Nonparametric discrete survival function estimation with uncertain endpoints using an internal validation subsample

• Published in: Biometrics Vol. 71; no. 3; pp. 772 - 781
• Main Authors: Zee, Jarcy, Xie, Sharon X.
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishing Ltd 01.09.2015; International Biometric Society
• Subjects: Alzheimer disease; Alzheimer Disease - diagnosis; Alzheimer Disease - mortality; Alzheimer's disease; BIOMETRIC PRACTICE; Biometrics; biometry; Computer Simulation; data collection; Data Interpretation, Statistical; Humans; Likelihood Functions; Measurement error; Medical imaging; Missing data; Models, Statistical; Neuroimaging - statistics & numerical data; Nonparametric survival analysis; Prevalence; Reproducibility of Results; risk; Risk Assessment - methods; Sample Size; Sensitivity and Specificity; Survival Analysis; Uncertain endpoints; Validation sample; Nonparametric survival analysis; Validation sample; Missing data; Uncertain endpoints; Measurement error
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.12316

When a true survival endpoint cannot be assessed for some subjects, an alternative endpoint that measures the true endpoint with error may be collected, which often occurs when obtaining the true endpoint is too invasive or costly. We develop an estimated likelihood function for the situation where we have both uncertain endpoints for all participants and true endpoints for only a subset of participants. We propose a nonparametric maximum estimated likelihood estimator of the discrete survival function of time to the true endpoint. We show that the proposed estimator is consistent and asymptotically normal. We demonstrate through extensive simulations that the proposed estimator has little bias compared to the naïve Kaplan–Meier survival function estimator, which uses only uncertain endpoints, and more efficient with moderate missingness compared to the complete-case Kaplan–Meier survival function estimator, which uses only available true endpoints. Finally, we apply the proposed method to a data set for estimating the risk of detecting Alzheimer's disease from the Alzheimer's Disease Neuroimaging Initiative.