Simon Christoffer Ziersen PhD Defense

Invitation to PhD defense

Simon Christoffer Ziersen

Causal inference in time-to-event analysis

Date Thursday, 12 December 2024, at 14.00

Venue Øster Farimagsgade 5, 1353 Copenhagen K, room 35-01-06 (CSS)

The defense will be followed by a reception in room 5.2.46 (CSS)

Academic Advisors

• Professor Esben Budtz-Jørgensen, Section of Biostatistics, University of Copenhagen

• Professor Thomas Alexander Gerds, Section of Biostatistics, University of Copenhagen

• Clinical Professor Lars Vedel Kessing, Copenhagen Affective Disorder Research Center (CADIC), Psychiatric Center Copenhagen and Department of Clinical Medicine, University of Copenhagen

• Associate Professor Brice Maxime Hugues Ozenne, Section of Biostatistics, University of Copenhagen

Assessment Committee

• Associate professor Helene Charlotte Wiese Rytgaard (Chairperson), Section of Biostatistics, University of Copenhagen

• Associate professor Stefan Nygaard Hansen, Department of Public Health – Biostatistics, Aarhus University

• Professor Sarah Friedrich, Mathematical Statistics and Artificial Intelligence in Medicine, Ausburg University

Summary

The aim of this thesis is to provide statistical methods for assessing treatment effects with registry data, where the outcome of interest is time to an event.  Often, only a censored version of the underlying event time is available, and methods from survival analysis allowing for competing risks must be combined with causal inference methodology for inferring the treatment effect. The thesis is comprised of a synopsis and three manuscripts. The synopsis provides an introduction to semiparametric efficiency theory and the use of data-adaptive methods for estimation of causal estimands, which form the basis of the methodological work undertaken in the manuscripts. The contributions of the manuscripts are grouped into two categories:

Average treatment effect estimation with censoring and competing risks

Manuscript I considers estimation of the average treatment effect based on the τ -year absolute risk with a high-dimensional set of potential confounders. We derive an estimator for the target parameter that allows for penalized regressions for nuisance parameter estimation. The method is applied to a study comparing the response to different antidepressants using data from the Danish national registers. Manuscript III derives a measure of treatment effect based on the number of life years lost due to a specific event. This definition of treatment effect returns the interpretation to the timescale of the study, which is easier to communicate compared to risks. We derive an estimator that allows for data-adaptive estimation of the nuisance parameters and give high-level assumptions for valid inference of the estimator.

Assessment of heterogeneous treatment effects

Manuscript II extends a treatment effect variable importance measure to censored data. The measure is used to assess the amount of treatment effect heterogeneity explained by a given set of covariates. Additionally, a new measure is derived as a best partially linear projection of the conditional average treatment effect. The projection measures the heterogeneity explained by a single covariate, and it has interpretation as a regression coefficient. Manuscript III extends the projection measure from Manuscript II to the treatment effect based on the number of life years lost due to a specific event. The method is applied to the register study on response to different antidepressants.