Semiparametric Approach for Regression with Covariate Subject to Limit of Detection

• Activity Number: 194
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Shengchun Kong*+ and Bin Nan
• Companies: and University of Michigan
• Keywords: Limit of detection ; Semiparametric model ; Maximum likelihood method

Abstract

We consider regression analysis with left-censored covariate due to the lower limit of detection (LOD). The complete case analysis by eliminating observations with values below LOD may yield valid estimates for regression coefficients, but is less efficient. Existing substitution or maximum likelihood method usually relies on parametric models for the unobservable tail probability, thus may suffer from model misspecification. To obtain robust results, we propose a likelihood based approach for the regression parameters using a semiparametric accelerated failure time model for the covariate that is left-censored by LOD. A two-stage estimation procedure is considered, where the conditional distribution of the covariate with LOD given other variables is estimated first before maximizing the likelihood function for the regression parameters. The proposed method outperforms the traditional complete case analysis and the simple substitution methods in simulation studies. Technical conditions for desirable asymptotic properties will be discussed.