Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

• 成果类型: Article
• 署名作者: Zhao, Qingyuan; Small, Dylan S.; Bhattacharya, Bhaswar B.
• 署名单位: University of Pennsylvania
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12327
• 发表日期: 2019
• 页码: 735-761
• 关键词: propensity score; inference; selection; hypotheses; covariate; outcomes; regions

摘要

To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the 'missingness at random' and 'no unmeasured confounder' assumptions. However, these assumptions are unverifiable by using empirical data and pose serious threats to the validity of the qualitative conclusions of statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. We consider a marginal sensitivity model which is a natural extension of Rosenbaum's sensitivity model that is widely used for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that asymptotically the intervals have at least nominal coverage of the estimand whenever the data-generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax-maximin inequality to transform this intractable problem into a linear fractional programming problem, which can be solved very efficiently. We illustrate our method by using a real data set to estimate the causal effect of fish consumption on blood mercury level.