Title: Extrapolation before imputation reduces bias when imputing heavily censored covariates Authors:  Sarah Lotspeich - Wake Forest University (United States) [presenting]
Abstract: Modelling symptom progression to identify informative subjects for a new Huntington 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 the survival function of the censored covariate from the censored value to infinity. Existing methods use the semiparametric Cox model with Breslow's estimator to estimate the survival function flexibly. Then, for integration, the trapezoidal rule is used, but the trapezoidal rule is not designed for improper integrals and leads to bias. Calculating the conditional mean is proposed with adaptive quadrature instead, which can handle the improper integral. Yet, even with adaptive quadrature, the integrand (the survival function) is undefined beyond the observed data, so the Weibull extension is identified as the best method to extrapolate and then integrate. In simulation studies, it is shown that replacing the trapezoidal rule with adaptive quadrature and adopting the Weibull extension corrects the bias seen with existing methods. It further shows how imputing with corrected conditional means helps prioritize patients for future clinical trials.