Kernel hazard estimation for visualisation of the effect of a continuous covariates on time-to-event endpoints

The problem of associating a continuous covariate, or biomarker, against a time-to-event outcome, is that it often requires categorisation of the covariate. This can lead to bias, loss of information and a poor representation of any underlying relationship. Here, two methods are proposed for estimating the effects of a continuous covariate on a time-to-event endpoint using weighted kernel estimators. The first method aims to estimate a density function for a time-to-event endpoint conditional on some covariate value whilst the second uses a joint density estimator. The results are visualisations in the form of surface plots that show the effects of a covariate without any need for categorisation. Both methods can aid interpretation and analysis of covariates against a time-to-event endpoint.