Two-Stage Clonal Expansion Model Using Conditional Likelihood to Discern the Initiation and Promotion Effects: Numerical Study

The two-stage clonal expansion (TSCE) model has been developed to investigate the mechanistic processes in cancer development on carcinogenesis based on the knowledge of molecular biology. The model assumes three states of cells (normal, intermediate, and malignant) and four transition rate parameters to describe the rate at which a cell changes its state. Despite the need for statistically sound and biologically meaningful estimation methods, no reliable inference method has yet been established. A major trouble with TSCE model is that iteration algorithms searching for the maximum likelihood estimates of the model’s parameters are generally non-convergent. Regarding the problem, Nakamura and Hoel [10] proposed a new likelihood termed “conditional likelihood”. This study conducted simulations with small sample sizes to assess the performance of the conditional likelihood to distinguish between the initiation and promotion effects. Data generation was performed using parameter values based on dioxin [6] and radiation [3] experimental data. Several estimation models were applied to each dataset to determine whether it was generated from the initiation or the promotion model. The correct identification rate was 98%.