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Modeling symptom progression to identify informative subjects for a newHuntington's disease clinical trial is problematic since time to diagnosis, akey covariate, can be heavily censored. Imputation is an appealing strategywhere censored covariates are replaced with their conditional means, butexisting methods saw over 200% bias under heavy censoring. Calculating theseconditional means well requires estimating and then integrating over thesurvival function of the censored covariate from the censored value toinfinity. To estimate the survival function flexibly, existing methods use thesemiparametric Cox model with Breslow's estimator, leaving the integrand forthe conditional means (the estimated survival function) undefined beyond theobserved data. The integral is then estimated up to the largest observedcovariate value, and this approximation can cut off the tail of the survivalfunction and lead to severe bias, particularly under heavy censoring. Wepropose a hybrid approach that splices together the semiparametric survivalestimator with a parametric extension, making it possible to approximate theintegral up to infinity. In simulation studies, our proposed approach ofextrapolation then imputation substantially reduces the bias seen with existingimputation methods, even when the parametric extension was misspecified. Wefurther demonstrate how imputing with corrected conditional means helps toprioritize patients for future clinical trials.

Extrapolation before imputation reduces bias when imputing censored covariates