re: st: Checking reliability of a measurement device

[David Airey <david.airey@vanderbilt.edu>]

This package seems to have an aspect of what you want:

http://www.stata.com/stb/stb45/sg84_1/concord.hlp:
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 help for concord                       (STB-43: sg84; STB-45: sg84.1)
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 Concordance correlation coefficient
 -----------------------------------

   concord var1 var2 [weight] [if exp] [in range]
          [ , summary graph(ccc|loa) snd(sndvar[, replace])
              noref reg by(byvar) level(level) graph_options ]


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

 concord computes Lin's (1989) concordance correlation coefficient
 for agreement on a continuous measure obtained by two persons
 or methods.  The Lin coefficient combines measures of both precision
 and accuracy to determine whether the observed data significantly
 deviate from the line of perfect concordance (i.e., the line at 45
 degrees).  Lin's coefficient increases in value as a function of the
 nearness of the data's reduced major axis to the line of perfect
 concordance (the accuracy of the data) and of the tightness of the
 data about its reduced major axis (the precision of the data). The
 Pearson correlation coefficient, r, the bias-correction factor, C_b,
 and the equation of the reduced major axis are reported to show these
 components. Note that the concordance correlation coefficient, rho_c,
 can be expressed as the product of r, the measure of precision,
 and C_b, the measure of accuracy.  The optional concordance graph
 plots the observed data, the reduced major axis of the data, and the
 line of perfect concordance as a graphical display of the observed
 concordance of the measures.

 concord also provides statistics and optional graphics for Bland and
 Altman's limits-of-agreement, "loa", procedure (1986).  The loa, a
 data-scale assessment of the degree of agreement, is a complementary
 approach to the relationship-scale approach of Lin.

 The user provides the pairs of measurements for a single property as
 observations in variables var1 and var2.  Frequency weights may
 be specified and used.  Missing values (if any) are deleted in a
 casewise manner.


 Options
 -------

 graph(ccc) requests a graphical display of the data, the line of
 perfect concordance and the reduced major axis of the data.  The
 reduced major axis or SD line goes through the intersection of the
 means and has slope given by the sign of Pearson's r and the ratio
 of the standard deviations.  The SD line serves as a summary of
 the center of the data.

 graph(loa) requests a graphical display of the loa, the mean
 difference, and the data presented as paired differences plotted
 against pair-wise means.  A Normal plot for the differences is
 also shown.

 snd(sndvar[, replace]) saves the standard normal deviates
 produced for the Normal plot generated by graph(loa).  The values
 are saved in variable sndvar.  If sndvar does not exist, it is
 created.  If  sndvar exists, an error will occur unless replace
 is also specified.  This option is ignored if graph(loa) is not
 requested.

 noref suppresses the reference line at y=0 in the loa plot.
 This option is ignored if graph(loa) is not requested.

 reg adds a regression line to the loa plot fitting the paired
 differences to the pair-wise means.  This option is ignored if
 graph(loa) is not requested.

 summary requests summary statistics.

 by(byvar) produces separate results for groups of observations
 defined by byvar.

 level sets the confidence level % for the CI; default is 95%.

 graph_options are those allowed with graph, twoway.  Setting
 t1title(.) blanks out the default t1title.  The default
 graph_options for graph(ccc) are connect(.l) symbol(o.) pen(22)
 for the data points and SD line, respectively, along with default
 titles and labels.  The default graph_options for graph(loa)
 include connect(lll.l) symbol(...o.) pen(35324) for the lower
 confidence interval limit, the mean difference, the upper confidence
 interval limit, the data points, and the regression line (if
 requested) respectively, along with default titles and labels.
 (The user is not allowed to modify the graph options for the Normal
 probability plot.)


 Saved values (if by option not used)
 ------------

 S_1   number of observations compared
 S_2   concordance correlation coefficient rho_c
 S_3   standard error of rho_c
 S_4   lower CI limit (asymptotic)
 S_5   upper CI limit (asymptotic)
 S_6   lower CI limit (z-transform)
 S_7   upper CI limit (z-transform)
 S_8   bias-correction factor C_b
 S_9   mean difference
 S_10  standard deviation of mean difference
 S_11  lower loa CI limit
 S_12  upper loa CI limit


 Examples
 --------

 . concord rater1 rater2

 . concord rater1 rater2 [fw=freq]

 . concord rater1 rater2, s g(c)

 . concord rater1 rater2, level(90) by(grp)

 . concord rater1 rater2, g(l)


 Authors
 -------

       Thomas J. Steichen
       RJRT
       steicht@rjrt.com

       Nicholas J. Cox
       University of Durham, UK
       n.j.cox@durham.ac.uk


 References
 ----------

 Bland, J. M., Altman, D. G. 1986. Statistical methods for
 assessing agreement between two methods of clinical measurement.
 Lancet I, 307-310.

 Lin, L. I-K. 1989.  A concordance correlation coefficient to
 evaluate reproducibility. Biometrics 45: 255-268.


 Also see
 --------

     STB:  sg84.1 (STB-45), sg84 (STB-43)

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> Hi Statalisters,
>
> a Dentistry PhD student did some measurements on 12
> teeth with varying conditions and he asked me how
> could he show that the device used for the
> measurements is reliable. More specifically each one
> of the 12 teeth has been measured by this device by 2
> raters (a and b) X 2 time points (week 1 and week 2) X
> 6 relative positions =   24 measurements. The goal is
> to show that the discrepancies among measurements are
> not statistically significant.
You might look at Stata's "kappa" and "alpha" commands...

-Dave

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