Modeling overdetection resulting from screening often uses the conventional competing risk model. This model assigns screen-detected cases dying from other causes as overdetection modeled by a one-jump process, which may not be true for the censored overdetected cases. To relax this restrictive assumption, accommodate a finite Markov process for overdetection, and dispense with long-term follow-up until death, we propose a generalized Coxian phase-type Markov process to distinguish the progressive latent multistate pathway from the nonprogressive (overdetected) latent multistate pathway. Various new likelihood functions were developed to estimate the transition parameters with the available data accrued at the time of diagnosis. The proportion of overdetected cancers by the cured model was further estimated by using parameters with and without distinguishing between the two latent pathways. While perturbation analyses were conducted by changing their parameters to assess their effects on overdetection, the results, including of asymptotic analyses, were very robust for an overdetection rate higher than 20% but not for low overdetection rates. These two scenarios were demonstrated by applying the Coxian phase-type model to prostate cancer and breast cancer screening, yielding a substantial proportion of overdetected prostate cancer (60%) attributed to the prostate specific antigen test and a small fraction of overdetected breast cancer (3%) detected by mammography. This kind of variation in overdetection elucidated by the Coxian phase-type Markov process provides new insights into the quantitative mechanisms producing overdetection, which is informative for evaluating the benefits and risks of various types of population-based cancer screening programs.