Graphical exploration of covariate effects on survival data through nonparametric quantile curves

Kaplan-Meier curves provide an effective means of presenting the distributi onal pattern in a sample of survival data. However, in order to assess the effect of a covariate, a standard scatterplot is often difficult to interpr et because of the presence of censored observations. Several authors have p roposed a running median as an effective way of indicating the effect of a covariate. This article proposes a form of kernel estimation, employing dou ble smoothing, that can be applied in a simple and efficient manner to cons truct an estimator of a percentile of the survival distribution as a functi on of one or two covariates. Permutations and bootstrap samples can be used to construct reference bands that help identify whether particular feature s of the estimates indicate real features of the underlying curve or whethe r this may be due simply to random variation. The techniques are illustrate d on data from a study of kidney transplant patients.