Chapter 1 Overview

Welcome! This tutorial provides a roadmap for sensitivity analyses to assess the impact of loss to follow-up on causal effect estimates. In particular, we introduce and implement a multiple-imputation-based pattern-mixture approach to MNAR mechanisms based on previous work by Leurent et al. (2018 Pharmacoeconomics).

1.1 Who is this for?

This tutorial is intended for any public health researcher who is seeking an easily implemented, transparent approach to testing the impacts of differential loss to follow-up (LTFU) on their causal effect estimate of interest. Since methods are widely available for performing multiple imputation when outcome data are missing at random conditional on measured covariates, here we focus on the frequently co-occurring scenario of outcome data missing not at random – making this LTFU non-ignorable.

The methods and sample code provided in this guide will be particularly useful for researchers who have completed the analysis phase of a study, and who want to test the robustness of their results to a range of missing outcome data mechanisms. The researcher may have conducted a complete case analysis or have previously imputed outcome data according to their preferred method(s) but may be questioning whether variables outside of their data also inform missingness. The researcher may or may not have some evidence (whether anecdotal or in the literature) for potential missing data mechanisms which they are unable to measure. This tutorial will aid such researchers to understand and report on the impact of these non-ignorable mechanisms on their causal effect of interest.

1.2 What will I find here?

We begin this practical guide with a discussion of “the problem” of non-ignorable LTFU, with a particular emphasis on limitations for causal inference. We then guide the user through possible non-ignorable LTFU scenarios and how to conduct sensitivity analyses to test their impact on the causal effect of interest.

In this guide you will find an original analytic strategy, sample R code, and recommended output. The practical guide is organized as follows:

Section 2: Background for why we wrote this tutorial.

Section 3: A description of techniques typically employed for sensitivity analysis for data missing not at random and our general approach to applying pattern-mixture modeling.

Section 4: A description of four missing data scenarios that may drive loss-to-follow-up, emphasizing that multiple mechanisms can operate concurrently to produce missing outcome data.

Section 5: A description of the methods to apply pattern-mixture modeling technique to our four missing data scenarios.

Section 6: A demonstration for how to implement sensitivity analysis in R according to each missing data scenario.

Section 7: A beginner’s guide to selecting priors in the context of pattern-mixture modeling for sensitivity analysis of data missing not at random.

Section 8: An applied example for how to interpret and report sensitivity analyses in scientific articles, including tables and figures.

Section 9: A concluding discussion of the strengths, weaknesses, and extensions of our approach.

Section 10: A list of conceptual and applied articles, books, and other resources.