SPARCC: Semi-Parametric Robust Estimation in a Right-Censored Covariate Model

In Huntington disease research, a current goal is to understand how symptoms change prior to a clinical diagnosis. Statistically, achieving this goal entails modeling symptom severity as a function of the covariate 'time of diagnosis,' which is often heavily right-censored in observational studies. Existing estimators that handle right-censored covariates, such as the complete case estimator and maximum likelihood estimator, vary in their statistical efficiency and robustness to misspecifications of nuisance parameters (i.e., densities for the censored covariate and censoring variable). We propose a new "SPARCC" estimator (SemiPArametric Robust estimation in a right-Censored Covariate model) that is robust and efficient. When the nuisance parameters are modeled parametrically, the SPARCC estimator is doubly robust, i.e., consistent if at least one nuisance parameter is correctly specified, and semiparametric efficient if both are correctly specified. When the nuisance parameters are estimated via nonparametric or machine learning methods that converge sufficiently fast, the SPARCC estimator is consistent and semiparametric efficient. We show empirically that the proposed estimator, implemented in the R package sparcc, has its claimed properties, and we apply it to estimate Huntington disease symptom trajectories using data from the Enroll-HD study.