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Purpose: Individual-level simulation models often require sampling times to events, however efficient parametric distributions for many processes may often not exist. For example, time to death from life tables cannot be accurately sampled from existing parametric distributions. We propose an efficient nonparametric method to sample times to events that does not require any parametric assumption on the hazards. Methods: We developed a nonparametric sampling (NPS) approach that simultaneously draws multiple time-to-event samples from a categorical distribution. This approach can be applied to univariate and multivariate processes. The probabilities for each time interval are derived from the time interval-specific constant hazards. The times to events can then be used directly in individual-level simulation models. We compared the accuracy of our approach in sampling time-to-events from common parametric distributions, including exponential, Gamma, and Gompertz. In addition, we evaluated the method's performance in sampling age to death from US life tables and sampling times to events from parametric baseline hazards with time-dependent covariates. Results: The NPS method estimated similar expected times to events from 1 million draws for the three parametric distributions, 100,000 draws for the homogenous cohort, 200,000 draws from the heterogeneous cohort, and 1 million draws for the parametric distributions with time-varying covariates, all in less than a second. Conclusion: Our method produces accurate and computationally efficient samples for time-to-events from hazards without requiring parametric assumptions. This approach can substantially reduce the computation time required to simulate individual-level models.

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Decision models can combine information from different sources to simulate the long-term consequences of alternative strategies in the presence of uncertainty. A cohort state-transition model (cSTM) is a decision model commonly used in medical decision making to simulate the transitions of a hypothetical cohort among various health states over time. This tutorial focuses on time-independent cSTM, in which transition probabilities among health states remain constant over time. We implement time-independent cSTM in R, an open-source mathematical and statistical programming language. We illustrate time-independent cSTMs using a previously published decision model, calculate costs and effectiveness outcomes, and conduct a cost-effectiveness analysis of multiple strategies, including a probabilistic sensitivity analysis. We provide open-source code in R to facilitate wider adoption. In a second, more advanced tutorial, we illustrate time-dependent cSTMs.

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The use of open-source programming languages, such as R, in health decision sciences is growing and has the potential to facilitate model transparency, reproducibility, and shareability. However, realizing this potential can be challenging. Models are complex and primarily built to answer a research question, with model sharing and transparency relegated to being secondary goals. Consequently, code is often neither well documented nor systematically organized in a comprehensible and shareable approach. Moreover, many decision modelers are not formally trained in computer programming and may lack good coding practices, further compounding the problem of model transparency. To address these challenges, we propose a high-level framework for model-based decision and cost-effectiveness analyses (CEA) in R. The proposed framework consists of a conceptual, modular structure and coding recommendations for the implementation of model-based decision analyses in R. This framework defines a set of common decision model elements divided into five components: (1) model inputs, (2) decision model implementation, (3) model calibration, (4) model validation, and (5) analysis. The first four components form the model development phase. The analysis component is the application of the fully developed decision model to answer the policy or the research question of interest, assess decision uncertainty, and/or to determine the value of future research through value of information (VOI) analysis. In this framework, we also make recommendations for good coding practices specific to decision modeling, such as file organization and variable naming conventions. We showcase the framework through a fully functional, testbed decision model, which is hosted on GitHub for free download and easy adaptation to other applications. The use of this framework in decision modeling will improve code readability and model sharing, paving the way to an ideal, open-source world.

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