title: Simple methods of determining confidence intervals for functions of estimates in published results.
abstract: Often, the reader of a published paper is interested in a comparison of parameters that has not been presented. It is not possible to make inferences beyond point estimation since the standard error for the contrast of the estimated parameters depends upon the (unreported) correlation. This study explores approaches to obtain valid confidence intervals when the correlation [Formula: see text] is unknown. We illustrate three proposed approaches using data from the National Health Interview Survey. The three approaches include the Bonferroni method and the standard confidence interval assuming [Formula: see text] (most conservative) or [Formula: see text] (when the correlation is known to be non-negative). The Bonferroni approach is found to be the most conservative. For the difference in two estimated parameter, the standard confidence interval assuming [Formula: see text] yields a 95% confidence interval that is approximately 12.5% narrower than the Bonferroni confidence interval; when the correlation is known to be positive, the standard 95% confidence interval assuming [Formula: see text] is approximately 38% narrower than the Bonferroni. In summary, this article demonstrates simple methods to determine confidence intervals for unreported comparisons. We suggest use of the standard confidence interval assuming [Formula: see text] if no information is available or [Formula: see text] if the correlation is known to be non-negative.
authors.affiliation: McLean Hospital Laboratory for Psychiatric Biostatistics, Belmont, Massachusetts, United States of America.
authors.forename: Garrett
authors.initials: G
authors.lastname: Fitzmaurice
authors.affiliation: Division of Internal Medicine, Brigham and Women's Hospital, Boston, Massachusetts, United States of America; Ariadne Labs, Boston, Massachusetts, United States of America.
authors.forename: Stuart
authors.initials: S
authors.lastname: Lipsitz
authors.affiliation: Department of Medicine, New York University School of Medicine, New York, New York, United States of America.
authors.forename: Sundar
authors.initials: S
authors.lastname: Natarajan
authors.affiliation: Ariadne Labs, Boston, Massachusetts, United States of America.
authors.forename: Atul
authors.initials: A
authors.lastname: Gawande
authors.affiliation: Department of Statistics, Florida State University, Tallahassee, Florida, United States of America.
authors.forename: Debajyoti
authors.initials: D
authors.lastname: Sinha
authors.affiliation: Department of Surgery, University of Wisconsin, Madison, Wisconsin, United States of America.
authors.forename: Caprice
authors.initials: C
authors.lastname: Greenberg
authors.affiliation: Departments of Nutrition and Epidemiology, Harvard School of Public Health, Boston, Massachusetts, United States of America.
authors.forename: Edward
authors.initials: E
authors.lastname: Giovannucci
mesh_terms: D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D008297:Male; D008403:Mass Screening / Q000706:statistics & numerical data; D017430:Prostate-Specific Antigen / Q000032:analysis; D013223:Statistics as Topic / Q000379:methods*
chemical_list: D017430:Prostate-Specific Antigen