Calibration Targets.

Background Simulation models of opioid use disorder (OUD) aim at evaluating the impact of different treatment strategies on population-level outcomes. Researching Effective Strategies to Prevent Opioid Death (RESPOND) is a dynamic population, state-transition model that simulates the Massachusetts OUD population synthesizing data from multiple sources. Structural complexity and scarcity of available data for opioid modeling pose a special challenge to model calibration. We propose an empirical calibration approach applicable to complex simulation models in general. Methods We implement an empirical approach to calibrate RESPOND to multiple targets: annual fatal opioid-related overdoses, detox admissions, and OUD population sizes. The empirical calibration involves Latin hypercube sampling for searching a multidimensional parameter space comprising arrivals, overdose rates, treatment transition rates, and substance use state transition probabilities. The algorithm accepts proposed parameters when the respective model outputs lie within pre-determined target uncertainty ranges. This is an iterative process resulting in a set of parameter values for which the model closely fits all the calibration targets. We validated the model assessing its accuracy to projections important for shared decision-making of OUD outside the training data. Results The empirical calibration resulted in a model that fits well both calibration and validation targets. The flexibility of the algorithm allowed us to explore structural and parameter uncertainty, reveal underlying relationships between model parameters and identify areas of model improvement for a more accurate representation of the OUD dynamics. Discussion The proposed empirical calibration approach is an efficient tool for approximating parameter distributions of complex models, especially under complete uncertainty. Empirically calibrated parameters can be used as a starting point for a more comprehensive calibration exercise, e.g., to inform priors of a Bayesian calibration. The calibrated RESPOND model can be used to improve shared decision-making for OUD.

背景
阿片类使用障碍（opioid use disorder, OUD）模拟模型旨在评估不同治疗策略对人群层面结局的影响。"预防阿片类死亡有效策略研究（Researching Effective Strategies to Prevent Opioid Death, RESPOND）"是一款动态人群状态转换模型（dynamic population, state-transition model），该模型整合多源数据对马萨诸塞州的阿片类使用障碍人群开展模拟。阿片类建模的结构复杂性与可用数据匮乏，给模型校准带来了特殊挑战。本研究提出了一种通用的、可适用于各类复杂模拟模型的经验校准方法。

方法
本研究采用经验校准方法，将RESPOND模型匹配至多个校准目标：年度阿片类相关致命过量用药数、脱毒收治人数以及阿片类使用障碍人群规模。该经验校准采用拉丁超立方抽样（Latin hypercube sampling）对多维参数空间进行搜索，参数空间涵盖人群流入率、过量用药率、治疗转换率以及物质使用状态转换概率。当对应模型输出落在预先设定的目标不确定性区间内时，算法将接受所提出的参数组合。这一迭代过程最终可得到一组参数值，使得模型能够精准匹配所有校准目标。本研究在训练数据集之外，针对阿片类使用障碍共同决策所需的关键预测结果，评估模型准确性以完成模型验证。

结果
经验校准最终得到了同时良好匹配校准与验证目标的模型。该算法的灵活性使得我们能够探究结构与参数不确定性、揭示模型参数间的内在关联，并明确模型的改进方向，从而更精准地刻画阿片类使用障碍的动态变化特征。

讨论
本研究提出的经验校准方法是一种高效工具，可用于拟合复杂模型的参数分布，尤其适用于完全不确定的场景。经经验校准得到的参数可作为更全面校准工作的起点，例如为贝叶斯校准（Bayesian calibration）提供先验信息。经校准后的RESPOND模型可用于优化阿片类使用障碍患者的共同决策实践。