Assumption-Lean Estimation of the Relative Risk Function

Specialeforsvar: Emilie Wessel Søgaard

Titel: Assumption-Lean Estimation of the Relative Risk Function 

Abstract: In this thesis, we aim to perform assumption-lean estimation of the relative risk function. We are motivated by the easy interpretation of this measure of association. In particular, we wish to propose a novel, assumption-lean method of estimating the relative risk for survival data.
To our knowledge, there exists no current standard approach for estimating the relative risk in survival data, neither parametrically nor assumption-lean.
We initially consider the log odds product model proposed by Richardson, Robins, and Wang 2017, which solves the computational difficulties that are associated with the current standard approach of modeling the relative risk via binomial regression with log link function. We present this proposal which involves the construction of a semiparametric locally efficient estimator for the relative risk. This estimator is doubly robust, that is, consistent and asymptotically linear if we have correctly specified either one of two nuisance models.
We seek to generalize this approach to also handle survival data. However, as we come to discover, the approach does not seem to have a natural generalization to survival analysis, as the natural proposal still suffers from the computational problems related to the variational dependence of the baseline risk and target parameter.
Therefore we direct our focus towards the assumption-lean proposal of Vansteelandt and Dukes 2020. The idea of this approach is to formulate nonparametric definitions of main effect estimands which reduce to standard main effect parameters in generalized linear models, such as the relative risk, when these models are correctly specified. We will present the main results
of this approach together with a slightly different approach of deriving the essential remainder terms needed in order to perform nonparametric estimation. It turns out that this proposal does indeed have a natural generalization to survival data.
Thus, we achieve the main goal of the thesis by proposing a novel method for estimating the relative risk function for survival data highly inspired by the method of Vansteelandt and Dukes 2020. Although this generalization is in some sense natural, it requires some work to derive the influence function under the assumption of right-censored data. Finally, we compute the remainder term of this estimand and examine under which assumptions this will be asymptotically negligible. We conclude the thesis with a brief simulation study to illustrate the proposed methods for survival data.

Vejledere: Susanne Ditlevsen,
Frank Eriksson, Torben Martinussen, SUND
Censor: Klaus Kähler Holst, Mærsk