Thanks to Kit Baum, a new version of the -somersd- package is now
available for download from SSC. In Stata, use the -ssc- command to do
this.
The -somersd- command (described as below on my website) calculates
confidence intervals for a wide range of rank statistics. The new
version adds a third module -censlope- to the existing modules -somersd-
and -cendif-. -censlope- is an extended version of -somersd-, which also
calculates confidence intervals for the Theil-Sen median slope. These
confidence intervals are robust to the possibility that the conditional
distributions of the Y-variable, given each value of the X-variable,
differ in ways other than location. For instance, the conditional
variances may vary, and so may the other moments about the mean. This is
in contrast to the original confidence interval formula of Sen (1968),
which assumes that the contitional distributions differ only in
location.
The Theil-Sen slope can be defined in terms of Somers' D, which comes in
many versions, such as clustered, within-cluster or within-strata
versions of Somers' D. If the user asks -censlope- for a clustered,
within-cluster or within-strata version of Somers' D, then the Theil-Sen
slope will also be clustered, within-cluster or within-strata. For
instance, the user may ask for a within-strata Theil-Sen slope, with
strata based on values of a confounder, or on values of multiple
confounders, or on a propensity score summarizing many confounders. In
this case, the Theil-Sen slope will be confounder-adjusted, as well as
being expressed in useful units in which to express a difference, such
as Y-units, or Y-units per X-unit. This is a useful thing to be able to
do, if we intend to use rank methods to make monetary or other practical
decisions.
I would like to thank my former colleague Nigel Smeeton of King's
College London, UK, for drawing my attention to the Theil-Sen slope and
to his very useful book on rank methods, co-authored with Peter Sprent
(Sprent and Smeeton, 2001). I would also like to thank all at StataCorp
for providing their very powerful Mata programming language, without
which the new version of -somersd- would probably not have been
feasible.
Best wishes
Roger
References
Sen P. K. 1968. Estimates of the regression coefficient based on
Kendall's tau. Journal of the American Statistical Association 63(324):
1379-1389. Also downloadable from JSTOR at
http://uk.jstor.org/
Sprent P. and N. C. Smeeton. 2001. Applied Nonparametric Statistical
Methods. Boca Raton, FA: Chapman & Hall/CRC.
Roger Newson
Lecturer in Medical Statistics
POSTAL ADDRESS:
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute at Imperial College London
St Mary's Campus
Norfolk Place
London W2 1PG
STREET ADDRESS:
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute at Imperial College London
47 Praed Street
Paddington
London W1 1NR
TELEPHONE: (+44) 020 7594 0939
FAX: (+44) 020 7594 0942
EMAIL: [email protected]
WEBSITE: http://www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.
------------------------------------------------------------------------
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package somersd from http://www.imperial.ac.uk/nhli/r.newson/stata9
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TITLE
somersd: Kendall's tau-a, Somers' D and percentile slopes
DESCRIPTION/AUTHOR(S)
The somersd package contains the programs somersd, censlope and
cendif,
which calculate confidence intervals for a range of parameters
behind
rank or "nonparametric" statistics. somersd calculates confidence
intervals for generalized Kendall's tau-a or Somers' D parameters,
and stores the estimates and their covariance matrix as estimation
results.
It can be used on left-censored, right-censored, clustered and/or
stratified data. censlope is an extended version of somersd, which
also
calculates confidence limits for the generalized Theil-Sen median
slopes
(or other percentile slopes) corresponding to the version of
Somers' D
or Kendall's tau-a estimated. cendif is an easy-to-use program to
calculate confidence intervals for Hodges-Lehmann median
differences
(or other percentile differences) between two groups. The somersd
package
can be used to calculate confidence intervals for a wide range of
rank-based parameters, which are special cases of Kendall's tau-a,
Somers' D or percentile slopes. These parameters include
differences
between proportions, Harrell's c index, areas under receiver
operating
characteristic (ROC) curves, differences between Harrell's c
indices or
ROC areas, Gini coefficients, population attributable fractions,
median
differences, ratios, slopes and per-unit ratios, and the
parameters
behind the sign test and the Wilcoxon-Mann-Whitney or
Breslow-Gehan
ranksum tests. Full documentation of the programs (including
methods and
formulas) can be found in the manual files somersd.pdf,
censlope.pdf and
cendif.pdf, which can be viewed using the Adobe Acrobat Reader.
Author: Roger Newson
Distribution-date: 21 May 2006
Stata-version: 9
INSTALLATION FILES (click here to
install)
cendif.ado
censlope.ado
somers_p.ado
somersd.ado
cendif.hlp
censlope.hlp
censlope_iteration.hlp
mf_bcsf_bracketing.hlp
mf_blncdtree.hlp
mf_somdtransf.hlp
mf_u2jackpseud.hlp
somersd.hlp
somersd_mata.hlp
_bcsf_bisect.mata
_bcsf_bracketing.mata
_bcsf_regula.mata
_bcsf_ridders.mata
_blncdtree.mata
_somdtransf.mata
_u2jackpseud.mata
_v2jackpseud.mata
blncdtree.mata
tidot.mata
tidottree.mata
lsomersd.mlib
ANCILLARY FILES (click here to get)
cendif.pdf
censlope.pdf
somersd.pdf
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