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From |
David Airey <david.airey@vanderbilt.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
re: st: Checking reliability of a measurement device |

Date |
Fri, 26 Nov 2004 11:55:28 -0600 |

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)

(remote file ends)

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(click here to return to the previous screen)

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 * * 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/

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