Nonparametric discrete survival function estimation with uncertain endpoints using an internal validation subsample.
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.
Department of Biostatistics and Epidemiology, University of Pennsylvania, 607 Blockley Hall, 423 Guardian Drive, Philadelphia, Pennsylvania 19104, U.S.A.
Jarcy
J
Zee
Department of Biostatistics and Epidemiology, University of Pennsylvania, 607 Blockley Hall, 423 Guardian Drive, Philadelphia, Pennsylvania 19104, U.S.A.
Sharon X
SX
Xie
D000544:Alzheimer Disease / Q000175:diagnosis* / Q000401:mortality*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D059906:Neuroimaging / Q000706:statistics & numerical data*; D015995:Prevalence; D015203:Reproducibility of Results; D018570:Risk Assessment / Q000379:methods; D018401:Sample Size; D012680:Sensitivity and Specificity; D016019:Survival Analysis
Measurement error; Missing data; Nonparametric survival analysis; Uncertain endpoints; Validation sample