School of Health and Related Research, University of Sheffield, Sheffield, UK (PJD).
Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD (JJP, DWD).
Med Decis Making. 2018 Nov;38(8):930-941. doi: 10.1177/0272989X18807438.
Cost-effectiveness models for infectious disease interventions often require transmission models that capture the indirect benefits from averted subsequent infections. Compartmental models based on ordinary differential equations are commonly used in this context. Decision trees are frequently used in cost-effectiveness modeling and are well suited to describing diagnostic algorithms. However, complex decision trees are laborious to specify as compartmental models and cumbersome to adapt, limiting the detail of algorithms typically included in transmission models.
We consider an approximation replacing a decision tree with a single holding state for systems where the time scale of the diagnostic algorithm is shorter than time scales associated with disease progression or transmission. We describe recursive algorithms for calculating the outcomes and mean costs and delays associated with decision trees, as well as design strategies for computational implementation. We assess the performance of the approximation in a simple model of transmission/diagnosis and its role in simplifying a model of tuberculosis diagnostics.
When diagnostic delays were short relative to recovery rates, our approximation provided a good account of infection dynamics and the cumulative costs of diagnosis and treatment. Proportional errors were below 5% so long as the longest delay in our 2-step algorithm was under 20% of the recovery time scale. Specifying new diagnostic algorithms in our tuberculosis model was reduced from several tens to just a few lines of code.
For conditions characterized by a diagnostic process that is neither instantaneous nor protracted (relative to transmission dynamics), this novel approach retains the advantages of decision trees while embedding them in more complex models of disease transmission. Concise specification and code reuse increase transparency and reduce potential for error.
传染病干预措施的成本效益模型通常需要能够捕捉到避免后续感染所带来的间接收益的传播模型。基于常微分方程的房室模型在这种情况下被广泛应用。决策树常用于成本效益建模，非常适合描述诊断算法。然而，复杂的决策树很难作为房室模型来指定，并且难以适应，限制了通常包含在传播模型中的算法的详细程度。
我们考虑了一种近似方法，即用单个保留状态替换决策树，适用于诊断算法的时间尺度比疾病进展或传播相关的时间尺度短的系统。我们描述了用于计算决策树相关的结果和平均成本和延迟的递归算法，以及用于计算实现的设计策略。我们评估了该近似方法在传播/诊断的简单模型中的性能，以及其在简化结核病诊断模型中的作用。
当诊断延迟相对于恢复率较短时，我们的近似方法很好地描述了感染动态以及诊断和治疗的累积成本。只要我们的两步算法中最长的延迟不超过恢复时间尺度的 20%，则比例误差低于 5%。在我们的结核病模型中指定新的诊断算法，从数十行减少到只有几行代码。
对于具有诊断过程既不是即时的也不是漫长的（相对于传播动态）的情况，这种新方法保留了决策树的优势，同时将其嵌入更复杂的疾病传播模型中。简洁的规范和代码重用提高了透明度并减少了出错的可能性。
