  Modeling symptom progression to identify informative subjects for a new
Huntington's disease clinical trial is problematic since time to diagnosis, a
key covariate, can be heavily censored. Imputation is an appealing strategy
where censored covariates are replaced with their conditional means, but
existing methods saw over 200% bias under heavy censoring. Calculating these
conditional means well requires estimating and then integrating over the
survival function of the censored covariate from the censored value to
infinity. To estimate the survival function flexibly, existing methods use the
semiparametric Cox model with Breslow's estimator, leaving the integrand for
the conditional means (the estimated survival function) undefined beyond the
observed data. The integral is then estimated up to the largest observed
covariate value, and this approximation can cut off the tail of the survival
function and lead to severe bias, particularly under heavy censoring. We
propose a hybrid approach that splices together the semiparametric survival
estimator with a parametric extension, making it possible to approximate the
integral up to infinity. In simulation studies, our proposed approach of
extrapolation then imputation substantially reduces the bias seen with existing
imputation methods, even when the parametric extension was misspecified. We
further demonstrate how imputing with corrected conditional means helps to
prioritize patients for future clinical trials.
