Increasing the Efficiency of Monte Carlo Cohort Simulations with Variance Reduction Techniques

Comparison of Decision Modeling Approaches for Health Technology and Policy Evaluation

We discuss tradeoffs and errors associated with approaches to modeling health economic decisions. Through an application in pharmacogenomic (PGx) testing to guide drug selection for individuals with a genetic variant, we assessed model accuracy, optimal decisions, and computation time for an identical decision scenario modeled 4 ways: using 1) coupled-time differential equations (DEQ), 2) a cohort-based discrete-time state transition model (MARKOV), 3) an individual discrete-time state transition microsimulation model (MICROSIM), and 4) discrete event simulation (DES). Relative to DEQ, the net monetary benefit for PGx testing (v. a reference strategy of no testing) based on MARKOV with rate-to-probability conversions using commonly used formulas resulted in different optimal decisions. MARKOV was nearly identical to DEQ when transition probabilities were embedded using a transition intensity matrix. Among stochastic models, DES model outputs converged to DEQ with substantially fewer simulated patients (1 million) v. MICROSIM (1 billion). Overall, properly embedded Markov models provided the most favorable mix of accuracy and runtime but introduced additional complexity for calculating cost and quality-adjusted life year outcomes due to the inclusion of "jumpover" states after proper embedding of transition probabilities. Among stochastic models, DES offered the most favorable mix of accuracy, reliability, and speed.

Economic evaluations with agent-based modelling: an introduction

Agent-based modelling (ABM) is a relatively new technique, which overcomes some of the limitations of other methods commonly used for economic evaluations. These limitations include linearity, homogeneity and stationarity. Agents in ABMs are autonomous entities, who interact with each other and with the environment. ABMs provide an inductive or 'bottom-up' approach, i.e. individual-level behaviours define system-level components. ABMs have a unique property to capture emergence phenomena that otherwise cannot be predicted by the combination of individual-level interactions. In this tutorial, we discuss the basic concepts and important features of ABMs. We present a case study of an application of a simple ABM to evaluate the cost effectiveness of screening of an infectious disease. We also provide our model, which was developed using an open-source software program, NetLogo. We discuss software, resources, challenges and future research opportunities of ABMs for economic evaluations.

Using common random numbers in health care cost-effectiveness simulation modeling

OBJECTIVES

To identify the problem of separating statistical noise from treatment effects in health outcomes modeling and analysis. To demonstrate the implementation of one technique, common random numbers (CRNs), and to illustrate the value of CRNs to assess costs and outcomes under uncertainty.

METHODS

A microsimulation model was designed to evaluate osteoporosis treatment, estimating cost and utility measures for patient cohorts at high risk of osteoporosis-related fractures. Incremental cost-effectiveness ratios (ICERs) were estimated using a full implementation of CRNs, a partial implementation of CRNs, and no CRNs. A modification to traditional probabilistic sensitivity analysis (PSA) was used to determine how variance reduction can impact a decision maker's view of treatment efficacy and costs.

RESULTS

The full use of CRNs provided a 93.6 percent reduction in variance compared to simulations not using the technique. The use of partial CRNs provided a 5.6 percent reduction. The PSA results using full CRNs demonstrated a substantially tighter range of cost-benefit outcomes for teriparatide usage than the cost-benefits generated without the technique.

CONCLUSIONS

CRNs provide substantial variance reduction for cost-effectiveness studies. By reducing variability not associated with the treatment being evaluated, CRNs provide a better understanding of treatment effects and risks.

The DYNAMO-HIA Model: An Efficient Implementation of a Risk Factor/Chronic Disease Markov Model for Use in Health Impact Assessment (HIA)

In Health Impact Assessment (HIA), or priority-setting for health policy, effects of risk factors (exposures) on health need to be modeled, such as with a Markov model, in which exposure influences mortality and disease incidence rates. Because many risk factors are related to a variety of chronic diseases, these Markov models potentially contain a large number of states (risk factor and disease combinations), providing a challenge both technically (keeping down execution time and memory use) and practically (estimating the model parameters and retaining transparency). To meet this challenge, we propose an approach that combines micro-simulation of the exposure information with macro-simulation of the diseases and survival. This approach allows users to simulate exposure in detail while avoiding the need for large simulated populations because of the relative rareness of chronic disease events. Further efficiency is gained by splitting the disease state space into smaller spaces, each of which contains a cluster of diseases that is independent of the other clusters. The challenge of feasible input data requirements is met by including parameter calculation routines, which use marginal population data to estimate the transitions between states. As an illustration, we present the recently developed model DYNAMO-HIA (DYNAMIC MODEL for Health Impact Assessment) that implements this approach.

Assessing the relationship between computational speed and precision: a case study comparing an interpreted versus compiled programming language using a stochastic simulation model in diabetes care

BACKGROUND

Simulation techniques are well suited to modelling diseases yet can be computationally intensive. This study explores the relationship between modelled effect size, statistical precision, and efficiency gains achieved using variance reduction and an executable programming language.

METHODS

A published simulation model designed to model a population with type 2 diabetes mellitus based on the UKPDS 68 outcomes equations was coded in both Visual Basic for Applications (VBA) and C++. Efficiency gains due to the programming language were evaluated, as was the impact of antithetic variates to reduce variance, using predicted QALYs over a 40-year time horizon.

RESULTS

The use of C++ provided a 75- and 90-fold reduction in simulation run time when using mean and sampled input values, respectively. For a series of 50 one-way sensitivity analyses, this would yield a total run time of 2 minutes when using C++, compared with 155 minutes for VBA when using mean input values. The use of antithetic variates typically resulted in a 53% reduction in the number of simulation replications and run time required. When drawing all input values to the model from distributions, the use of C++ and variance reduction resulted in a 246-fold improvement in computation time compared with VBA - for which the evaluation of 50 scenarios would correspondingly require 3.8 hours (C++) and approximately 14.5 days (VBA).

CONCLUSIONS

The choice of programming language used in an economic model, as well as the methods for improving precision of model output can have profound effects on computation time. When constructing complex models, more computationally efficient approaches such as C++ and variance reduction should be considered; concerns regarding model transparency using compiled languages are best addressed via thorough documentation and model validation.

The impact of inpatient boarding on ED efficiency: a discrete-event simulation study

In this study, a discrete-event simulation approach was used to model Emergency Department's (ED) patient flow to investigate the effect of inpatient boarding on the ED efficiency in terms of the National Emergency Department Crowding Scale (NEDOCS) score and the rate of patients who leave without being seen (LWBS). The decision variable in this model was the boarder-released-ratio defined as the ratio of admitted patients whose boarding time is zero to all admitted patients. Our analysis shows that the Overcrowded(+) (a NEDOCS score over 100) ratio decreased from 88.4% to 50.4%, and the rate of LWBS patients decreased from 10.8% to 8.4% when the boarder-released-ratio changed from 0% to 100%. These results show that inpatient boarding significantly impacts both the NEDOCS score and the rate of LWBS patient and this analysis provides a quantification of the impact of boarding on emergency department patient crowding.

Improving the efficiency of physical examination services

The objective of our project was to improve the efficiency of the physical examination screening service of a large hospital system. We began with a detailed simulation model to explore the relationships between four performance measures and three decision factors. We then attempted to identify the optimal physician inquiry starting time by solving a goal-programming problem, where the objective function includes multiple goals. One of our simulation results shows that the proposed optimal physician inquiry starting time decreased patient wait times by 50% without increasing overall physician utilization.

Keeping the noise down: common random numbers for disease simulation modeling

Disease simulation models are used to conduct decision analyses of the comparative benefits and risks associated with preventive and treatment strategies. To address increasing model complexity and computational intensity, modelers use variance reduction techniques to reduce stochastic noise and improve computational efficiency. One technique, common random numbers, further allows modelers to conduct counterfactual-like analyses with direct computation of statistics at the individual level. This technique uses synchronized random numbers across model runs to induce correlation in model output thereby making differences easier to distinguish as well as simulating identical individuals across model runs. We provide a tutorial introduction and demonstrate the application of common random numbers in an individual-level simulation model of the epidemiology of breast cancer.

Modeling human papillomavirus and cervical cancer in the United States for analyses of screening and vaccination

Background

To provide quantitative insight into current U.S. policy choices for cervical cancer prevention, we developed a model of human papillomavirus (HPV) and cervical cancer, explicitly incorporating uncertainty about the natural history of disease.

Methods

We developed a stochastic microsimulation of cervical cancer that distinguishes different HPV types by their incidence, clearance, persistence, and progression. Input parameter sets were sampled randomly from uniform distributions, and simulations undertaken with each set. Through systematic reviews and formal data synthesis, we established multiple epidemiologic targets for model calibration, including age-specific prevalence of HPV by type, age-specific prevalence of cervical intraepithelial neoplasia (CIN), HPV type distribution within CIN and cancer, and age-specific cancer incidence. For each set of sampled input parameters, likelihood-based goodness-of-fit (GOF) scores were computed based on comparisons between model-predicted outcomes and calibration targets. Using 50 randomly resampled, good-fitting parameter sets, we assessed the external consistency and face validity of the model, comparing predicted screening outcomes to independent data. To illustrate the advantage of this approach in reflecting parameter uncertainty, we used the 50 sets to project the distribution of health outcomes in U.S. women under different cervical cancer prevention strategies.

Results

Approximately 200 good-fitting parameter sets were identified from 1,000,000 simulated sets. Modeled screening outcomes were externally consistent with results from multiple independent data sources. Based on 50 good-fitting parameter sets, the expected reductions in lifetime risk of cancer with annual or biennial screening were 76% (range across 50 sets: 69–82%) and 69% (60–77%), respectively. The reduction from vaccination alone was 75%, although it ranged from 60% to 88%, reflecting considerable parameter uncertainty about the natural history of type-specific HPV infection. The uncertainty surrounding the model-predicted reduction in cervical cancer incidence narrowed substantially when vaccination was combined with every-5-year screening, with a mean reduction of 89% and range of 83% to 95%.

Conclusion

We demonstrate an approach to parameterization, calibration and performance evaluation for a U.S. cervical cancer microsimulation model intended to provide qualitative and quantitative inputs into decisions that must be taken before long-term data on vaccination outcomes become available. This approach allows for a rigorous and comprehensive description of policy-relevant uncertainty about health outcomes under alternative cancer prevention strategies. The model provides a tool that can accommodate new information, and can be modified as needed, to iteratively assess the expected benefits, costs, and cost-effectiveness of different policies in the U.S.

Can discrete event simulation be of use in modelling major depression?

BACKGROUND

Depression is among the major contributors to worldwide disease burden and adequate modelling requires a framework designed to depict real world disease progression as well as its economic implications as closely as possible.

OBJECTIVES

In light of the specific characteristics associated with depression (multiple episodes at varying intervals, impact of disease history on course of illness, sociodemographic factors), our aim was to clarify to what extent "Discrete Event Simulation" (DES) models provide methodological benefits in depicting disease evolution.

METHODS

We conducted a comprehensive review of published Markov models in depression and identified potential limits to their methodology. A model based on DES principles was developed to investigate the benefits and drawbacks of this simulation method compared with Markov modelling techniques.

RESULTS

The major drawback to Markov models is that they may not be suitable to tracking patients' disease history properly, unless the analyst defines multiple health states, which may lead to intractable situations. They are also too rigid to take into consideration multiple patient-specific sociodemographic characteristics in a single model. To do so would also require defining multiple health states which would render the analysis entirely too complex. We show that DES resolve these weaknesses and that its flexibility allow patients with differing attributes to move from one event to another in sequential order while simultaneously taking into account important risk factors such as age, gender, disease history and patients attitude towards treatment, together with any disease-related events (adverse events, suicide attempt etc.).

CONCLUSION

DES modelling appears to be an accurate, flexible and comprehensive means of depicting disease progression compared with conventional simulation methodologies. Its use in analysing recurrent and chronic diseases appears particularly useful compared with Markov processes.