We will have two talks, separated by a pause with light refreshments.
- Speaker: Ruth Keogh (Department of Medical Statistics, London School of Hygiene and Tropical Medicine)
- Title: Investigating time-varying effects in Cox regression in the presence of missing data: a strategy for imputation
- Abstract: In Cox regression analyses it is often of interest to study whether there are time-varying effects of exposures, including as a way to test the proportional hazards assumption. I will discuss the use of multiple imputation (MI) to handle missing data on exposures in this context, to avoid the loss of efficiency and potential bias that result from the ‘complete-case’ approach of dropping individuals with missing data. White and Royston (Statistics in Medicine 2009) and Bartlett et al. (SMMR 2015) described two different MI methods suitable for use with Cox regression. However, no MI methods have been devised which handle time-varying effects of exposures. I will describe extensions of the two MI methods to this setting. I will focus on time-varying effects modelled using restricted cubic splines and will outline a model building strategy which incorporates both MI and selection of time-varying effects. I will present some results from simulation studies, showing that the proposed imputation methods perform well. Failure to account for time-varying effects results in the imputation results in biased estimates and in incorrect tests for proportional hazards, even when there are in truth no time varying effects. The methods will be illustrated using data from the Rotterdam Breast Cancer Study.
- Speaker: Maximilian Coblenz (Institute of Operations Research, Karlsruhe Institute of Technology)
- Title: Nonparametric Estimation of Multivariate Quantiles
- Abstract: In many applications of hydrology quantiles provide important insights in the statistical problems considered. In this paper, we focus on the estimation of multivariate quantiles based on copulas. We provide a nonparametric estimation procedure for a specific notion of multivariate quantiles. These quantiles are based on particular level sets of copulas and admit the usual probabilistic interpretation that a p-quantile comprises a probability mass p. We also explore the usefulness of a smoothed bootstrap in the estimation process. Our simulation results show that the nonparametric estimation procedure yields excellent results and that the smoothed bootstrap can be beneficially applied.