Delta-Adjusted Tipping-Point Sensitivity Analysis

Delta-adjusted tipping-point analysis multiply imputes missing outcomes under missing at random, shifts the imputed values by a range of δ to represent departures from it, and finds where the conclusion changes.

결측 결과를 MAR 가정으로 다중대체한 뒤 대체값을 여러 δ 만큼 옮겨 MAR 이탈을 표현하고, 결론이 바뀌는 지점을 찾는 민감도 분석입니다.

In my trial 20% of outcomes are missing and the effect is significant under multiple imputation. How far from missing at random would the dropouts have to be before the conclusion changes?

시험에서 결과의 20%가 빠졌고 다중대체로는 효과가 유의해요. 탈락자가 MAR 에서 얼마나 벗어나야 결론이 뒤집히나요?

Run a tipping-point analysis: impute missing outcomes under missing at random, add a shift δ to the imputed values in one arm, re-estimate the treatment effect and pool across imputations for each δ. The δ at which the result stops being significant is the tipping point, and you then judge whether a shift that large is clinically plausible.

When to use Delta-Adjusted Tipping-Point Sensitivity Analysis

• A randomised or observational comparison has missing outcomes and the primary analysis assumes MAR.
• Regulators or reviewers ask for a sensitivity analysis to missing-not-at-random assumptions.
• You want to express robustness as an interpretable outcome shift.

When to use something else

• Covariates also have substantial missing values; impute them first with chained equations.
• You have a credible model of the dropout mechanism; use a selection model instead.

Assumptions and requirements

• At δ = 0, outcomes are missing at random given treatment arm and covariates.
• Departures from MAR are a constant mean shift δ of the missing outcomes in the chosen arm.
• The imputation model (Bayesian normal linear regression within arm) and the analysis model (ANCOVA) are adequate.

What the analysis reports

• Pooled treatment effect, SE, Barnard–Rubin df, p and CI for each δ
• Tipping δ in each direction and the interpolated δ where p crosses α
• Fraction of missing information

How to report it

Under MAR multiple imputation (m = [value]), the treatment effect was [value] (SE = [value], p = [value]); in a delta-adjusted tipping-point analysis shifting imputed outcomes in the treated arm, the conclusion changed at δ = [value].

Related methods

• Multiple Imputation (MICE) with Pooled Regression
• Missingness Mechanism Analysis
• Inverse Probability Weighting for Missing Data

Run Delta-Adjusted Tipping-Point Sensitivity Analysis on Quorant