Nonparametric Estimation of Transition Probabilities for a General Progressive Multi-State Model Under Cross-Sectional Sampling

• Published in: Biometrics Vol. 74; no. 4; pp. 1203 - 1212
• Main Authors: de Uña-Álvarez, Jacobo, Mandel, Micha
• Format: Journal Article
• Language: English
• Published: United States Wiley-Blackwell 01.12.2018; Blackwell Publishing Ltd
• Subjects: Acute Disease - mortality; Acute Disease - therapy; Biased data; BIOMETRIC METHODOLOGY; biometry; Biometry - methods; Computer Simulation; Cross-Sectional Studies; Estimators; Humans; Illness‐death model; Intensive Care Units; Inverse weighting; Left truncation; Monte Carlo simulation; Multi‐state models; Nonparametric statistics; Oversampling; patients; probability; Regression analysis; Sampling; Statistics as Topic - methods; Survival; Time Factors; Transition probabilities; Left truncation; Multi-state models; Biased data; Illness-death model; Inverse weighting
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.12874

Nonparametric estimation of the transition probability matrix of a progressive multi-state model is considered under cross-sectional sampling. Two different estimators adapted to possibly right-censored and left-truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub-samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left-truncation times associated with the cross-sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs).