title: Assessing treatment effects with surrogate survival outcomes using an internal validation subsample.
abstract: BACKGROUND
  In studies with surrogate outcomes available for all subjects and true outcomes available for only a subsample, survival analysis methods are needed that incorporate both endpoints in order to assess treatment effects.
  
  
  METHODS
  We develop a semiparametric estimated likelihood method for the proportional hazards model with discrete time data and a binary covariate of interest. Our proposed method allows for real-time validation of surrogate outcomes and flexible censoring mechanisms.
  
  
  RESULTS
  Our proposed estimator is consistent and asymptotically normal. Through numerical studies, we showed that our proposed method for estimating a covariate effect is unbiased compared to the naïve estimator that uses only surrogate endpoints and is more efficient with moderate missingness compared to the complete-case estimator that uses only true endpoints. We further demonstrated the advantages of our proposed method in comparison with existing approaches when there is real-time validation. We also illustrated the use of our proposed method by estimating the effect of gender on time to detection of Alzheimer's disease using data from the Alzheimer's Disease Neuroimaging Initiative.
  
  
  CONCLUSIONS
  The proposed method is able to account for the uncertainty of surrogate outcomes using a validation subsample of true outcomes in estimating a binary covariate effect. The proposed estimator can outperform standard semiparametric survival analysis methods and can therefore save on costs of a trial or improve power in detecting treatment effects.
authors.affiliation: Department of Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, PA, USA.
authors.forename: Jarcy
authors.initials: J
authors.lastname: Zee
authors.affiliation: Department of Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, PA, USA sxie@mail.med.upenn.edu.
authors.forename: Sharon X
authors.initials: SX
authors.lastname: Xie
mesh_terms: D015415:Biomarkers; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D017063:Outcome Assessment, Health Care; D016016:Proportional Hazards Models; D015203:Reproducibility of Results; D016019:Survival Analysis
chemical_list: D015415:Biomarkers
keywords: Semiparametric survival analysis; measurement error; missing data; proportional hazards model; surrogate outcomes; validation subsample