It's integral: Replacing the trapezoidal rule to remove bias and correctly impute censored covariates with their conditional means

Imputing censored covariates with conditional means is appealing, but existing methods saw >100% bias. Calculating conditional means requires estimating and integrating over the survival function of the censored covariate from the censored value to infinity. Existing methods semiparametrically estimate the survival function but incur bias by using the trapezoidal rule, thereby treating this indefinite integral as a definite one. We integrate with adaptive quadrature instead. Yet, the integrand is undefined beyond the data, so we identify the best extrapolation method to use with quadrature. Our approach leads to unbiased imputation in simulations and helps prioritize patients for Huntington's disease clinical trials.