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# AW: AW: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-

 From "Vasyl Druchkiv" To Subject AW: AW: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian- Date Thu, 15 Nov 2012 22:41:40 +0100

```Hello Roger,

thank you for your advice! I have applied -censlope- with -cluster- option to estimate differences between medians. It works great! To your question about the fraction of values equal to median. To answer this question let me return to the example, where I try to find the relationship between the ocular side and the difference between the central and thinnest points of cornea. The dependent variable is here CCT-TPCT. First I would like to describe the distribution of cct-tpct conditional on ocular side. In right eye the median is equal to 8 and 800 eyes from 8436 (9.5%) have the value of 8. In left eye the median is 7 and 756 eyes from 8436 ( 9%) have the value 7. For the right and left eyes -bpmedian- estimates missing standard errors and CIs. However, I don't really know how high must be fraction of values being equal to median to cause the zero standard errors.  On the contrary -parmset- displays "correctly" the se of 0 and 95% CIs of 8.  The same is for the left eye but !
with value 7. The difference is trivial. However it is necessary to report the statistical significance.

Since eyes are not statistically independent (as you correctly pointed out) I used -censlope- with option -cluster- to estimate the differences between the eyes. The Somers' D as expected is negative (and with negative CIs) showing that the propensity to have a lower difference for the left eye is higher than that for the right eye (p<0.001). The difference between right and left eyes is -1 with CI -1 and 0 for 50th percentile; -4 (-5;-4) for 25th percentile; and 3 (3:3) for 75th percentile. Can it be said that the eyes are different in median? Or is it better to say that the propensity is significant? I ask because the upper CI for 50th percentile includes 0.

However, I have another question. Is it possible to control for confounder in  -censlope-? I consulted your paper* where you reported differences adjusted for confounder. However, I am not sure, how I should proceed if I have clustered data. As I understood I have to estimate propensity score defined as the predicted odds from the logistic regression where eye is a dependent variable. Though, I don't know whether this model should  be a simple logistic model or rather a logistic model with ID as a random effect?

Sorry for long explanations and for your time!

Regards,
Vasyl

*Newson, R. (2006): Confidence intervals for rank statistics: Percentile slopes, differences, and ratios. In: Stata Journal 6 (4), S. 497-520(24). Online verfügbar unter http://www.stata-journal.com/article.html?article=snp15_7.

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Roger B. Newson
Gesendet: Wednesday, November 14, 2012 1:11 PM
An: statalist@hsphsun2.harvard.edu
Betreff: Re: AW: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-

Another point has occurred to me. You seem to be comparing left and right eyes in the same subjects (correct me if I'm wrong). So, if I am right, then your methods should be clustered by subject, because left and right eyes in the same subjects are not statistically independent.
And -qreg- doesn't seem to have options for clustering yet.

If you want to estimate a median difference between left and right eyes in the same group of subjects, then it might be a good idea to use the
-censlope- module of the -somersd- package, which you can also download from SSC, with a -cluster()- option.

I hope this helps. Let me know if you have any queries, especially about -censlope-.

Best wishes

Roger

Roger B Newson BSc MSc DPhil
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: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:

Opinions expressed are those of the author, not of the institution.

On 13/11/2012 22:55, Vasyl Druchkiv wrote:
> Hello Nick and Roger,
>
> thank you for your quick reply! Sorry, that I haven't provided background to the data. The variable from the example contains astigmatism of  the eyes that describes cornea steepness. This variable is not symmetric. In fact it is extremely skewed to the left. To get an idea of the data here are some descriptive statistics:
>                            astigmatism
> -------------------------------------------------------------
>        Percentiles      Smallest
>   1%         -4.5             -7
>   5%           -3           -6.5
> 10%         -2.3           -6.5       Obs               16872
> 25%         -1.3           -6.5       Sum of Wgt.       16872
>
> 50%          -.8                      Mean          -1.005293
>                          Largest       Std. Dev.      .9449402
> 75%          -.3              0
> 90%            0              0       Variance       .8929119
> 95%            0              0       Skewness      -1.812464
> 99%            0              0       Kurtosis       7.150496
>
> So, you can see that the variable is not a constant one: there is a variation, although 54% of the eyes had an astigmatism  of -.8. I've applied already -parmest-  (-bpmedian- and -parmest- I downloaded from SSC) as suggested by Roger and indeed got the confidence intervals that are equal to median.
> However it is not only the confidence intervals that concern me. In another case I try to run a quantile regression with bootstrap estimation method and  the difference between  thinnest and central points of the cornea as dependent variable. The dependent variable is also not symmetric and has positive skewness:
>             cct-tpct
> -------------------------------------------------------------
>        Percentiles      Smallest
>   1%            3              0
>   5%            4              0
> 10%            4              1       Obs               16872
> 25%            5              1       Sum of Wgt.       16872
>
> 50%            8                      Mean           9.485479
>                          Largest       Std. Dev.      8.423524
> 75%           11            122
> 90%           16            124       Variance       70.95575
> 95%           20            380       Skewness       14.34001
> 99%           33            380       Kurtosis       487.1662
>
> When I use for instance ocular side (right/left) as a dummy independent variable I get:
>
> Median regression, bootstrap(20) SEs                 Number of obs =     16872
>    Raw sum of deviations    68401 (about 8)
>    Min sum of deviations    68061                     Pseudo R2     =    0.0050
>
> ------------------------------------------------------------------------------
>       ccttpct |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+--------------------------------------------------------
> -------------+--------
>           eye |         -1          .        .       .            .           .
>         _cons |          8          .        .       .            .           .
> ----------------------------------------------------------------------
> -------- So, there is a difference between eyes. However there are no
> statistics to report. Of course I could use for example Wilcoxon  signed-rank test to check the differences (and would probably find insignificant results). But my idea is to fit a multivariate model with more independent variables.
> If you could help me further it would be great.
>
> Thank you in advance and sorry, if I was unclear about some points.
> Best regards,
> Vasyl
>
> -----Ursprüngliche Nachricht-----
> Von: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Roger B.
> Newson
> Gesendet: Tuesday, November 13, 2012 12:50 PM
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: Missing confidence intervals for median after using
> -bootstrap- or -bpmedian-
>
> The problem here seems to me to be a zero standard error for the median, caused by a zero variance for the median, caused by a constant variable.
> For some reason, Stata is displaying the confidence interval as if the standard error was missing. This may possibly have something to do with version control (-bpmedian- is a Stata Version 10 command).
>
> SSC) displays the confidence intervals for a Bonett-Price median of a
> constant variable "correctly", with a zero standard error and upper
> and lower confidence linits equal to the median. After -bpmedian-, the
> user may type
>
> parmest, list(,)
>
> and display the "correct" confidence interval. You might also like to try using the -sccendif- module of the -scsomersd- package, which can also be downloaded from SSC, and which also calculates confidence intervals for medians, allowing the possibility of clustering and/or sampling-probability weights.
>
> I hope this helps.
>
> Best wishes
>
> Roger
>
>
> Roger B Newson BSc MSc DPhil
> 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: r.newson@imperial.ac.uk
> Web page: http://www.imperial.ac.uk/nhli/r.newson/
> Departmental Web page:
> opgenetics/reph/
>
> Opinions expressed are those of the author, not of the institution.
>
> On 13/11/2012 00:49, Nick Cox wrote:
>> I am not a statistician; in fact many, perhaps most, people on this
>> list wouldn't call themselves statisticians.
>>
>> You are asked to make clear where user-written programs you refer to
>> come from. -bpmedian- is from SSC or Roger Newson's website.
>>
>> You don't tell us anything much about your data, either what it is
>> (the name "var" is not revealing) or any descriptive statistics. But
>> I see you have a large sample size. It seems likely therefore that
>> the confidence interval for anything will be narrow at worst.
>> However, it seems likely also from your results that you have lots of
>> ties. If so, the unusual result of a confidence interval of length 0
>> is likely to be an artefact of coarseness in data recording.  If so,
>> then reporting a confidence interval isn't really possible, as it
>> should be more like
>> .8 +/- smidgen where smidgen is less than the resolution of
>> measurement. By resolution, I mean the minimum difference between
>> reported measurements. If possible data are values like .7, .8, .9
>> the resolution is 0.1.
>>
>> Conversely, if I were reviewing or examining this research, I would
>> want a report on the fraction of values that were recorded as .8. In
>> fact I would want a graph of the data. Of course, you may intend to
>> do all that.
>>
>> Nick
>>
>> On Mon, Nov 12, 2012 at 9:32 PM, Vasyl Druchkiv <dvv1985@yahoo.de> wrote:
>>> Dear statisticians,
>>>
>>> I try to estimate CI's for the median with -bpmedian- or with
>>> -bootstrap- using
>>>
>>> *--------------------- begin example ------------------ centile var
>>> bootstrap median=r(p50): sum var, detail
>>> *--------------------- end example --------------------
>>>
>>> The problem is that I get empty cells on standard error and
>>> confidence intervals either by implementing -bpmediam- or -bootstrap-.
>>>
>>> *--------------------- begin example ------------------ Bonett-Price
>>> confidence interval for median of: var Number of observations: 16872
>>> --------------------------------------------------------------------
>>> -
>>> -------
>>> --
>>>          var |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
>>> -------------+------------------------------------------------------
>>> -------------+-
>>> -------------+-------
>>> --
>>>          _cons |        -.8          .        .       .            .
>>> .
>>> *--------------------- end example ------------------
>>>
>>>
>>> I looked for the calculation method used in -bpmedian- . This method
>>> is described in:
>>>       Bonett, D. G. and Price, R. M.  2002.  Statistical inference
>>> for a linear function of medians:  Confidence
>>>       intervals, hypothesis testing, and sample size requirements.
>>> Psychological Methods 7(3): 370-383.
>>>
>>> Furthermore, I tried  to estimate CI's with SPSS using bootstrap and
>>> got
>>> (-0.8;-0.8) for 95% CI's. It means that the problem occurs when both
>>> limits coincide with the median. However, the method described in
>>> Bonnett-Price uses the formula:
>>> sum(cjηj)±Za/2(sum(cj2varηj))^1/2  (pp: 372) So, even if the last
>>> term is equal to 0 due to the pointy distribution  (var ηj=0), lower
>>> and upper limits must be displayed in stata output and be equal to
>>> -0.8 in my example. Can I just assume that CI's are  equal to median?
>>
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