Advisory Committee Chair
Hemant K Tiwari
Advisory Committee Members
Dustin M Long
Date of Award
Degree Name by School
Doctor of Philosophy (PhD) School of Public Health
Instrumental variable (IV) methods are causal analysis techniques used on observational data to address confounding, provided that certain assumptions are met. In the usual observational setting, some exposure of interest �� is associated with some outcome of interest ��, but confounders �� could distort the measure of the association between �� and ��. A valid IV is a proxy of sorts for �� which behaves in a very specific way, in that the IV operates analogously to the treatment group assignment seen in randomized trials. Finding a valid IV is no trivial task, but if one exists and we identify it, then these are the only known methods to handle unobserved confounders and estimate the causal effect of �� on �� in observational data. These techniques originated in econometrics, but have gained recent traction in epidemiology and genetics. Genetic variants provide promising sources of potential IVs. The use of genetic variants as IVs has been dubbed as Mendelian randomization (MR). Numerous methods have been proposed for IV or MR analyses; including the Wald method, various two-stage least squares (2SLS) methods, maximum likelihood methods, and the generalized method of moments (GMM). These methods are well understood for the case of normally distributed variables, but much less so for other distributional scenarios. Few implementations in conventional statistical software exist for MR methods applicable to non-normal variates. iii The main aim of this dissertation is to investigate the bias and asymptotic properties of existing MR methods, and propose new methods, in various distributional scenarios. These scenarios include non-normal settings such as binary and count variates, the case of clustered or non-independent observations, and time-to-event measures. The three specific aims of this dissertation are 1) to develop software implementations in SAS and R for the simulation of confounded non-normal variates and MR analysis methods; 2) to develop novel methods for MR analysis of non-normal variates; and 3) to use simulations to investigate the bias and asymptotic properties of existing and new MR methods in non-normal scenarios, with special attention to the performance of methods in the presence of weak and composite instruments. This dissertation culminates by proposing several new statistical models for MR analysis and several peer-reviewed publications. First, in Paper 1, we adapt a bivariate Bernoulli distribution to an IV regression setting frequently seen in applications. Second, in Paper 2, we expand upon the bivariate Bernoulli adaption to scenarios with multiple instruments. Finally, in Paper 3, we generalize the correlated errors model of Burgess and Thompson to scenarios with non-normal variates. SAS programs are developed to fit the newly proposed models and perform simulations to compare their results to previously established statistical methods for MR. Additionally, framework is developed for future work including MR scenarios with count variates and a further extension of the correlated errors model for scenarios with clustering.
Allman, Phillip Hunter, "Statistical Methodology for Mendelian Randomiztion Analysis" (2021). All ETDs from UAB. 529.