Interval estimation for rank correlation coefficients based on the probit transformation with extension to measurement error correction of correlated ranked data.

Abstract:

:The Spearman (rho(s)) and Kendall (tau) rank correlation coefficient are routinely used as measures of association between non-normally distributed random variables. However, confidence limits for rho(s) are only available under the assumption of bivariate normality and for tau under the assumption of asymptotic normality of tau. In this paper, we introduce another approach for obtaining confidence limits for rho(s) or tau based on the arcsin transformation of sample probit score correlations. This approach is shown to be applicable for an arbitrary bivariate distribution. The arcsin-based estimators for rho(s) and tau (denoted by rho(s,a), tau(a)) are shown to have asymptotic relative efficiency (ARE) of 9/pi2 compared with the usual estimators rho(s) and tau when rho(s) and tau are, respectively, 0. In some nutritional applications, the Spearman rank correlation between nutrient intake as assessed by a reference instrument versus nutrient intake as assessed by a surrogate instrument is used as a measure of validity of the surrogate instrument. However, if only a single replicate (or a few replicates) are available for the reference instrument, then the estimated Spearman rank correlation will be downwardly biased due to measurement error. In this paper, we use the probit transformation as a tool for specifying an ANOVA-type model for replicate ranked data resulting in a point and interval estimate of a measurement error corrected rank correlation. This extends previous work by Rosner and Willett for obtaining point and interval estimates of measurement error corrected Pearson correlations.

journal_name

Stat Med

journal_title

Statistics in medicine

authors

Rosner B,Glynn RJ

doi

10.1002/sim.2547

subject

Has Abstract

pub_date

2007-02-10 00:00:00

pages

633-46

issue

3

eissn

0277-6715

issn

1097-0258

journal_volume

26

pub_type

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