High-dimensional partially linear functional Cox models

As a commonly employed method for analyzing time-to-event data involving functional predictors, the functional Cox model assumes a linear relationship between the functional principal component (FPC) scores of the functional predictors and the hazard rates. However, in practical scenarios, such as our study on the survival time of kidney transplant recipients, this assumption often fails to hold. To address this limitation, we introduce a class of high-dimensional partially linear functional Cox models, which accommodates the non-linear effects of functional predictors on the response and allows for diverging numbers of scalar predictors and FPCs as the sample size increases. We employ the group smoothly clipped absolute deviation method to select relevant scalar predictors and FPCs, and use B-splines to obtain a smoothed estimate of the non-linear effect. The finite sample performance of the estimates is evaluated through simulation studies. The model is also applied to a kidney transplant dataset, allowing us to make inferences about the non-linear effects of functional predictors on patients' hazard rates, as well as to identify significant scalar predictors for long-term survival time.