A multiple imputation procedure of censored values in family-based genetic association studies

Biological quantitative data are subjected to censoring when a portion of values cannot be quantified because they are smaller or greater than the limit of detection (LOD) of the laboratory assay. In genetic association studies of quantitative trait, the handling of censored data has received little attention and often the solutions are unsatisfactory. However, the approach used to deal with such data can have a substantial impact on the results of the analysis. While the Tobit model represents an appropriate method for independent data, there is no evidence on its performance in the presence of non-independent observations, typical of familyor pedigreebased studies. In the context of a family-based study, we propose a Bayesian approach which takes into account the uncertainty of the imputation procedure using several imputations for each censored value. In particular, assuming vague (uninformative) priors for all hyper-parameters, the imputation based on Gibbs sampling is applied to variance-components linear regression models, where the primary outcome is related to a secondary outcome. Through simulation, we describe the behavior of the Tobit model in the presence of different degrees of censoring and heritability of the trait compared with the Bayesian model and the naı̈ve approach of replacing all censored values with the LOD value.