• Sensitivity Analysis for MNAR
  • 1 Overview
    • 1.1 Who is this for?
    • 1.2 What will I find here?
  • 2 Background and Motivation
    • 2.1 The Problem
    • 2.2 Why did we write this tutorial?
  • 3 Description of the technique: pattern-mixture modeling
    • 3.1 Two approaches to MNAR sensitivity analysis
    • 3.2 Proposed approach
  • 4 Introducing four missing data scenarios
    • 4.1 Scenario 1 (MCAR)
    • 4.2 Scenario 2 (MAR)
    • 4.3 Scenario 3 (MAR + MNAR)
    • 4.4 Scenario 4 (MAR + MNAR)
  • 5 Methods
    • 5.1 Modeling framework
    • 5.2 Assumptions
    • 5.3 Application of pattern-mixture modeling
    • 5.4 Example dataset
  • 6 Implementation in R
    • Basic descriptive statistics
    • 6.1 Scenario 1: Loss to follow-up unrelated to exposure, outcome, and confounders (MCAR)
    • 6.2 Scenario 2: Loss to follow-up differential by exposure \(A\) and/or measured confounder \(C\) (MAR)
    • 6.3 Scenario 3: Loss to follow-up differential on disease/ disease + exposure status (MNAR)
      • Scenario 3a: Additive relationship between Y and data missingness (\(\delta\) method)
      • Scenario 3b: Multiplicative relationship between Y and data missingness (\(c\) scale method)
    • 6.4 Scenario 4: Loss to follow-up differential on unmeasured confounder (MNAR)
      • Example and sample code
      • Output
  • 7 Selecting your priors
    • 7.1 Model specification
    • 7.2 Selecting a range of plausible offset values: the role of expert opinion
    • 7.3 What to do in the absence of prior knowledge: an “e-value” approach
  • 8 Reporting your findings
    • 8.1 Methods
    • 8.2 Results
      • Scenario 3 (MNAR mechanism dependent on outcome \(Y\))
      • Scenario 4 (MNAR mechanism dependent on unmeasured confounder \(U\))
    • 8.3 Recommended interpretations
      • Scenario 3 (MNAR mechanism dependent on outcome \(Y\))
      • Scenario 4 (MNAR mechanism dependent on unmeasured confounder \(U\))
  • 9 Conclusions/ Final Thoughts
    • 9.1 Strengths
    • 9.2 Limitations
    • 9.3 Opportunities for extending methods presented
  • 10 Resource List
    • Helpful links to learn about modelling MNAR data mechanisms
    • Guides for reporting sensitivity analyses
    • Other resources
  • References
  • Published with bookdown

A Practical Guide to Sensitivity Analysis for Causal Effects in the Presence of Non-Ignorable Loss to Follow-Up

Chapter 10 Resource List

Helpful links to learn about modelling MNAR data mechanisms

  • Overview of pattern-mixture modelling and simple implementation (in this R Bookdown)

  • Leurent et al. 2018 Pharmacoeconomics tutorial on MI-based implementation of pattern-mixture models; our approach relied heavily on this paper for modelling LTFU based on outcome status

  • Little 1994 Biometrika paper providing theoretical basis for modelling MNAR mechanisms as an extension of MAR approaches

  • Van Buuren primer on pattern-mixture and selection approaches to modelling MNAR data, Section 3.8

  • An alternative to pattern-mixture models: an R package for implementing selection models (alternative option)

Guides for reporting sensitivity analyses

  • For RCTs: CONSORT guidelines

  • For observational studies: STROBE guidelines

  • For Bayesian analysis

Other resources

  • An introduction to reading and drawing DAGs

  • Guide to assumptions for causal inference