Quantiles in Nonrandom Samples and Observational Studies
作者:
PaulR. Rosenbaum,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1995)
卷期:
Volume 90,
issue 432
页码: 1424-1431
ISSN:0162-1459
年代: 1995
DOI:10.1080/01621459.1995.10476648
出版商: Taylor & Francis Group
关键词: Contingency tables;Holley's inequality;Nonrandomized studies;Order statistics;Savage's rank order lattice;Sensitivity analysis
数据来源: Taylor
摘要:
In a nonrandom sample or a nonrandomized comparison of treated and control groups, methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection. Quantiles of a single distribution and for a shift in two distributions are both discussed. These confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison. The inequality has additional applications. In particular, it greatly accelerates the computations in a sensitivity analysis for the Mantel–Haenszel statistic in a 2 × 2 ×Scontingency table. Examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas, an observational study of chromosome damage from mercury, and a study of the drug allopurinol as a cause of skin rash. The proof of the inequality makes use of Savage's lattice for ranks and Holley's inequality, which gives sufficient conditions for stochastic ordering in a lattice.
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