Local sensitivity approximations for selectivity bias

• Published in: J. Roy. Statist. Soc., B Vol. 63; no. 4; pp. 871 - 895
• Main Authors: Copas, John, Eguchi, Shinto
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishers Ltd 2001; Blackwell Publishers; Oxford University Press (OUP); Blackwell; Royal Statistical Society
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Approximation; Bias; Data analysis; Estimation bias; Exact sciences and technology; Ignorability; Inference; Mathematical expressions; Mathematical vectors; Mathematics; Missing data; Multivariate analysis; Parametric models; Prisons; Probability and statistics; Sciences and techniques of general use; Selection bias; Sensitivity analysis; Statistical methods; Statistics; Missing data; Data analysis; Sensitivity analysis; Approximation; Bias; Estimator robustness; Statistical estimation; Biased estimation
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/1467-9868.00318

Observational data analysis is often based on tacit assumptions of ignorability or randomness. The paper develops a general approach to local sensitivity analysis for selectivity bias, which aims to study the sensitivity of inference to small departures from such assumptions. If M is a model assuming ignorability, we surround M by a small neighbourhood N defined in the sense of Kullback-Leibler divergence and then compare the inference for models in N with that for M. Interpretable bounds for such differences are developed. Applications to missing data and to observational comparisons are discussed. Local approximations to sensitivity analysis are model robust and can be applied to a wide range of statistical problems.