.-
help for ^somersd^  (STB-55: snp15; STB-57: snp15.1; STB-58: snp15.2; STB-61: snp15.3)
.-

Somers' D or Kendall's tau-a with confidence intervals
-------------------------------------------------------

         ^somersd^ varlist [weight] [^if^ exp] [^in^ range]
                     [,^cl^uster^(^varname^)^ ^l^evel^(^#^)^ ^ta^ua  ^td^ist
                     ^tr^ansf^(^transformation_name^)^ ^ci^matrix^(^new_matrix^)^ ]

where transformation_name is one of

	^iden^ | ^z^ | ^asin^ | ^rho^ | ^zrho^

^fweights^, ^iweights^ and ^pweights^ are allowed; see help ^weights^.


Description
-----------

^somersd^ calculates values of Somers' D or Kendall's tau-a for the first
variable of varlist as a predictor of each of the other variables in varlist,
with estimates and jackknife variances and confidence intervals output as if
for the parameters of a maximum likelihood fit. It is possible to use @lincom@
to output confidence limits for differences between the population Somers' D or
tau-a values.


Options for use with ^somersd^
----------------------------

^cluster(^varname^)^ specifies the variable which defines sampling clusters.
    If ^cluster^ is defined, then the between-cluster Somers' D or tau-a is
    calculated, and the variances are calculated assuming that the data are
    sampled independently from a population of clusters, rather than from a
    population of observations

^level(^#^)^ specifies the confidence level, in percent, for confidence intervals
    of the estimates; see help for @level@.

^taua^ causes ^somersd^ to calculate Kendall's tau-a. If ^taua^ is absent, then
    Somers' D is calculated.

^tdist^ specifies that the estimates are assumed to have a
    t-distribution with n-1 degrees of freedom, where n is the number of
    clusters, or the number of observations if ^cluster^ is not specified.

^transf(^transformation_name^)^ specifies that the estimates are to be transformed,
    defining a confidence level for the transformed population value. ^iden^
    (identity or untransformed) is the default. ^z^ specifies Fisher's z (the
    hyperbolic arctangent), ^asin^ specifies Daniels' arcsine, ^rho^ specifies
    Greiner's rho (Pearson correlation estimated using Greiner's relation), and
    ^zrho^ specifies the z-transform of Greiner's rho.

^cimatrix(^new_matrix^)^ specifies an output matrix to be created, containing
    estimates and confidence limits for the untransformed Somers' D, Kendall's
    tau-a or Greiner's rho parameters. If ^transf()^ is specified, then the
    confidence limits will be asymmetric and based on symmetric confidence
    limits for the transformed parameters. This option (like ^level^) may be
    used in replay mode as well as in non-replay mode.


Remarks
-------

For variables X and Y, Kendall's tau-a is defined as

^tau-a(X,Y) = E[sign(X1-X2)sign(Y1-Y2)]^

where (X1,Y1) and (X2,Y2) are sampled from the bivariate distribution of
X and Y. Somers' D is defined as

^D(Y|X) = tau-a(X,Y)/tau-a(X,X)^

In the case of a binary X-variable, Somers' D is the parameter tested for a
zero value by the Mann-Whitney U-test. If X is a disease indicator and Y is a
quantitative diagnostic measure, then Somers' D is related to the area A under
the receiver-operator characteristic (ROC) curve by the formula ^A=[D(Y|X)+1]/2^.
The covariance matrix is estimated by jackknifing the underlying U-statistics
and using Taylor polynomials. Confidence intervals for differences and other
contrasts can be calculated using ^lincom^.


Examples
--------

   . ^somersd foreign mpg weight,tr(z)^

   . ^somersd us gpm weight^
   . ^lincom weight-gpm^

   . ^somersd mpg weight displ,taua tr(z) cluster(manuf)^


Author
------

Roger Newson, Guy's, King's and St Thomas' School of Medicine, London, UK.
email: ^roger.newson@@kcl.ac.uk^


Also see
--------

 Manual:  ^[R] spearman, [R] signrank, [R] roc^
    STB:  STB-55: snp15, STB-57: snp15.1, STB-58: snp15.2
On-line:  help for @ktau@, @ranksum@, @roc@, help for @jknife@ if installed