Ingrid Van Keilegom received her PhD in Statistics in 1998 from Limburgs Universitair Centrum (now called Hasselt University) in Belgium. She is, since 2016, professor of statistics at KU Leuven. Previously she was a professor at Pennsylvania State University, Eindhoven University of Technology (Netherlands), and UCLouvain in Belgium, where she still has a part-time position today. Ingrid’s research interests include survival analysis (cure models, dependent censoring, instrumental regression with censored data), semi- and nonparametric regression, measurement error problems, quantile regression, among others. Ingrid received an honorary doctorate from the University of A Coruña (Spain) in 2022; she is an elected member of the Royal Flemish Academy of Belgium for Science and the Arts since 2021; and she is a Fellow of the American Statistical Association (2013) and of the IMS (2008). She has been joint editor of the Journal of the Royal Statistical Society–Series B (2012–15), and is currently Associate Editor of the Journal of the American Statistical Association, the Annals of Statistics, Biometrika, the Annual Review of Statistics and Its Application, and the Electronic Journal of Statistics. She has been holder of a Starting Grant and an Advanced Grant of the European Research Council.

This Medallion Lecture will be given at the Joint Statistical Meetings in Toronto, August 5–10, 2023.


Copula-based Cox proportional hazards model for dependent censoring

In survival analysis it is commonly assumed that the time to the event of interest (survival time) and the right censoring time are independent. This is often satisfied in practice, for example, in the case of administrative censoring or when censoring happens because of reasons that are unrelated to the event of interest. There are however numerous situations in practice in which this assumption might be violated. Consider, for example, the case where the patient leaves the study for reasons relating to their health, or where they die of another related disease. In such cases it is important to take the dependence between the survival time (T) and censoring time (C) into account in the model.

The seminal paper by Tsiatis (1975) shows that the bivariate distribution of T and C is not identifiable in a completely nonparametric setting. Parametric or semiparametric assumptions are therefore necessary to make the model identifiable. In this talk we will start by reviewing the existing literature on this topic, both in the case with and without covariates. A popular approach is to work with copulas, which allows one to model the marginal laws of T and C separately from the relation between T and C. Most papers in the literature assume however that the copula is fully known, which is often unrealistic in practice. The approaches in these papers can be used for sensitivity analyses, but are often not useful for point estimation. The assumption of a known copula can however be overcome in many cases.

We will discuss first the case without covariates, for which we develop a fully parametric copula-based model, that is identifiable under certain conditions on the copula and the margins. These conditions are then checked for a wide range of common copulas and marginals.

Next, we consider how covariates can be incorporated in the model,
by making parametric or semiparametric assumptions on the copula
and/or the margins. We develop sufficient conditions under which the model is identifiable and propose an estimation procedure. The weak convergence of the estimated model components is established, a goodness-of-fit test for the model is suggested, and a bootstrap procedure is proposed to do inference.

Finally, adaptations to cure models (with a proportion of infinite survival times), quantile regression, situations with both independent and dependent censoring, and competing risks are also discussed.

Related models where dependent censoring occurs (such as measurement error models with censored data, dynamic covariates subject to censoring, etc.) are also given some attention, and we finish the presentation with some ideas for future research on this topic.