title: Transition probability estimates for non-Markov multi-state models.
abstract: Non-parametric estimation of the transition probabilities in multi-state models is considered for non-Markov processes. Firstly, a generalization of the estimator of Pepe et al., (1991) (Statistics in Medicine) is given for a class of progressive multi-state models based on the difference between Kaplan-Meier estimators. Secondly, a general estimator for progressive or non-progressive models is proposed based upon constructed univariate survival or competing risks processes which retain the Markov property. The properties of the estimators and their associated standard errors are investigated through simulation. The estimators are demonstrated on datasets relating to survival and recurrence in patients with colon cancer and prothrombin levels in liver cirrhosis patients.
authors.affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.
authors.forename: Andrew C
authors.initials: AC
authors.lastname: Titman
mesh_terms: D001699:Biometry / Q000379:methods; D017024:Chemotherapy, Adjuvant; D003110:Colonic Neoplasms / Q000188:drug therapy / Q000401:mortality; D003198:Computer Simulation; D006801:Humans; D008103:Liver Cirrhosis / Q000097:blood / Q000188:drug therapy; D008390:Markov Chains; D015233:Models, Statistical; D011241:Prednisone / Q000627:therapeutic use; D011336:Probability; D011516:Prothrombin / Q000378:metabolism; D018709:Statistics, Nonparametric; D016019:Survival Analysis
chemical_list: D011516:Prothrombin; D011241:Prednisone
keywords: Aalen-Johansen estimator; Multi-state model; Non-Markov; Non-parametric; Robust estimation; Transition probabilities