Locally Estimated Scatterplot Smoothing for Censored Survival Data

In the absence of censoring, locally estimated scatterplot smoothing (LOESS) is a powerful tool to estimate the relationship between a continuous covariate and the probability of an event and is often used to visually assess calibration of prognostic models. Since follow-up in prognostic studies is often incomplete, we aimed to study the extension of LOESS to right-censored data. In line with other work, we first obtained inverse-probability-of-censoring (IPC) weights through Kaplan-Meier estimation. When censoring varied by covariate levels, we used Cox regression with a spline function of the covariate to obtain IPC weights. We then applied LOESS to the weighted event indicators to estimate the relationship between the covariate and the probability of an event within a specific time horizon. We illustrated the application of LOESS for censored data (LOESScd) using patients with complex coronary artery disease. We used the LOESScd to estimate the association between continuous predictors and the probability of death within 10 years. LOESScd estimates closely followed grouped Kaplan-Meier estimates, especially in case of weak smoothing. Covariate-dependent IPC weights improved LOESScd when censoring varied by covariate levels. We then examined the finite-sample behavior of LOESScd in simulations motivated by four typical prognostic model validation scenarios. In 2000 samples of 1800 patients, bias was limited and coverage was close to nominal. In conclusion, LOESScd is a promising estimator of the relationship of a continuous covariate with the probability of an event in the presence of right-censoring. LOESScd is especially useful for estimating calibration curves when validating prognostic models.