Thanks so much for pointing me in the Somers D collection of papers and
software!
The comments from statalist were very useful, especially as I had not
thought of using the wstrata option. I already had an age group variable,
however it was not equally weighted as in your example. I had planned an
adjustment to logistic regression using the continuous variable age. This
has the downside of assuming that age is linear (not usually a correct
assumption). Also, age group can be unequally distributed when created
manually. So this method of creating a new equal decile age group is very
useful.
How does the use of Somers D compare to a logistic regression? Is it always
better to use a rank, ordinal approach such as Somers D and tau-a when
trying to assess the significance of ordinal categorical variables? Or is
it useful to also examine the logistic regressions (using xi to identify
ordinal/categorical independent variables)?
Regards,
Deidra
On 7/12/06 4:12 AM, "Newson, Roger B" <[email protected]>
> In reply to Query 2, if I want to know whether mobility or age predicts
> autism better (in the same direction), then I would usually compare the
> 2 Somers' D parameters, rather than the 2 Kendall's tau-a parameters.
> The difference will be in the same firection. However, I think that
> Somers' D is a better predictor performance indicator, because in this
> case it is expressed on a scale from -1 for the best possible negative
> predictor of autism to +1 for the best possible positive predictor of
> autism, given the number of pairs of subjects whose autism level is
> equal.
>
> However, in reply to Query 1, the parameter measured by lincom is not an
> age-adjusted Somers' D. It is a difference between 2 Somers' D
> parameters. If you want an age-adjusted Somers' D of mobility with
> respect to autism, then group age into groups and estimate a
> within-strata Somers' D of mobility with respect to autism, using the
> wstrata() option of somersd. For instance, to group age into 10 deciles,
> you might type
>
> xtile agegp=age, nquantiles(10)
> tabulate agegp autism
> somersd autism mobility, transf(z) tdist wstrata(age)
>
> and somersd will give you a confidence interval for Somers' D of
> mobility with respect to autism, restricted to comparisons within the
> same age group. This Somers' D is equal to the difference between the
> probability that a randomly-chosen autistic has a higher mobility than a
> randomly-chosen non-autistic and the probability that a randomly-chosen
> non-autistic has a higher mobility than a randomly-chosen autistic,
> assuming that the autistic and the non-autistic are in the same age
> group. (The tabulate command checks that each age group contains both
> autistics and non-autistics.)
>
> The wstrata() option can also use strata defined by multiple grouping
> variables, eg age group and gender. The groups may defined either using
> one variable or using a propensity score defined using multiple
> variables. Examples are discussed in the manuals somersd.pdf and
> censlope.pdf (distributed with the somersd package), and Newson (2006a),
> Newson (2006b) and Newson (2006c), drafts of which can be downloaded
> from my website if unfortunately you do not have access to The Stata
> Journal (which of course everybody should subscribe to).
>
> References
>
> Newson R. 2006a. On the central role of Somers' D. Presented at the 12th
> UK Stata User Meeting, 11-12 September, 2006.
>
> Newson R. 2006b. Confidence intervals for rank statistics: Somers' D and
> extensions. The Stata Journal 6(3): 309-334.
>
> Newson R. 2006c. Confidence intervals for rank statistics: Percentile
> slopes, differences, and ratios. The Stata Journal 6(4): 497-520.
>
>
> Roger Newson
> Lecturer in Medical Statistics
> Respiratory Epidemiology and Public Health Group
> National Heart and Lung Institute
> Imperial College London
> Royal Brompton campus
> Room 33, Emmanuel Kaye Building
> 1B Manresa Road
> London SW3 6LR
> UNITED KINGDOM
> Tel: +44 (0)20 7352 8121 ext 3381
> Fax: +44 (0)20 7351 8322
> Email: [email protected]
> www.imperial.ac.uk/nhli/r.newson/
>
> Opinions expressed are those of the author, not of the institution.
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of Deidra Young
> Sent: 06 December 2006 16:31
> To: [email protected]
> Subject: Re: st: probability and z-statistic
>
> Dear Roger,
>
> 1. If I wanted to conduct the somersd test and adjust for age, do I
> then
> need to include a lincom command which provides the age adjusted
> confidence
> interval (see below)? [I referred to p. 10 of params.pdf]
>
> 2. In this case, is it more appropriate to chose somersd, rather than
> tau-a
> as the test of association (for an ordered categorical ?
>
> . somersd autism mobility age, tr(z) tdist
> . lincom (mobility-age)/2
>
> Results:
>
> . somersd autism mobility age, tr(z) tdist
>
> Somers' D with variable: autism
> Transformation: Fisher's z
> Valid observations: 305
> Degrees of freedom: 304
>
> Symmetric 95% CI for transformed Somers' D
> ------------------------------------------------------------------------
> ----
> | Jackknife
> autism | Coef. Std. Err. t P>|t| [95% Conf.
> Interval]
> -------------+----------------------------------------------------------
> ----
> mobility | -.3910524 .0899135 -4.35 0.000 -.5679839 -.2141209
> Age | .0271106 .0782949 0.35 0.729 -.1269579 .1811791
> ------------------------------------------------------------------------
> ----
>
> Asymmetric 95% CI for untransformed Somers' D
> Somers_D Minimum Maximum
> Mobility -.37226715 -.51387713 -.21090749
> age .02710392 -.12628019 .1792223
>
>
> . lincom (mobility - age)/2
>
> (1) .5 mobility - .5 age = 0
>
> ------------------------------------------------------------------------
> ----
> autism | Coef. Std. Err. t P>|t| [95% Conf. Interval]
> -------------+----------------------------------------------------------
> ----
> (1) | -.2090815 .0567701 -3.68 0.000 -.3207935 -.0973694
> ------------------------------------------------------------------------
> ----
>
> Regards,
> Deidra
>
>
> On 6/12/06 9:04 PM, "Newson, Roger B" <[email protected]>
>
>> Briefly, Kendall's tau-a is the difference between the probability of
>> concordance and discordance, where "concordance" is the event that the
>> larger of 2 X-values is associated with the larger of the 2
>> corresponding Y-values, and discordance is the event that the larger
>> X-value is associated with the smaller Y-value. Somers' D of Y with
>> respect to X, denoted D_YX, is the difference between the 2
>> corresponding CONDITIONAL probabilities, assuming that the 2 X-values
>> are ordered (instead of being tied). And Kendall's tau-b is the
> quantity
>>
>> taub_XY = sign(taua_XY) * sqrt(D_XY * D_YX)
>>
>> or (in other words) the common sign of D_XY and D_YX multiplied by the
>> geometric mean of their 2 absolute values.
>>
>> I personally am more keen on having confidence intervals for Somers' D
>> and Kendall's tau-a because they can be interpreted in words as
>> differences between probabilities, which you cannot do with Kendall's
>> tau-b. There are a large number of downloadable articles,
>> pre-publication drafts and presentations on my website (see my
> signature
>> below) about the "Kendall family" of rank parameters, which are all
>> defined in terms of Kendall's tau-a and also include median slopes,
>> differences and ratios.
>>
>> I hope this helps.
>>
>> Best wishes
>>
>> Roger
>>
>>
>> Roger Newson
>> Lecturer in Medical Statistics
>> Respiratory Epidemiology and Public Health Group
>> National Heart and Lung Institute
>> Imperial College London
>> Royal Brompton campus
>> Room 33, Emmanuel Kaye Building
>> 1B Manresa Road
>> London SW3 6LR
>> UNITED KINGDOM
>> Tel: +44 (0)20 7352 8121 ext 3381
>> Fax: +44 (0)20 7351 8322
>> Email: [email protected]
>> www.imperial.ac.uk/nhli/r.newson/
>>
>> Opinions expressed are those of the author, not of the institution.
>>
>> -----Original Message-----
>> From: [email protected]
>> [mailto:[email protected]] On Behalf Of Joseph
>> Coveney
>> Sent: 06 December 2006 05:18
>> To: Statalist
>> Subject: Re: st: probability and z-statistic
>>
>> Deidra Young wrote:
>>
>> Hi Roger,
>>
>> Only one thing I don't quite follow...
>> The tab command will produce Kendall's tau-b and approximate SE.
>> However,
>> Sommers' D produces tau-a only.
>>
>> How do tau-a and tau-b differ?
>>
>>
> ------------------------------------------------------------------------
>> --------
>>
>> You'll find a description of each on Roger's website. Take a look at
>> Section 2 on Page 2 of
>>
>> www.imperial.ac.uk/nhli/r.newson/papers/params.pdf
>>
>> Joseph Coveney
>>
>>
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
