Bayesian analysis of censored response data in family‐based genetic association studies

Abstract

Biomarkers are subject to censoring whenever some measurements are not quantifiable given a laboratory detection limit. Methods for handling censoring have received less attention in genetic epidemiology, and censored data are still often replaced with a fixed value. We compared different strategies for handling a left-censored continuous biomarker in a family-based study, where the biomarker is tested for association with a genetic variant, S, adjusting for a covariate, X. Allowing different correlations between X and S, we compared: simple substitution of censored observations with the detection limit followed by a linear mixed effect model (LMM); Bayesian model with non-informative priors; Tobit model with robust standard errors; the mutiple imputation (MI) with and without S in the imputation followed by a LMM. Our comparison was based on real and simulated data in which 20% and 40% censoring were artificially induced. The complete data was also analysed with a LMM. In the MICROS study, the Bayesian model gave results closer to those obtained with the complete data. In the simulations, simple substitution was always the most biased method; the Tobit approach gave the least biased estimates at all censoring levels and correlation values; the Bayesian model and both MI approaches gave slightly biased estimates but smaller root mean square errors. On the basis of these results the Bayesian approach is highly recommended for candidate gene studies; however, the computationally simpler Tobit and the MI without S are both good options for genome-wide studies.

Lasso regularization for left-censored Gaussian outcome and high-dimensional predictors

“…Indeed, HIV viral load appears to have an underlying Gaussian distribution truncated by the detection limit that justifies the normality hypothesis [ 13 – 15 , 17 , 18 ]. As expected, approaches accounting for left-censoring outperform simple imputation of a constant [ 2 , 4 , 13 – 16 , 18 , 20 – 22 ].…”

“…Several statistical methods have been proposed to account for left-censoring of such quantitative variables in cross-sectional (with one measure per subject) and longitudinal (with several measures per subject) studies. Standard methods include multiple imputation [ 1 – 4 ], reverse survival analysis methods [ 2 , 5 – 7 ], quantile regression [ 8 , 9 ] and censored quantile regression [ 10 , 11 ]. Furthermore, the Tobit model with censored outcome which is supposed to be normally distributed can be estimated by maximum likelihood [ 12 – 18 ] or by the Buckley-James estimator [ 18 , 19 ].…”