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Time to event analytic methods for health economic evaluation

This session explores analytic methods for health economic evaluation, focusing on time to event (TTE) data analysis techniques. It covers challenges, model-based evaluations, data sources, and methods for various types of data. The presentation examines the state of the science for TTE analysis in cost-effectiveness analysis (CEA) and discusses guidelines and best practices. Different TTE methods for handling single, non-recurrent events, multiple outcomes, and time-varying exposures and confounding are reviewed, including semi-parametric and parametric models. Competing risks and methods for addressing them are also explored, along with adjusting hazards for recurrent events and handling time-dependent exposures and confounding. The use of marginal structural models in analyzing time-dependent exposures and confounding is discussed, alongside practical examples and the challenges of each method.

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Time to event analytic methods for health economic evaluation

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  1. Time to event analytic methods for health economic evaluation BohdanNosyk, PhD Associate Professor St. Paul’s Hospital Canfar Chair in HIV/AIDS Research Faculty of Health Sciences, Simon Fraser University Research Scientist, Health Economics Michael Smith Foundation for Health Research Scholar BC Centre for Excellence in HIV/AIDS

  2. Disclosure of conflicts of interest • None to declare

  3. Outline • Context & key challenge • State of the science for TTE analysis in CEA • Three techniques to address methodological challenges of TTE data • Next steps

  4. Context • Model-based health economic evaluation • Sculpher et al., Health Economics. 2006; 15: 677-87. • Applications in chronic disease • recurrent course • Multiple comobidities/outcomes • Problem: How do we estimate accurate transition probabilities in the presence of: • Competing risks • Recurrent events • Time-varying exposure, measured/unmeasured confounding • Cohort-based models: Allowance for time-dependence in transition probabilities • Markov model: • According to time in model • Within initial health state • Semi-Markov model: • According to time in model • Within initial health state • Within subsequent health states

  5. State of the science for TTE analysis in CEA • CEA ‘Best Practices’ guidelines: • Generally not specific in describing methods to deal with TTE data • Latimer et al (2014) review for TTE analysis: • Specific to extrapolation of (single episode, single outcome) RCT data • “Analyst should demonstrate that all standard parametric models (exponential, Weibull, Gompertz, log-logistic) have been considered and compared”. • Briggs, Sculpher and Claxton (2006) text: • Parametric (Weibull) regression model • Allows for time-dependence in transition probability • Regression-based approach can handle heterogeneity • Underlying theoretical distribution can be sampled from in PSA

  6. Data sources for CEA • Clinical trial data: • Limited duration, chronicity, recurrence likely to be inadequately captured • Published literature: • Sparse, incompatible outputs for CEA, limited external validity • Observational data: • Prospective cohort studies • Disease registries • Retrospective studies, based on health administrative databases (ie. treatment utilization) • Comparison of effectiveness of competing treatment regimens may be biased (endogeneity/selection bias)

  7. TTE methods for different forms of data • Standard: single, non-recurrent event • Semi-parametric: Cox Proportional Hazards (CPH) model • Parametric: Accelerated Failure Time models (exponential, Weibull, Gompertz) • Multiple outcomes • Semi-parametric: CPH Competing risks models (Cause-specific hazards, subdistribution hazards) • Semi-parametric: Multi-state Markov Models • Non-terminal, recurrent events • Semi-parametric: CPH frailty models • Time varying exposure, confounding • Semi-parametric: CPH model with time-varying covariates • Marginal structural models

  8. An important distinction among competing risks models cause-specific hazard: outcome: {duration, censor} subdistribution hazard: outcome: {duration, multinomial} csHR: (strong) assumption of independent competing risks required for valid inference Lau et al, Am J Epidemiol., 2009; 170: 244-56

  9. 1. Capturing competing risks • Multi-state Markov modeling: • Regression-based approach; • Can handle heterogeneity • Designed for multiple outcomes, continuous-time data • Outputs represent • subdistribution hazards CD4>500 • Nosyk et al, J Acquir Immune DeficSyndr. 2013;63(5):653-659. • Craig and Sendi, Health Econ. 2002; 11: 33-42. • R code: msm package: http://cran.r-project.org/web/packages/msm/index.html Death CD4: 350-499 Off ART: CD4: 350-499 CD4: 200-349 • Semi-parametric method: no direct means of handling time-dependence; • not useful for PSA • High dimensionality – problems with model convergence

  10. 2. Adjusting the hazard of TTE of successive ‘recurrent’ episodes CPH frailty model form: hij(t) = h0(t)vjexp(β’Zij) where vj~γ(1/θ, 1/θ) % 3rd episode: 2nd episode: 1st episode: • Mixed effects model; can adjust for unmeasured confounding that is fixed over time • Semi-parametric method; no accounting for time-dependence* • Cannot account for multiple outcomes t Time in health state Nosyk et al., Am J Epidemiol., 2009; 170 (6): 783-92. Nosyk et al., CMAJ, 2012; 84 (6): E317-28. R code: surv package: https://stat.ethz.ch/R-manual/R-patched/library/survival/html/Surv.html

  11. 3. Handling time-dependent exposure, confounding • Marginal Structural Models • Context: outcome can also be a predictor of exposure; other time-varying confounding • Effect of OST in standard GEE with time-varying covariates: • OR: 1.91 (1.68, 2.19) • Effect of OST in MSM model: • OR: 1.68 (1.48, 1.92) • Assumes no unmeasured confounding • Cannot account for multiple outcomes • Robins JM, Hernan MA, Brumback B. Epidemiology 2000;11:550 –560. • Nosyket al., AIDS. 2015. IN PRESS

  12. Next Steps • Continued methodological development in TTE analytic methods needed: • Parametric competing risks model • Jeong and Fine, Biostatistics 2007; 8(2): 184-96. • Competing risks CPH Frailty model • Kauermann& Khomski, 2006. R package ‘CompetingRiskFrailty’ no longer functional • Competing risks Marginal structural model • None available to date • Improved optimization algorithms for high-dimensional multi-state Markov models • How do differences, limitations in existing methods affect CEA results?

  13. Acknowledgements • BC-CfE Health Economics Team: Emanuel Krebs, Jeong Min, Michelle Olding, BatoolYazdani • UCLA Integrated Substance Abuse Programs; Centre for Advancing Longitudinal Drug Abuse (CALDAR) : Elizabeth Evans, Libo Li, Yih-IngHser • [NIDA Grant No. P30 DA016383] • Dr. Lei Liu, Northwestern University • An empirical investigation into recovery from illicit drug abuse using recurrent event analytic methods • [NIDA Grant No. R01-DA033424] • Addiction and Urban Health Research Unit (UHRI), BC-CfE • [NIDA Grant No. R01-DA011591, R01-DA021525, R01-DA028532] • Seek and Treat for Optimal Prevention of HIV/AIDS (STOP-HIV/AIDS) Program Evaluation • [BC Ministry of Health, Healthy Living and Sport]

  14. Questions, Comments? Thank you for your attention. Bohdan Nosyk: bnosyk@cfenet.ubc.ca

  15. State of the science for TTE analysis in CEA?

  16. State of the science for TTE analysis in CEA?

  17. State of the science for TTE analysis in CEA?

  18. State of the science for TTE analysis in CEA?

  19. State of the science for TTE analysis in CEA?

  20. Nosyk et al, CMAJ. 2012; 184(6):E317-28.

  21. The primary finding of this study was that patients experiencing multiple treatment episodes tended to stay in treatment for progressively longer periods in later episodes. Nosyk et al, Am J Epidemiol. 2009; 170(6):783-92.

  22. Cycle=3 Death Death DAM1 MMT3 Relapse3 Abstinence Relapse3 Abstinence Cycle, j=4-6 MMTj DAMj-2 Decision Analytic Model Allocated to MMT Allocated to DAM MMT-PD3

  23. Model parameterization • Supplemented trial TTE data with external data: BC linked health database • Estimated weibull regressions to extrapolate TTE data • Implemented by making use of R’s functionality with multi-dimensional arrays described by Hawkins, Sculpher and Epstein (2005) in order to program time dependence within each of the model states • Multiplied adjusted hazards for episode j with adjusted hazard ratios, drawn from frailty models, for durations of episodes j+k • Adjusted for age, gender, state-specific mortality risks • Assumed dirichlet distribution for transitions to multiple states

  24. Impact of changing distributional assumption on TTE curves *Gamma distributions set for time to discontinuation of each health state.

  25. CPH Frailty models demonstrated durations of daily use diminished in Successive episodes over time. MSM models revealed primary stimulant users had more erratic longitudinal patterns of drug use, transitioning more Rapidly between periods of treatment, abstinence, non-daily and daily use. Nosyk et al., Drug Alcohol Depend. 2014; 140: 69-77.

  26. 1. Capturing competing risks (option b) Parametric regression methods for competing risks: Cumulative incidence functions for 2 competing risks: Probability of having Syncitium-inducing (SI) HIV phenotype AIDS+SI Probability of developing AIDS • Allows for time-dependent transition probabilities, heterogeneity and competing risks; • Only basic control of baseline confounders Putter H, Fiocco M, Geskus B. Stat Med. 2007; 26:2389-2430. Jeong J-H, Fine JP. Biostatistics. 2007; 8(2): 184-96.

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