Nonparametric Estimation of Transition Probabilities in Illness-Death Model based on Ranked Set Sampling

The ranked set sampling (RSS) design is applied widely in agriculture, environmental science, and medical research where the exact measurements of sampling units is costly, but sampling units can be ranked by a correlated concomitant variable. RSS is usually a cost-efficient alternate to simple random sampling (SRS) for selecting more representative samples. This study presents a novel methodology to investigate the nonparametric estimation of transition probabilities in illness-death model using the RSS design. We study the Aalen–Johansen estimator of transition probabilities in illness-death Markov model based on RSS design under random right censoring time and propose nonparametric estimators of the transition probabilities. We compare the performance of the suggested estimators with their SRS counterparts via simulation study, in which two censoring levels are considered. Our results show that the proposed estimator under RSS design outperforms its competitors in SRS design in many simulation scenarios. When sample size is big with the highest set number, the proposed estimator performs the best. Conventional and RSS modified Aalen Johansen estimators are applied to healthy start project and colon cancer dataset correspondingly for illustration. The Aalen-Johansen estimator under RSS design possesses higher efficiency as compared with its SRS competitor from simulation study and real research datasets