Supplementary figures: Improved estimation of overall survival and progression-free survival for state transition modeling

These are peer-reviewed supplementary figures for the article 'Improved estimation of overall survival and progression-free survival for state transition modeling' published in the Journal of Comparative Effectiveness Research. Figure S1: Standard approach: Overview of distributions by health state transitionsFigure S2: Novel approach: Overview of distributions by health state transitionsAim: National Institute for Health and Care Excellence guidance (Technical Support Document 19) highlights a key challenge of state transition models (STMs) being their difficulty in achieving a satisfactory fit to the observed within-trial endpoints. Fitting poorly to data over the trial period can then have implications for long-term extrapolations. A novel estimation approach is defined in which the predicted overall survival (OS) and progression-free survival (PFS) extrapolations from an STM are optimized to provide closer estimates of the within-trial endpoints. Materials & methods: An STM was fitted to the SQUIRE trial data in non-small-cell lung cancer (obtained from Project Data Sphere). Two methods were used: a standard approach whereby the maximum likelihood was utilized for the individual transitions and the best-fitting parametric model selected based on AIC/BIC, and a novel approach in which parameters were optimized by minimizing the area between the STM-predicted OS and PFS curves and the corresponding OS and PFS Kaplan–Meier curves. Sensitivity analyses were conducted to assess uncertainty. Results: The novel approach resulted in closer estimations to the OS and PFS Kaplan–Meier for all combinations of parametric distributions analyzed compared with the standard approach. Though the uncertainty associated with the novel approach was slightly larger, it provided better estimates to the restricted mean survival time in 10 of the 12 parametric distributions analyzed. Conclusion: A novel approach is defined which provides an alternative STM estimation method enabling improved fits to modeled endpoints, which can easily be extended to more complex model structures.

本数据集为发表于《比较效果研究杂志》（Journal of Comparative Effectiveness Research）的论文《状态转移模型的总生存期与无进展生存期优化估计》的同行评议补充图表。
图S1：标准方法：基于健康状态转移的分布概览
图S2：新方法：基于健康状态转移的分布概览

研究背景与目标：英国国家卫生与保健优化研究所（National Institute for Health and Care Excellence）发布的指南（技术支持文件19）指出，状态转移模型（state transition models, STMs）的核心挑战之一，在于难以对试验内观测终点实现令人满意的拟合。若试验周期内的数据拟合效果不佳，将对长期外推结果产生不利影响。为此本研究提出一种全新的估计方法，通过对状态转移模型预测的总生存期（overall survival, OS）与无进展生存期（progression-free survival, PFS）外推结果进行优化，使其更贴近试验内观测终点的估计值。

材料与方法：本研究针对从Project Data Sphere获取的非小细胞肺癌SQUIRE试验数据拟合状态转移模型。采用两种方法开展建模：其一为标准方法，即对各状态转移使用极大似然估计，并基于赤池信息准则（Akaike Information Criterion, AIC）与贝叶斯信息准则（Bayesian Information Criterion, BIC）选择拟合效果最优的参数模型；其二为新方法，通过最小化状态转移模型预测的OS、PFS曲线与对应OS、PFS卡普兰-迈耶（Kaplan-Meier）曲线之间的面积来优化模型参数。此外开展敏感性分析以评估结果的不确定性。

研究结果：相较于标准方法，新方法在所有分析的参数分布组合下，对OS和PFS的卡普兰-迈耶曲线均实现了更贴合的估计。尽管新方法对应的不确定性略高于标准方法，但在12种分析的参数分布中，有10种分布下新方法对受限平均生存期的估计效果更优。

结论：本研究提出了一种全新的状态转移模型估计方法，可实现对建模终点更精准的拟合，且该方法可便捷拓展至更复杂的模型结构中。