Risk ratios and Scanlan’s HRX

Hoben Thomas () and Thomas P. Hettmansperger ()
Additional contact information
Hoben Thomas: Department of Psychology
Thomas P. Hettmansperger: Department of Statistics

Journal of Statistical Distributions and Applications, 2017, vol. 4, issue 1, 1-15

Abstract: Abstract Risk ratios are distribution function tail ratios and are widely used in health disparities research. Let A and D denote advantaged and disadvantaged populations with cdfs F A (x) and F D (x) respectively, F A (x)≤F D (x). Consider a selection setting where those selected have x>c a critical value. Scanlan observed in empirical data that as c is lowered the failure ratio F R(c)=F D (c)/F A (c) and success ratio S R(c)=[1−F D (c)]/[1−F A (c)] can both be increasing with decreasing c, a surprising result Scanlan calls Heuristic Rule X (HRX). The consequences of HRX for disparities research have not been well understood, and appear to be often ignored. The analytical conditions for HRX to hold have not, heretofore, been proven. In the normal case, HRX holds if the variances are equal. In general, HRX is not a robust condition. Settings and distributional conditions necessary for HRX to hold are discussed, including mixture settings of normal and other variables.

Keywords: HRX; Mixture models; Risk ratios; Tail ratios; Disparity; 60E99 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1186/s40488-017-0071-6 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0071-6

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/40488

DOI: 10.1186/s40488-017-0071-6

Access Statistics for this article

Journal of Statistical Distributions and Applications is currently edited by Felix Famoye and Carl Lee

More articles in Journal of Statistical Distributions and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().