Estimation of Mortality Rates for Disease Simulation Models Using Bayesian Evidence Synthesis

Bayesian road safety analysis: incorporation of past evidence and effect of hyper-prior choice

PROBLEM

This paper aims to address two related issues when applying hierarchical Bayesian models for road safety analysis, namely: (a) how to incorporate available information from previous studies or past experiences in the (hyper) prior distributions for model parameters and (b) what are the potential benefits of incorporating past evidence on the results of a road safety analysis when working with scarce accident data (i.e., when calibrating models with crash datasets characterized by a very low average number of accidents and a small number of sites).

METHOD

A simulation framework was developed to evaluate the performance of alternative hyper-priors including informative and non-informative Gamma, Pareto, as well as Uniform distributions. Based on this simulation framework, different data scenarios (i.e., number of observations and years of data) were defined and tested using crash data collected at 3-legged rural intersections in California and crash data collected for rural 4-lane highway segments in Texas.

RESULTS

This study shows how the accuracy of model parameter estimates (inverse dispersion parameter) is considerably improved when incorporating past evidence, in particular when working with the small number of observations and crash data with low mean. The results also illustrates that when the sample size (more than 100 sites) and the number of years of crash data is relatively large, neither the incorporation of past experience nor the choice of the hyper-prior distribution may affect the final results of a traffic safety analysis.

CONCLUSIONS

As a potential solution to the problem of low sample mean and small sample size, this paper suggests some practical guidance on how to incorporate past evidence into informative hyper-priors. By combining evidence from past studies and data available, the model parameter estimates can significantly be improved. The effect of prior choice seems to be less important on the hotspot identification.

IMPACT ON INDUSTRY

The results show the benefits of incorporating prior information when working with limited crash data in road safety studies.

Derivation of background mortality by smoking and obesity in cancer simulation models

BACKGROUND

Simulation models designed to evaluate cancer prevention strategies make assumptions on background mortality-the competing risk of death from causes other than the cancer being studied. Researchers often use the U.S. life tables and assume homogeneous other-cause mortality rates. However, this can lead to bias because common risk factors such as smoking and obesity also predispose individuals for deaths from other causes such as cardiovascular disease.

METHODS

We obtained calendar year-, age-, and sex-specific other-cause mortality rates by removing deaths due to a specific cancer from U.S. all-cause life tables. Prevalence across 12 risk factor groups (3 smoking [never, past, and current smoker] and 4 body mass index [BMI] categories [<25, 25-30, 30-35, 35+ kg/m(2)]) were estimated from national surveys (National Health and Nutrition Examination Surveys [NHANES] 1971-2004). Using NHANES linked mortality data, we estimated hazard ratios for death by BMI/smoking using a Poisson regression model. Finally, we combined these results to create 12 sets of BMI and smoking-specific other-cause life tables for U.S. adults aged 40 years and older that can be used in simulation models of lung, colorectal, or breast cancer.

RESULTS

We found substantial differences in background mortality when accounting for BMI and smoking. Ignoring the heterogeneity in background mortality in cancer simulation models can lead to underestimation of competing risk of deaths for higher-risk individuals (e.g., male, 60-year old, white obese smokers) by as high as 45%.

CONCLUSION

Not properly accounting for competing risks of death may introduce bias when using simulation modeling to evaluate population health strategies for prevention, screening, or treatment. Further research is warranted on how these biases may affect cancer-screening strategies targeted at high-risk individuals.

Chapter 3: Cohort life tables by smoking status, removing lung cancer as a cause of death

The purpose of this study was to develop life tables by smoking status removing lung cancer as a cause of death. These life tables are inputs to studies that compare the effectiveness of lung cancer treatments or interventions, and provide a way to quantify time until death from causes other than lung cancer. The study combined actuarial and statistical smoothing methods, as well as data from multiple sources, to develop separate life tables by smoking status, birth cohort, by single year of age, and by sex. For current smokers, separate life tables by smoking quintiles were developed based on the average number of cigarettes smoked per day by birth cohort. The end product is the creation of six non-lung-cancer life tables for males and six tables for females: five current smoker quintiles and one for never smokers. Tables for former smokers are linear combinations of the appropriate table based on the current smoker quintile before quitting smoking and the never smoker probabilities, plus added covariates for the smoking quit age and time since quitting.

Calibration of disease simulation model using an engineering approach

OBJECTIVES

Calibrating a disease simulation model's outputs to existing clinical data is vital to generate confidence in the model's predictive ability. Calibration involves two challenges: 1) defining a total goodness-of-fit (GOF) score for multiple targets if simultaneous fitting is required, and 2) searching for the optimal parameter set that minimizes the total GOF score (i.e., yields the best fit). To address these two prominent challenges, we have applied an engineering approach to calibrate a microsimulation model, the Lung Cancer Policy Model (LCPM).

METHODS

First, 11 targets derived from clinical and epidemiologic data were combined into a total GOF score by a weighted-sum approach, accounting for the user-defined relative importance of the calibration targets. Second, two automated parameter search algorithms, simulated annealing (SA) and genetic algorithm (GA), were independently applied to a simultaneous search of 28 natural history parameters to minimize the total GOF score. Algorithm performance metrics were defined for speed and model fit.

RESULTS

Both search algorithms obtained total GOF scores below 95 within 1000 search iterations. Our results show that SA outperformed GA in locating a lower GOF. After calibrating our LCPM, the predicted natural history of lung cancer was consistent with other mathematical models of lung cancer development.

CONCLUSION

An engineering-based calibration method was able to simultaneously fit LCPM output to multiple calibration targets, with the benefits of fast computational speed and reduced the need for human input and its potential bias.

Interpreting trial results in light of conflicting evidence: a Bayesian analysis of adjuvant chemotherapy for non-small-cell lung cancer

PURPOSE

When successive randomized trials contradict prior evidence, clinicians may be unsure how to evaluate them: Does accumulating evidence warrant changing practice? An increasingly popular solution, Bayesian statistics quantitatively evaluate new results in context. This study provides a clinically relevant example of Bayesian methods.

METHODS

Three recent non-small-cell lung cancer adjuvant chemotherapy trials were evaluated in light of prior conflicting data. Results were used from International Adjuvant Lung Trial (IALT), JBR.10, and Adjuvant Navelbine International Trialist Association (ANITA). Prior evidence was sequentially updated to calculate the probability of each survival benefit level (overall and by stage) and variance. Sensitivity analysis was performed using expert opinion and uninformed estimates of survival benefit prior probability.

RESULTS

The probability of a 4% survival benefit increased from 33% before IALT to 64% after IALT. After sequential updating with JBR.10 and ANITA, this probability was 82% (hazard ratio = 0.84; 95% CI, 0.77 to 0.91). IALT produced the largest decrease in variance (61%) and decreased the chance of survival decrement to 0%. Sensitivity analysis did not support a survival benefit after IALT. However, sequential updating substantiated a 4% survival benefit and, for stage II and III, more than 90% probability of a 6% benefit and 50% probability of a 12% benefit.

CONCLUSION

When evaluated in context with prior data, IALT did not support a 4% survival benefit. However, sequential updating with JBR.10 and ANITA did. A model for future assessments, this study demonstrates the unique ability of Bayesian analysis to evaluate results that contradict prior evidence.

Adopting helical CT screening for lung cancer: potential health consequences during a 15-year period

BACKGROUND

Simulation modeling can synthesize data from single-arm studies of lung cancer screening and tumor registries to investigate computed tomography (CT) screening. This study estimated changes in lung cancer outcomes through 2005, had chest CT screening been introduced in 1990.

METHODS

Hypothetical individuals with smoking histories representative of 6 US cohorts (white males and females aged 50, 60, and 70 years in 1990) were simulated in the Lung Cancer Policy Model, a comprehensive patient-level simulation model of lung cancer development, screening, and treatment. A no screening scenario corresponded to observed outcomes. We simulated 3 screening scenarios in current or former smokers with > or =20 pack-years as follows: 1-time screen in 1990; and annual, and twice-annually screenings beginning in 1990 and ending in 2005. Main outcomes were days of life between 1990 and 2005 and life expectancy in 1990 (estimated by simulating life histories past 2005).

RESULTS

All screening scenarios yielded reductions (compared with no screening) in lung cancer-specific mortality by 2005, with larger reductions predicted for more frequent screening. Compared with no screening, annual screening of ever-smokers with at least 20 pack-years of cigarette exposure provided ever-smokers with an additional 11 to 33 days of life by 2005, or an additional 3-10 weeks of (undiscounted) life expectancy. In sensitivity analyses, the largest effects on gains from annual screening were due to reductions in screening adherence and increased smoking cessation.

CONCLUSIONS

The adoption of CT screening, had it been available in 1990, might have resulted in a modest gain in life expectancy.

Estimating long-term effectiveness of lung cancer screening in the Mayo CT screening study

PURPOSE

To use individual-level data provided from the single-arm study of helical computed tomographic (CT) screening at the Mayo Clinic (Rochester, Minn) to estimate the long-term effectiveness of screening in Mayo study participants and to compare estimates from an existing lung cancer simulation model with estimates from a different modeling approach that used the same data.

MATERIALS AND METHODS

The study was approved by institutional review boards and was HIPAA compliant. Deidentified individual-level data from participants (1520 current or former smokers aged 50-85 years) in the Mayo Clinic helical CT screening study were used to populate the Lung Cancer Policy Model, a comprehensive microsimulation model of lung cancer development, screening findings, treatment results, and long-term outcomes. The model predicted diagnosed cases of lung cancer and deaths per simulated study arm (five annual screening examinations vs no screening). Main outcome measures were predicted changes in lung cancer-specific and all-cause mortality as functions of follow-up time after simulated enrollment and randomization.

RESULTS

At 6-year follow-up, the screening arm had an estimated 37% relative increase in lung cancer detection, compared with the control arm. At 15-year follow-up, five annual screening examinations yielded a 9% relative increase in lung cancer detection. The relative reduction in cumulative lung cancer-specific mortality from five annual screening examinations was 28% at 6-year follow-up (15% at 15 years). The relative reduction in cumulative all-cause mortality from five annual screening examinations was 4% at 6-year follow-up (2% at 15 years).

CONCLUSION

Screening may reduce lung cancer-specific mortality but may offer a smaller reduction in overall mortality because of increased competing mortality risks associated with smoking.

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.

Use of modeling to evaluate the cost-effectiveness of cancer screening programs

Cost-effectiveness analysis (CEA) is an analytic tool that provides a framework for comparing the health benefits and resource expenditures associated with competing medical and public health interventions, thereby allowing decision makers to identify interventions that yield the greatest amount of health, given their resource constraints. Models are important components of most, if not all, CEAs, and they play a key role in evaluating the cost-effectiveness of cancer screening programs, in particular. In this article, we describe the basic types of models used to evaluate cancer screening programs and provide examples of the use of models in CEAs and to guide cancer screening policy. Finally, we offer some suggestions for important concepts to consider when interpreting model results.