Multistate statistical models are often used to characterize the complex multi-compartment progression of the disease such as cancer. However, the derivation of multistate transition kernels is often involved with the intractable convolution that requires intensive computation. Moreover, the estimation of parameters pertaining to transition kernel requires the individualized time-stamped history data while the traditional likelihood function forms are constructed. In this paper, we came up with a novel likelihood function derived from Laplace transformation-based transition probabilities in conjunction with Expectation–Maximization algorithm to estimate parameters. The proposed method was applied to two large population-based screening data with only aggregated count data without relying on individual time-stamped history data.

多状态统计模型通常用于表征疾病（如癌症）的复杂多室进展。然而，多状态转换内核的推导通常涉及需要密集计算的棘手卷积。此外，与转换核相关的参数估计需要个性化的带时间戳的历史数据，同时构建传统的似然函数形式。在本文中，我们提出了一种新的似然函数，该函数源自基于拉普拉斯变换的转移概率，并结合期望最大化算法来估计参数。所提出的方法应用于两个基于人群的大型筛查数据，仅具有聚合计数数据，而不依赖于个体时间戳历史数据。