Sensitivity analyses for causal inference

Abstract

The validity of causal inference always rests on untestable assumptions. It is valuable to quantify the extent to which violations of different causal assumptions will alter the conclusions of a study. This is the motivation behind sensitivity analyses. The aim of this thesis is to develop sensitivity analyses for a variety of biases, including selection bias, coarsening bias in instrumental variable designs and familial and ancestral biases in genetic association studies.

The first chapter develops an approach to statistical inference in stochastic optimization problems when both the function to minimized, and the set over which it is minimized, must be estimated empirically. I apply this inference procedure to the problem of selection bias in large population cohorts such as UK Biobank. I propose a sensitivity analysis which is able to flexibly incorporate a wide variety of population-level information, while providing valid statistical inference.

The second chapter addresses the problem of coarsening bias in Mendelian randomization (MR) studies. In such studies, the exposure is often a coarsened approximation to some latent continuous trait. Genetically driven variation in the outcome can exist within categories of the exposure, violating the exclusion restriction. I derive a closed-form expression for the resulting bias and propose a simple correction that can be used with summary-level data to provide MR estimates with interpretable effect sizes.

The final chapter utilizes the increasing prevalence of within-family data to provide an "almost exact" approach to MR. I provide a formal justification for the validity of the MR design by building a causal model which includes features such as assortative mating, linkage disequilibrium, population stratification and transmission ratio distortion. I then propose an "almost exact" randomization test for MR based on explicitly modelling the distribution of crossovers. I apply this test to the Avon Longitudinal Study of Parents and Children (ALSPAC).

Date of Award	21 Mar 2023
Original language	English
Awarding Institution	University of Bristol
Supervisor	Kate M Tilling (Supervisor), Qingyuan Zhao (Supervisor), George Davey Smith (Supervisor), Rach Hughes (Supervisor) & Jack Bowden (Supervisor)