Sensitivity Analysis for Linear Structural Equation Models, Longitudinal Mediation With Latent Growth Models and Blended Learning in Biostatistics Education

Abstract

In chapter 1, we consider the biases that may arise when an unmeasured confounder is omitted from a structural equation model (SEM) and sensitivity analysis techniques to correct for such biases. We give an analysis of which effects in an SEM are and are not biased by an unmeasured confounder. It is shown that a single unmeasured confounder will bias not just one but numerous effects in an SEM. We present sensitivity analysis techniques to correct for biases in total, direct, and indirect effects when using SEM analyses, and illustrate these techniques with a study of aging and cognitive function.

In chapter 2, we consider longitudinal mediation with latent growth curves. We define the direct and indirect effects using counterfactuals and consider the assumptions needed for identifiability of those effects. We develop models with a binary treatment/exposure followed by a model where treatment/exposure changes with time allowing for treatment/exposure-mediator interaction. We thus formalize mediation analysis with latent growth curve models using counterfactuals, makes clear the assumptions and extends these methods to allow for exposure mediator interactions. We present and illustrate the techniques with a study on Multiple Sclerosis(MS) and depression.

In chapter 3, we report on a pilot study in blended learning that took place during the Fall 2013 and Summer 2014 semesters here at Harvard. We blended the traditional BIO 200: Principles of Biostatistics and created ID 200: Principles of Biostatistics and epidemiology. We used materials from the edX course PH207x: Health in Numbers: Quantitative Methods in Clinical \& Public Health Research and used. These materials were used as a video textbook in which students would watch a given number of these videos prior to class. Using surveys as well as exam data we informally assess these blended classes from the student's perspective as well as a comparison of these students with students in another course, BIO 201: Introduction to Statistical Methods in Fall 2013 as well as students from BIO 200 in Fall semesters of 1992 and 1993. We then suggest improvements upon our original course designs and follow up with an informal look at how these implemented changes affected the second offering of the newly blended ID 200 in Summer 2014.