Using Age-Specific Rates for Parametric Survival Function Estimation in Simulation Models

Abstract

Purpose To describe a procedure for incorporating parametric functions into individual-level simulation models to sample time to event when age-specific rates are available but not the individual data. Methods Using age-specific event rates, regression analysis was used to parametrize parametric survival distributions (Weibull, Gompertz, log-normal, and log-logistic), select the best fit using the R2 statistic, and apply the corresponding formula to assign random times to events in simulation models. We used stroke rates in the Spanish population to illustrate our procedure. Results The 3 selected survival functions (Gompertz, Weibull, and log-normal) had a good fit to the data up to 85 y of age. We selected Gompertz distribution as the best-fitting distribution due to its goodness of fit. Conclusions Our work provides a simple procedure for incorporating parametric risk functions into simulation models without individual-level data. Highlights We describe the procedure for sampling times to event for individual-level simulation models as a function of age from parametric survival functions when age-specific rates are available but not the individual data We used linear regression to estimate age-specific hazard functions, obtaining estimates of parameter uncertainty. Our approach allows incorporating parameter (second-order) uncertainty in individual-level simulation models needed for probabilistic sensitivity analysis in the absence of individual-level survival data.

A computationally efficient nonparametric sampling (NPS) method of time to event for individual-level models

“…The cumulative distribution function (CDF) of 𝑇 at time 𝑡, 𝐹 ! , is (2) where 𝛥𝑡 represents representing the time interval, defined above. For example, if the hazards are on a yearly scale and we want to sample monthly time-to-event data, we use, 𝛥𝑡 = % %& , and when the samples are in years, we use 𝛥𝑡 = 1.…”

“…In DES models, time-to-event data following a nonconstant hazard could be sampled from parametric distributions. 2 However, some events cannot be easily described by parametric distributions. For example, life tables, or events following hazards that are a function of time-varying covariates, such as smoking histories or tumor size, do not always follow standard parametric distributions.…”