A Bayesian State-Transition Model-Based Approach to Estimate Transition Rates From Aggregated Survival Data
Author(s)
David U. Garibay Treviño, BA, MSc1, Alexandra Moskalewicz, M.Sc., B.Sc.2, Hawre Jalal, Ph.D.3, Petros Pechlivanoglou, Ph.D.2, Fernando Alarid-Escudero, Ph.D.4;
1University of Ottawa, School of Epidemiology and Public Health, Ottawa, ON, Canada, 2The Hospital for Sick Children Research Institute, Toronto, ON, Canada, 3University of Ottawa, Ottawa, ON, Canada, 4Stanford University, Stanford, CA, USA
1University of Ottawa, School of Epidemiology and Public Health, Ottawa, ON, Canada, 2The Hospital for Sick Children Research Institute, Toronto, ON, Canada, 3University of Ottawa, Ottawa, ON, Canada, 4Stanford University, Stanford, CA, USA
OBJECTIVES: Typically, trial publications only provide aggregated overall survival (OS) and progression-free survival (PFS) rates, and no access to IPD. We developed a state-transition model (STM)-based approach to estimate the rates of progression and progression-specific mortality from aggregate clinical trial survival data using Bayesian calibration methods.
METHODS: We developed a four-state, time-dependent STM specified in continuous-time tosimulate a hypothetical cohort of progression-free (PF) patients in discrete time. Individuals in the model face a progression rate that follows a Weibull distribution as a function of age. Those who progress (P) face a time-constant excess progression-specific mortality rate. Individuals in the PF and P states are also at risk of age-, and sex-specific mortality from other causes. The model derives the time-dependent transition probability matrix by solving the Kolmogorov equations. We estimated the shape and scale of the Weibull hazard dictating the cancer progression and the exponential cancer progression rates by calibrating the STM to OS and PFS from a clinical trial of adjuvant chemotherapy for colon cancer using Bayesian methods. We used the Incremental Mixture Importance Sampling (IMIS) algorithm to draw a sample of 1,000 parameter sets from the posterior distribution.
RESULTS: The expected survival times from the trial’s data were 5.76 for the OS and 5.0 years for the PFS. The model estimated survival times were 5.85 [95% Credible Interval (CrI): 5.64-6.06] years for OS and 5.01 [95% CrI: 4.75-5.25] for PFS. The time-dependent progression rate decreased over time, with estimated scale and shape parameters of the Weibull hazard of 1.50 [95% CrI: 0.50-2.50] and 0.45 [95% CrI: 0.25-0.65], respectively. The estimated progression- specific mortality rate was 0.59 [95% CrI: 0.42-0.76].
CONCLUSIONS: Our method estimates rates of disease progression and progression-specific mortality from aggregated survival data in the absence of IPD. This method can be adapted to STMs with similar structures.
METHODS: We developed a four-state, time-dependent STM specified in continuous-time tosimulate a hypothetical cohort of progression-free (PF) patients in discrete time. Individuals in the model face a progression rate that follows a Weibull distribution as a function of age. Those who progress (P) face a time-constant excess progression-specific mortality rate. Individuals in the PF and P states are also at risk of age-, and sex-specific mortality from other causes. The model derives the time-dependent transition probability matrix by solving the Kolmogorov equations. We estimated the shape and scale of the Weibull hazard dictating the cancer progression and the exponential cancer progression rates by calibrating the STM to OS and PFS from a clinical trial of adjuvant chemotherapy for colon cancer using Bayesian methods. We used the Incremental Mixture Importance Sampling (IMIS) algorithm to draw a sample of 1,000 parameter sets from the posterior distribution.
RESULTS: The expected survival times from the trial’s data were 5.76 for the OS and 5.0 years for the PFS. The model estimated survival times were 5.85 [95% Credible Interval (CrI): 5.64-6.06] years for OS and 5.01 [95% CrI: 4.75-5.25] for PFS. The time-dependent progression rate decreased over time, with estimated scale and shape parameters of the Weibull hazard of 1.50 [95% CrI: 0.50-2.50] and 0.45 [95% CrI: 0.25-0.65], respectively. The estimated progression- specific mortality rate was 0.59 [95% CrI: 0.42-0.76].
CONCLUSIONS: Our method estimates rates of disease progression and progression-specific mortality from aggregated survival data in the absence of IPD. This method can be adapted to STMs with similar structures.
Conference/Value in Health Info
2025-05, ISPOR 2025, Montréal, Quebec, CA
Value in Health, Volume 28, Issue S1
Code
P58
Topic
Methodological & Statistical Research
Disease
No Additional Disease & Conditions/Specialized Treatment Areas, SDC: Oncology