AK‐nearest neighbors survival probability prediction method

Abstract

We introduce a nonparametric survival prediction method for right-censored data. The method generates a survival curve prediction by constructing a (weighted) Kaplan-Meier estimator using the outcomes of the K most similar training observations. Each observation has an associated set of covariates, and a metric on the covariate space is used to measure similarity between observations. We apply our method to a kidney transplantation data set to generate patient-specific distributions of graft survival and to a simulated data set in which the proportional hazards assumption is explicitly violated. We compare the performance of our method with the standard Cox model and the random survival forests method.

A Nonparametric Method for Predicting Survival Probabilities

“…Nevertheless, the predictive power of profiling models has been found to be relatively modest (see Berger et al (2001) for a comparison). Lowsky et al (2013) recently proposed a method similar to our weighted survival prediction method in the medical literature. However, whereas they use a simple Mahalanobis distance metric and constant weighting function, we consider alternative distance and weighting functions also taking into account the importance of individual characteristics for prediction of the duration outcome.…”

“…We add the weights to the computation of the number of exits and the number of spells at risk similar to what has been suggested by Lowsky et al (2013). The original Kaplan-Meier estimator is obtained when w ij = 1, ∀j = 1, ..., J.…”

“…Our approach differs from Lowsky et al (2013) in a number of ways. First, we consider all kinds of distance metrics that differ in the extent to which they account for unequal variances of covariates, correlation between covariates, and differences in the effects of the covariates on the duration outcome of interest.…”

“…First, we consider all kinds of distance metrics that differ in the extent to which they account for unequal variances of covariates, correlation between covariates, and differences in the effects of the covariates on the duration outcome of interest. Lowsky et al (2013) only use Mahalanobis distance, which does not take into account the importance of covariates. Furthermore, Lowsky et al (2013) use a k-nearest neighbor approach, but eventually use a constant weighting function w (·) = 1 only.…”

“…Lowsky et al (2013) only use Mahalanobis distance, which does not take into account the importance of covariates. Furthermore, Lowsky et al (2013) use a k-nearest neighbor approach, but eventually use a constant weighting function w (·) = 1 only. We consider various specifications of the weighting function, also allowing weights to decline with distance, to account for possible differences in predictive power as a result of differences in distances between individuals.…”