities by increasing accuracy of computer programming, transparency, accessibility, sharing, understandability, and trust of models.

Changing Cycle Lengths in State-Transition Models: Challenges and Solutions.

The choice of a cycle length in state-transition models should be determined by the frequency of clinical events and interventions. Sometimes there is need to decrease the cycle length of an existing state-transition model to reduce error in outcomes resulting from discretization of the underlying continuous-time phenomena or to increase the cycle length to gain computational efficiency. Cycle length conversion is also frequently required if a new state-transition model is built using observational data that have a different measurement interval than the model's cycle length. We show that a commonly used method of converting transition probabilities to different cycle lengths is incorrect and can provide imprecise estimates of model outcomes. We present an accurate approach that is based on finding the root of a transition probability matrix using eigendecomposition. We present underlying mathematical challenges of converting cycle length in state-transition models and provide numerical approximation methods when the eigendecomposition method fails. Several examples and analytical proofs show that our approach is more general and leads to more accurate estimates of model outcomes than the commonly used approach. MATLAB codes and a user-friendly online toolkit are made available for the implementation of the proposed methods.

Myths and Misconceptions of Within-Cycle Correction: A Guide for Modelers and Decision Makers.

Commonly used decision-analytic models for cost-effectiveness analysis simulate time in discrete steps. Use of discrete-time steps can introduce errors when calculating cumulative outcomes such as costs and quality-adjusted life-years. There are a number of myths or misconceptions concerning how to correct these errors and the need to do so. This tutorial shows that, by neglecting to apply within-cycle (sometimes referred to as half-cycle or continuity) correction methods to the results of discrete-time models, the analyst may arrive at the wrong recommendation regarding the use of a technology. We show that the standard half-cycle correction method results in the same cumulative outcome as the trapezoidal rule and life-table method. However, the trapezoidal rule has the added advantage of applying the correction at each cycle, not just the initial and final cycle. We further show that the Simpson's 1/3 rule is more accurate than the trapezoidal rule. We recommend using the Simpson's 1/3 rule in the base-case analysis and, if needed, showing the results with other methods in the sensitivity analysis. We also demonstrate that both the trapezoidal and Simpson's rules can easily be implemented in commonly used software.

The Impact of Enhanced Screening and Treatment on Hepatitis C in the United States.

BACKGROUND: The effectiveness of interferon-free direct-acting antivirals (DAA) in treating chronic hepatitis C virus (HCV) is limited by low screening and treatment rates, particularly among people who inject drugs (PWIDs). METHODS: To evaluate the levels of screening and treatment with interferon-free DAAs that are required to control HCV incidence and HCV-associated morbidity and mortality, we developed a transmission model, stratified by age and by injection drug use, and calibrated it to epidemiological data in the United States from 1992 to 2014. We quantified the impact of administration of DAAs at current and at enhanced screening and treatment rates, focusing on outcomes of HCV incidence, prevalence, compensated and decompensated cirrhosis, hepatocellular carcinoma, liver transplants, and mortality from 2015 to 2040. RESULTS: Increasing annual treatment of patients 4-fold-from the approximately 100 000 treated historically to 400 000-is predicted to prevent 526 084 (95% confidence interval, 466 615-593 347) cases of cirrhosis and 256 315 (201 589-316 114) HCV-associated deaths. By simultaneously increasing treatment capacity and increasing the number of HCV infections diagnosed, total HCV prevalence could fall to as low as 305 599 (222 955-422 110) infections by 2040. Complete elimination of HCV transmission in the United States through treatment with DAAs would require nearly universal screening of PWIDs, with an annual treatment rate of at least 30%. CONCLUSIONS: Interferon-free DAAs are projected to achieve marked reductions in HCV-associated morbidity and mortality. Aggressive expansion in HCV screening and treatment, particularly among PWIDs, would be required to eliminate HCV in the United States.

Theoretical Foundations and Practical Applications of Within-Cycle Correction Methods.

BACKGROUND: Modeling guidelines recommend applying a half-cycle correction (HCC) to outcomes from discrete-time state-transition models (DTSTMs). However, there is still no consensus on why and how to perform the correction. The objective was to provide theoretical foundations for HCC and to compare (both mathematically and numerically) the performance of different correction methods in reducing errors in outcomes from DTSTMs. METHODS: We defined 7 methods from the field of numerical integration: Riemann sum of rectangles (left, midpoint, right), trapezoids, life-table, and Simpson's 1/3rd and 3/8th rules. We applied these methods to a standard 3-state disease progression Markov chain to evaluate the cost-effectiveness of a hypothetical intervention. We solved the discrete- and continuous-time (our gold standard) versions of the model analytically and derived expressions for various outcomes including discounted quality-adjusted life-years, discounted costs, and incremental cost-effectiveness ratios. RESULTS: The standard HCC method gave the same results as the trapezoidal rule and life-table method. We found situations where applying the standard HCC can do more harm than good. Compared with the gold standard, all correction methods resulted in approximation errors. Contrary to conventional wisdom, the errors need not cancel each other out or become insignificant when incremental outcomes are calculated. We found that a wrong decision can be made with a less accurate method. The performance of each correction method vastly improved when a shorter cycle length was selected; Simpson's 1/3rd rule was the fastest method to converge to the gold standard. CONCLUSION: Cumulative outcomes in DTSTMs are prone to errors that can be reduced with more accurate methods like Simpson's rules. We clarified several misconceptions and provided recommendations and algorithms for practical implementation of these methods.

Public Health Impact and Cost-Effectiveness of Hepatitis A Vaccination in the United States: A Disease Transmission Dynamic Modeling Approach.

OBJECTIVE: To assess the population-level impact and cost-effectiveness of hepatitis A vaccination programs in the United States. METHODS: We developed an age-structured population model of hepatitis A transmission dynamics to evaluate two policies of administering a two-dose hepatitis A vaccine to children aged 12 to 18 months: 1) universal routine vaccination as recommended by the Advisory Committee on Immunization Practices in 2006 and 2) Advisory Committee on Immunization Practices's previous regional policy of routine vaccination of children living in states with high hepatitis A incidence. Inputs were obtained from the published literature, public sources, and clinical trial data. The model was fitted to hepatitis A seroprevalence (National Health and Nutrition Examination Survey II and III) and reported incidence from the National Notifiable Diseases Surveillance System (1980-1995). We used a societal perspective and projected costs (in 2013 US $), quality-adjusted life-years, incremental cost-effectiveness ratio, and other outcomes over the period 2006 to 2106. RESULTS: On average, universal routine hepatitis A vaccination prevented 259,776 additional infections, 167,094 outpatient visits, 4781 hospitalizations, and 228 deaths annually. Compared with the regional vaccination policy, universal routine hepatitis A vaccination was cost saving. In scenario analysis, universal vaccination prevented 94,957 infections, 46,179 outpatient visits, 1286 hospitalizations, and 15 deaths annually and had an incremental cost-effectiveness ratio of $21,223/quality-adjusted life-year when herd protection was ignored. CONCLUSIONS: Our model predicted that universal childhood hepatitis A vaccination led to significant reductions in hepatitis A mortality and morbidity. Consequently, universal vaccination was cost saving compared with a regional vaccination policy. Herd protection effects of hepatitis A vaccination programs had a significant impact on hepatitis A mortality, morbidity, and cost-effectiveness ratios.

Characterizing Heterogeneity Bias in Cohort-Based Models.

PURPOSE: Previous research using numerical methods suggested that use of a cohort-based model instead of an individual-based model can result in significant heterogeneity bias. However, the direction of the bias is not known a priori. We characterized mathematically the conditions that lead to upward or downward bias. METHOD: We used a standard three-state disease progression model to evaluate the cost effectiveness of a hypothetical intervention. We solved the model analytically and derived expressions for life expectancy, discounted quality-adjusted life years (QALYs), discounted lifetime costs and incremental net monetary benefits (INMB). An outcome was calculated using the mean of the input under the cohort-based approach and the whole input distribution for all persons under the individual-based approach. We investigated the impact of heterogeneity on outcomes by varying one parameter at a time while keeping all others constant. We evaluated the curvature of outcome functions and used Jensen's inequality to determine the direction of the bias. RESULTS: Both life expectancy and QALYs were underestimated by the cohort-based approach. If there was heterogeneity only in disease progression, total costs were overestimated, whereas QALYs gained, incremental costs and INMB were under- or overestimated, depending on the progression rate. INMB was underestimated when only efficacy was heterogeneous. Both approaches yielded the same outcome when the heterogeneity was only in cost or utilities. CONCLUSION: A cohort-based approach that does not adjust for heterogeneity underestimates life expectancy and may underestimate or overestimate other outcomes. Characterizing the bias is useful for comparative assessment of models and informing decision making.