Laplace regression with censored data

Biom J. 2010 Aug;52(4):487-503. doi: 10.1002/bimj.200900310.


We consider a regression model where the error term is assumed to follow a type of asymmetric Laplace distribution. We explore its use in the estimation of conditional quantiles of a continuous outcome variable given a set of covariates in the presence of random censoring. Censoring may depend on covariates. Estimation of the regression coefficients is carried out by maximizing a non-differentiable likelihood function. In the scenarios considered in a simulation study, the Laplace estimator showed correct coverage and shorter computation time than the alternative methods considered, some of which occasionally failed to converge. We illustrate the use of Laplace regression with an application to survival time in patients with small cell lung cancer.

MeSH terms

  • Analysis of Variance
  • Antineoplastic Agents / therapeutic use
  • Clinical Trials as Topic
  • Humans
  • Likelihood Functions
  • Lung Neoplasms / drug therapy
  • Probability
  • Regression Analysis*
  • Small Cell Lung Carcinoma / drug therapy
  • Survival Analysis


  • Antineoplastic Agents