Inverse Probability Weighting for Missing Data

Inverse probability weighting for missing data fits the analysis model to complete cases weighted by the inverse of their estimated probability of being observed, so they represent the full sample.

완전 사례를 관측될 추정 확률의 역수로 가중해 전체 표본을 대표하게 한 뒤 분석 모형을 적합하는 결측 자료 보정 방법입니다.

Follow-up outcomes are missing more often for younger participants. How can I correct my complete-case regression for this selective dropout?

추적 조사 결과가 젊은 참여자에게서 더 자주 빠졌어요. 이런 선택적 탈락을 고려해 완전 사례 회귀를 보정하려면 어떻게 하나요?

Model the probability that the outcome is observed with a logistic regression on covariates such as age, then weight each complete case by the inverse of that probability, stabilised and trimmed. Fit the regression with these weights and robust sandwich standard errors, and check that the weighted complete cases reproduce the covariate means of the full sample.

When to use Inverse Probability Weighting for Missing Data

• The outcome is missing at random given fully observed covariates.
• You prefer to model the missingness process rather than the outcome distribution.
• You want a simple correction of a complete-case analysis that can be reported alongside it.

When to use something else

• Some response probabilities are close to zero, giving extreme weights; use multiple imputation instead.
• Covariates themselves have many missing values; use multiple imputation or FIML instead.

Assumptions and requirements

• Missingness of the outcome depends only on the covariates in the response model (MAR).
• Every case has a non-negligible probability of being observed (positivity).
• The logistic response model is correctly specified; the sandwich standard errors ignore uncertainty from estimating the weights.

What the analysis reports

• Weighted regression coefficients with sandwich SEs, z, p and CI
• Complete-case estimates for comparison
• Weight range, mean and effective sample size
• Standardised mean differences before and after weighting
• Response-model likelihood-ratio test

How to report it

Complete cases (n = [value] of [value]) were weighted by the inverse of the estimated probability of response from a logistic model (stabilised, trimmed); the weighted estimate for [predictor] was b = [value], robust SE = [value], p = [value], 95% CI [[value], [value]] (effective n = [value]).

Related methods

• Inverse Probability Weighting (IPW)
• Multiple Imputation (MICE) with Pooled Regression
• Missingness Mechanism Analysis

Run Inverse Probability Weighting for Missing Data on Quorant