Calibration of prediction rules for life-time outcomes using prognostic Cox regression survival models and multiple imputations to account for missing predictor data with cross
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In this paper, we expand the methodology presented in Mertens et. al (2020, Biometrical Journal) to the study of life-time (survival) outcome which is subject to censoring and when imputation is used to account for missing values. We consider the problem where missing values can occur in both the calibration data as well as newly - to-be-predicted - observations (validation). We focus on the Cox model. Methods are described to combine imputation with predictive calibration in survival modeling subject to censoring. Application to cross-validation is discussed. We demonstrate how conclusions broadly confirm the first paper which restricted to the study of binary outcomes only. Specifically prediction-averaging appears to have superior statistical properties, especially smaller predictive variation, as opposed to a direct application of Rubin's rules. Distinct methods for dealing with the baseline hazards are discussed when using Rubin's rules-based approaches.
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