title: Nonlinear multiple imputation for continuous covariate within semiparametric Cox model: application to HIV data in Senegal.
abstract: Multiple imputation is commonly used to impute missing covariate in Cox semiparametric regression setting. It is to fill each missing data with more plausible values, via a Gibbs sampling procedure, specifying an imputation model for each missing variable. This imputation method is implemented in several softwares that offer imputation models steered by the shape of the variable to be imputed, but all these imputation models make an assumption of linearity on covariates effect. However, this assumption is not often verified in practice as the covariates can have a nonlinear effect. Such a linear assumption can lead to a misleading conclusion because imputation model should be constructed to reflect the true distributional relationship between the missing values and the observed values. To estimate nonlinear effects of continuous time invariant covariates in imputation model, we propose a method based on B-splines function. To assess the performance of this method, we conducted a simulation study, where we compared the multiple imputation method using Bayesian splines imputation model with multiple imputation using Bayesian linear imputation model in survival analysis setting. We evaluated the proposed method on the motivated data set collected in HIV-infected patients enrolled in an observational cohort study in Senegal, which contains several incomplete variables. We found that our method performs well to estimate hazard ratio compared with the linear imputation methods, when data are missing completely at random, or missing at random.
authors.affiliation: Institut de Recherche pour le Développement (IRD), Université Montpellier 1, UMI 233, Montpellier, France; Ecole Nationale Supérieure Polytechnique (ENSP), Université Yaoundé 1, Yaoundé, Cameroun.
authors.forename: Jules Brice Tchatchueng
authors.initials: JB
authors.lastname: Mbougua
authors.forename: Christian
authors.initials: C
authors.lastname: Laurent
authors.forename: Ibra
authors.initials: I
authors.lastname: Ndoye
authors.forename: Eric
authors.initials: E
authors.lastname: Delaporte
authors.forename: Henri
authors.initials: H
authors.lastname: Gwet
authors.forename: Nicolas
authors.initials: N
authors.lastname: Molinari
mesh_terms: D019380:Anti-HIV Agents / Q000627:therapeutic use; D001499:Bayes Theorem; D015331:Cohort Studies; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015658:HIV Infections / Q000188:drug therapy; D006801:Humans; D016016:Proportional Hazards Models; D012675:Senegal
chemical_list: D019380:Anti-HIV Agents
keywords: HIV; linear Bayesian regression; multiple imputation; semiparametric Cox model; splines function