When an infectious disease recurs, it may be due to treatment failure or a new infection. Being able to distinguish and classify these two different outcomes is critical in effective disease control. A multi-state model based on Markov processes is a typical approach to estimating the transition probability between the disease states. However, it can perform poorly when the disease state is unknown. This article aims to demonstrate that the transition likelihoods of baseline covariates can distinguish one cause from another with high accuracy in infectious diseases such as malaria. A more general model for disease progression can be constructed to allow for additional disease outcomes. We start from a multinomial logit model to estimate the disease transition probabilities and then utilize the baseline covariate's transition information to provide a more accurate classification result. We apply the expectation-maximization (EM) algorithm to estimate unknown parameters, including the marginal probabilities of disease outcomes. A simulation study comparing our classifier to the existing two-stage method shows that our classifier has better accuracy, especially when the sample size is small. The proposed method is applied to determining relapse vs reinfection outcomes in two Plasmodium vivax treatment studies from Cambodia that used different genotyping approaches to demonstrate its practical use.

中文翻译：

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使用期望最大化算法的转移可能性对疾病复发进行分类

当传染病复发时，可能是由于治疗失败或新的感染。能够区分和分类这两种不同的结果对于有效的疾病控制至关重要。基于马尔可夫过程的多状态模型是估计疾病状态之间转移概率的典型方法。然而，当疾病状态未知时，它可能表现不佳。本文旨在证明，在疟疾等传染病中，基线协变量的转变可能性可以高精度地区分一种原因与另一种原因。可以构建更通用的疾病进展模型以考虑额外的疾病结果。我们从多项 Logit 模型开始估计疾病转移概率，然后利用基线协变量的转移信息来提供更准确的分类结果。我们应用期望最大化（EM）算法来估计未知参数，包括疾病结果的边际概率。将我们的分类器与现有的两阶段方法进行比较的模拟研究表明，我们的分类器具有更好的准确性，特别是当样本量较小时。所提出的方法用于确定柬埔寨两项间日疟原虫治疗研究中的复发与再感染结果，这些研究使用不同的基因分型方法来证明其实际用途。