Failure time regression with continuous covariates measured with error

We consider failure time regression analysis with an auxiliary variable in the presence of a validation sample. We extend the nonparametric inference procedure of Zhou and Pepe to handle a continuous auxiliary or proxy covariate. We estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates. We present some asymptotic properties for the kernel estimator and provide some simulation results. The method proposed is illustrated with a data set from an on‐going epidemiologic study.

[1]  E. Nadaraya.  On Estimating Regression , 1964 .

[2]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[3]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[4]  N. Breslow.  Covariance analysis of censored survival data. , 1974, Biometrics.

[5]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[6]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[7]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[8]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[9]  R. Prentice.  Covariate measurement errors and parameter estimation in a failure time regression model , 1982 .

[10]  Steven G. Self,et al.  Asymptotic Distribution Theory for Cox-Type Regression Models with General Relative Risk Form , 1983 .

[11]  R. Neth,et al.  Premature labor contractions and the value of serum ferritin during pregnancy. , 1988, Gynecologic and obstetric investigation.

[12]  R. Prentice,et al.  Further results on covariate measurement errors in cohort studies with time to response data. , 1989, Statistics in medicine.

[13]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[14]  R. Fischer,et al.  Anemia vs iron deficiency: increased risk of preterm delivery in a prospective study. , 1992, The American journal of clinical nutrition.

[15]  Z. Ying,et al.  Cox Regression with Incomplete Covariate Measurements , 1993 .

[16]  M. Hughes,et al.  Regression dilution in the proportional hazards model. , 1993, Biometrics.

[17]  M. Pepe,et al.  Auxiliary covariate data in failure time regression , 1995 .

[18]  Raymond J. Carroll,et al.  DIMENSION REDUCTION IN A SEMIPARAMETRIC REGRESSION MODEL WITH ERRORS IN COVARIATES , 1995 .

[19]  J G Ibrahim,et al.  Using the EM-algorithm for survival data with incomplete categorical covariates , 1996, Lifetime data analysis.

[20]  D A Savitz,et al.  Determinants of participation in an epidemiological study of preterm delivery. , 1999, Paediatric and perinatal epidemiology.