Parametric survival models for interval-censored data with time-dependent covariates

Biostatistics. 2006 Oct;7(4):599-614. doi: 10.1093/biostatistics/kxj028. Epub 2006 Apr 5.


We present a parametric family of regression models for interval-censored event-time (survival) data that accomodates both fixed (e.g. baseline) and time-dependent covariates. The model employs a three-parameter family of survival distributions that includes the Weibull, negative binomial, and log-logistic distributions as special cases, and can be applied to data with left, right, interval, or non-censored event times. Standard methods, such as Newton-Raphson, can be employed to estimate the model and the resulting estimates have an asymptotically normal distribution about the true values with a covariance matrix that is consistently estimated by the information function. The deviance function is described to assess model fit and a robust sandwich estimate of the covariance may also be employed to provide asymptotically robust inferences when the model assumptions do not apply. Spline functions may also be employed to allow for non-linear covariates. The model is applied to data from a long-term study of type 1 diabetes to describe the effects of longitudinal measures of glycemia (HbA1c) over time (the time-dependent covariate) on the risk of progression of diabetic retinopathy (eye disease), an interval-censored event-time outcome.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Biometry / methods
  • Data Interpretation, Statistical
  • Diabetes Mellitus, Type 1 / blood
  • Diabetic Retinopathy / blood
  • Diabetic Retinopathy / etiology
  • Glycated Hemoglobin / metabolism
  • Humans
  • Models, Statistical*
  • Regression Analysis
  • Risk Factors
  • Survival Analysis*
  • Time Factors


  • Glycated Hemoglobin A