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

Purpose . The authors propose a Bayesian approach for estimating competing risks for inputs to disease simulation models. This approach is suggested when modeling a disease that causes a large proportion of all-cause mortality, particularly when mortality from the disease of interest and other-cause mortality are both affected by the same risk factor. Methods . The authors demonstrate a Bayesian evidence synthesis by estimating other-cause mortality, stratified by smoking status, for use in a simulation model of lung cancer. National (US) survey data linked to death registries (National Health Interview Survey [NHIS]—Multiple Cause of Death files) were used to fit cause-specific hazard models for 3 causes of death (lung cancer, heart disease, and all other causes), controlling for age, sex, race, and smoking status. Synthesis of NHIS data with national vital statistics data on numbers and causes of deaths was performed in WinBUGS (version 1.4.1, MRC Biostatistics Unit, UK). Correction for inconsistencies between the NHIS and vital statistics data is described. A published cohort study was a source of prior information for smoking-related mortality. Results . Marginal posterior densities of annual mortality rates for lung cancer and other-cause death (further divided into heart disease and all other causes), stratified by 5-year age interval, race (white and black), gender, and smoking status (current, former, never), were estimated, specific to a time period (1987-1995). Overall, black current smokers experienced the highest mortality rates. Conclusions . Bayesian evidence synthesis is an effective method for estimation of cause-specific mortality rates, stratified by demographic factors.

[1]  M. Joffe.  Using information on realized effects to determine prospective causal effects , 2001 .

[2]  A E Ades,et al.  Markov Chain Monte Carlo Estimation of a Multiparameter Decision Model: Consistency of Evidence and the Accurate Assessment of Uncertainty , 2002, Medical decision making : an international journal of the Society for Medical Decision Making.

[3]  Ross D. Shachter,et al.  An Introduction to a Bayesian Method for Meta-analysis , 1990, Medical decision making : an international journal of the Society for Medical Decision Making.

[4]  J. Enstrom.  Cancer and total mortality among active mormons , 1978, Cancer.

[5]  M Lunn,et al.  Applying Cox regression to competing risks. , 1995, Biometrics.

[6]  E. Pollack,et al.  What are the odds that smoking will kill you? , 1987, American journal of public health.

[7]  Peter Congdon.  Bayesian statistical modelling , 2002 .

[8]  J. Robins,et al.  Marginal Structural Models and Causal Inference in Epidemiology , 2000, Epidemiology.

[9]  C. Begg,et al.  Variations in lung cancer risk among smokers. , 2003, Journal of the National Cancer Institute.

[10]  Fei Gao,et al.  Age at diagnosis and the choice of survival analysis methods in cancer epidemiology. , 2003, Journal of clinical epidemiology.

[11]  A. Kopstein.  Tobacco Use in America: Findings From the 1999 National Household Survey on Drug Abuse , 2001 .

[12]  M J Buxton,et al.  Modelling in economic evaluation: an unavoidable fact of life. , 1997, Health economics.

[13]  H M Rosenberg,et al.  Comparability of cause of death between ICD-9 and ICD-10: preliminary estimates. , 2001, National vital statistics reports : from the Centers for Disease Control and Prevention, National Center for Health Statistics, National Vital Statistics System.

[14]  J. Samet.  The health benefits of smoking cessation. , 1991, The Medical clinics of North America.

[15]  Laurence L. George,et al.  The Statistical Analysis of Failure Time Data , 2003, Technometrics.

[16]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.

[17]  P. Allison.  Survival analysis using the SAS system : a practical guide , 1995 .

[18]  A E Ades,et al.  A chain of evidence with mixed comparisons: models for multi‐parameter synthesis and consistency of evidence , 2003, Statistics in medicine.

[19]  David J. Spiegelhalter,et al.  WinBUGS user manual version 1.4 , 2003 .

[20]  E. Arias,et al.  Deaths: final data for 2000. , 2002, National vital statistics reports : from the Centers for Disease Control and Prevention, National Center for Health Statistics, National Vital Statistics System.

[21]  M. Sculpher,et al.  Probabilistic sensitivity analysis for NICE technology assessment: not an optional extra. , 2005, Health economics.

[22]  David R. Jones,et al.  Hierarchical models in generalized synthesis of evidence: an example based on studies of breast cancer screening. , 2000, Statistics in medicine.

[23]  Massey Jt,et al.  Design and estimation for the National Health Interview Survey 1985-94. , 1989 .

[24]  D. Rubin.  The Bayesian Bootstrap , 1981 .

[25]  Hammond Ec,et al.  Smoking in relation to the death rates of one million men and women. , 1966 .

[26]  D. Kleinbaum,et al.  Applied Regression Analysis and Other Multivariate Methods , 1978 .

[27]  Mohamed M. Ali,et al.  Competing approaches to analysis of failure times with competing risks , 2001, Statistics in medicine.

[28]  David J Spiegelhalter,et al.  Bayesian approaches to multiple sources of evidence and uncertainty in complex cost‐effectiveness modelling , 2003, Statistics in medicine.

[29]  K R Abrams,et al.  Bayesian methods in meta-analysis and evidence synthesis. , 2001, Statistical methods in medical research.

[30]  T O Tengs,et al.  Public Health Impact of Changes in Smoking Behavior: Results From the Tobacco Policy Model , 2001, Medical care.

[31]  L. Russell,et al.  Modeling all-cause mortality: projections of the impact of smoking cessation based on the NHEFS. NHANES I Epidemiologic Follow-up Study. , 1998, American journal of public health.

[32]  Ross D. Shachter,et al.  A Bayesian Method for Synthesizing Evidence: The Confidence Profile Method , 1990, International Journal of Technology Assessment in Health Care.

[33]  Sharon L. Lohr,et al.  Sampling: Design and Analysis , 1999 .

[34]  P. V. Rao,et al.  Applied Survival Analysis: Regression Modeling of Time to Event Data , 2000 .

[35]  A. Gelfand,et al.  Identifiability, Improper Priors, and Gibbs Sampling for Generalized Linear Models , 1999 .

[36]  B. Carlin,et al.  Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models. , 2000, Statistics in medicine.

[37]  D. Mannino,et al.  Lung cancer deaths in the United States from 1979 to 1992: an analysis using multiple-cause mortality data. , 1998, International journal of epidemiology.

[38]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[39]  E L Korn,et al.  Applications of crude incidence curves. , 1992, Statistics in medicine.

[40]  K D Kochanek,et al.  Deaths: final data for 1999. , 2001, National vital statistics reports : from the Centers for Disease Control and Prevention, National Center for Health Statistics, National Vital Statistics System.

[41]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[42]  Richard Doll,et al.  Smoking, smoking cessation, and lung cancer in the UK since 1950: combination of national statistics with two case-control studies , 2000, BMJ : British Medical Journal.

[43]  E. Rogot,et al.  Smoking and causes of death among U.S. veterans: 16 years of observation. , 1980, Public health reports.

[44]  J Crowley,et al.  Estimation of failure probabilities in the presence of competing risks: new representations of old estimators. , 1999, Statistics in medicine.

[45]  M. Thun,et al.  Smoking vs other risk factors as the cause of smoking-attributable deaths: confounding in the courtroom. , 2000, JAMA.

[46]  J P Klein,et al.  Statistical methods for dependent competing risks , 1995, Lifetime data analysis.

[47]  F. Stenbäck,et al.  Relation between Clinical and Autopsy Diagnoses, Especially as Regards Cancer , 1980, Scandinavian journal of social medicine.

[48]  L. Breslow.  Some sequels to the Surgeon General's Report on Smoking and Health: thirty years later. , 1996, Annals of epidemiology.

[49]  K Abrams,et al.  A Bayesian approach to Weibull survival models—Application to a cancer clinical trial , 1996, Lifetime data analysis.

[50]  J. Robins,et al.  Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. , 2000, Epidemiology.

[51]  D. Schottenfeld,et al.  The autopsy as a measure of accuracy of the death certificate. , 1982, Bulletin of the New York Academy of Medicine.

[52]  L. Garfinkel.  Selection, follow-up, and analysis in the American Cancer Society prospective studies. , 1985, National Cancer Institute monograph.

[53]  B. McNeil,et al.  Probabilistic Sensitivity Analysis Using Monte Carlo Simulation , 1985, Medical decision making : an international journal of the Society for Medical Decision Making.

[54]  A. Whittemore,et al.  Reliability of recalled physical activity, cigarette smoking, and alcohol consumption. , 1992, Annals of epidemiology.