Confidence intervals for rank statistics: Percentile slopes, differences, and ratios
Abstract. I present a program, censlope, for calculating confidence intervals
for generalized Theil–Sen median (and other percentile) slopes (and
per-unit ratios) of Y with respect to X. The confidence intervals are robust
to the possibility that the conditional population distributions of Y ,
given different values of X, differ in ways other than location, such as
having unequal variances. censlope uses the program somersd
and is part of the somersd package. censlope can therefore estimate
confounder-adjusted percentile slopes, limited to comparisons within strata
defined by values of confounders, or by values of a propensity score
representing multiple confounders. Iterative numerical methods have been
implemented in the Mata language, enabling efficient calculation of
percentile slopes and their confidence limits in large samples. I give
example analyses from the auto dataset and from the Avon Longitudinal Study
of Pregnancy and Childhood (ALSPAC).
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Roger Newson
View all articles with these keywords:
somersd, censlope, ALSPAC, robust, confidence interval, rank, nonparametric, median, percentile, slope, difference, ratio, Kendall's τ, Somers' D, Theil–Sen, Hodges–Lehmann, confounder adjusted, propensity score
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