Semiparametrically imputed regression model for survival data

This paper presents a new methodology for survival analysis: the semiparametrically imputed regression model for survival data (SPIRES). Survival data is inherently challenging due to censoring, which imposes various limitations on analysis. The primary obstacle in analyzing censored data comes from incomplete information on the survival times of some individuals, making ordinary regression techniques inapplicable. SPIRES addresses this issue by semiparametrically imputing censored observations. Following imputation, SPIRES applies a regression-based analysis to the imputed survival data. A key advantage of SPIRES is its ability to directly predict survival times, facilitating straightforward evaluation of its modeling performance. Additionally, existing prediction models from bagging, boosting methods, or neural networks can be integrated into the regression component of SPIRES. Although our primary focus is on predicting survival time, we also propose a method for estimating survival probabilities within the SPIRES framework which enables us to compare SPIRES with existing survival models. When evaluating SPIRES against survival models such as the Cox proportional hazards (Cox PH) model and random survival forests (RSF) using the c-index, SPIRES exhibits better predictive accuracy in non-proportional hazards scenarios in simulations. In proportional hazards scenarios, all models perform comparably well. When comparing models based on the coverage of prediction intervals through simulation, SPIRES again outperforms the Cox-PH and RSF models. Moreover, SPIRES demonstrates superior predictive performance in real data applications.