Rights statement: This is the peer reviewed version of the following article: Titman, A.C. (2015) Transition Probability Estimates for Non-Markov Multi-State Models. Biometrics. DOI:10.111/biom.12349, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/biom.12349/abstract This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Transition probability estimates for non-Markov multi-state models
AU - Titman, Andrew
N1 - This is the peer reviewed version of the following article: Titman, A.C. (2015) Transition Probability Estimates for Non-Markov Multi-State Models. Biometrics. DOI:10.111/biom.12349, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/biom.12349/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
PY - 2015/12
Y1 - 2015/12
N2 - 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.
AB - 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.
KW - multi-state model
KW - Transition probabilities
KW - Non-parametric
KW - Non-Markov
KW - robust estimation
U2 - 10.1111/biom.12349
DO - 10.1111/biom.12349
M3 - Journal article
VL - 71
SP - 1034
EP - 1041
JO - Biometrics
JF - Biometrics
SN - 0006-341X
IS - 4
ER -