Improved computational efficiency and stability when imputing censored covariates: Analytic and numerical approaches

Imputation is a popular approach to handling censored, missing, and error-prone covariates -- all coarsened data types for which the true values are unknown. However, there are nuances to imputing these different data types based on the mechanism dominating the unobserved values and other available information. For example, in prospective studies, the time to a disease diagnosis will be incompletely observed if only some patients are diagnosed by the end of the follow-up. Some will be randomly right-censored, and patients' disease-free follow-up times must be incorporated into their imputed values. Assuming noninformative censoring, censored values are replaced with their conditional means, which are calculated by estimating the conditional survival function of the censored covariate and then integrating over it. Semiparametric approaches are common, which estimate the survival with a Cox model and then the integral with the trapezoidal rule. While these approaches offer robustness, they come at the cost of computational efficiency and stability in numerically approximating an improper integral. After modeling the survival function parametrically, we derive analytic solutions for conditional mean imputed values under many common distributions. We define stabilized calculations for other distributions. Parametric imputation using various distributions and calculations is implemented in the R package, speedyCMI.