Likelihood function for estimating parameters in multistate disease process with Laplace-transformation-based transition probabilities

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.