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276 lines
9.1 KiB
Plaintext
276 lines
9.1 KiB
Plaintext
{smcl}
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{* 6oct2004/23aug2005/14may2006/9aug2007}
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{hline}
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{hi:help concord} {right:(SJ7-3: st0015_4)}
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{hline}
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{title:Title}
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{p2colset 5 16 18 2}{...}
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{p2col:{hi:concord} {hline 2}}Concordance correlation coefficient and associated measures, tests, and graphs{p_end}
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{p2colreset}{...}
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{title:Syntax}
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{p 8 17 2}
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{cmd:concord}
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{it:vary} {it:varx}
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{ifin}
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{weight}
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[{cmd:,}
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{cmd:by(}{it:byvar}{cmd:)}
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{cmdab:s:ummary}
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{cmdab:le:vel(}{it:#}{cmd:)}
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{cmd:ccc}[{cmd:(noref} {it:ccc_options}{cmd:)}]
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{cmd:loa}[{cmd:(noref} {cmdab:reg:line} {it:loa_options}{cmd:)}]
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{cmd:qnormd}[{cmd:(}{it:qnormd_options}{cmd:)}]]
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{title:Description}
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{p 4 4 2}
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{cmd:concord} computes Lin's (1989, 2000) concordance correlation coefficient
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for agreement on a continuous measure obtained by two persons or methods. (The
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measure was introduced earlier by Krippendorff (1970).) The concordance
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correlation coefficient combines measures of both precision and accuracy to
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determine how far the observed data deviate from the line of perfect
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concordance (i.e., the line at 45 degrees on a square scatter plot). Lin's
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coefficient increases in value as a function of the nearness of the data's
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reduced major axis to the line of perfect concordance (the accuracy of the
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data) and of the tightness of the data about its reduced major axis (the
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precision of the data). The Pearson correlation coefficient, r, the
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bias-correction factor, C_b, and the equation of the reduced major axis are
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reported to show these components. Note that the concordance correlation
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coefficient, rho_c, can be expressed as the product of r, the measure of
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precision, and C_b, the measure of accuracy.
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{p 4 4 2}
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{cmd:concord} also provides results for Bland and Altman's
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limits-of-agreement, "loa", procedure (1986). The loa, a data-scale assessment
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of the degree of agreement, is a complementary approach to the
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relationship-scale approach of Lin.
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{p 4 4 2}
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Finally, two other results are reported:
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{p 8 8 2}
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1. The correlation between difference and mean. In one interpretation
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this is a test statistic for a null hypothesis of equal variances given
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bivariate normality (Pitman 1939; also see Snedecor and Cochran 1989, 192-193).
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Alternatively, it is an exploratory diagnostic.
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A value near zero implies concordance.
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{p 8 8 2}
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2. An F test of equality of means and variances. Note that this too
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assumes bivariate normality (Bradley and Blackwood 1989).
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See also Hsu (1940) and Reynolds and Gregoire (1991).
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Nonsignificance implies concordance.
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{p 4 4 2}
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The user provides the pairs of measurements for a single property as
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observations in variables {it:vary} and {it:varx}. Frequency weights may be
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specified and used. Missing values (if any) are deleted in a casewise manner.
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{p 4 4 2}
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Various associated graphs may be obtained through options.
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See below for explanations of the options {cmd:ccc}, {cmd:loa}, and
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{cmd:qnormd}.
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{title:Options}
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{p 4 8 2}
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{cmd:by(}{it:byvar}{cmd:)} produces separate results for groups of
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observations defined by {it:byvar}.
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{p 4 8 2}
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{cmd:summary} requests summary statistics.
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{p 4 8 2}
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{cmd:level(}{it:#}{cmd:)} sets the confidence level % for the CI; default is
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{cmd:c(level)}.
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{p 4 8 2}
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{cmd:ccc} requests a graphical display of the data and the reduced major axis
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of the data. The reduced major axis or SD line goes through the intersection of
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the means and has slope given by the sign of Pearson's r and the ratio of the
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standard deviations. The SD line serves as a summary of the center of the data.
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{p 8 8 2}
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{cmd:ccc()} suboption {cmd:noref} suppresses the reference line of
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perfect concordance, y=x.
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{p 8 8 2}
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{cmd:ccc()} may also be specified with other options, which should
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be options of {helpb scatter}. For example, the scheme may be changed by a
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call such as {cmd:ccc(scheme(lean1)}.
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{p 4 8 2}
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{cmd:loa} requests a graphical display of the loa, the mean difference, and
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the data presented as paired differences plotted against pair-wise means.
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{p 8 8 2}
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{cmd:loa()} suboption {cmd:noref} suppresses the reference line of perfect
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average agreement, y=0.
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{p 8 8 2}
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{cmd:loa()} suboption {cmd:regline} adds a regression line to the loa plot
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fitting the paired differences to the pair-wise means.
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{p 8 8 2}
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{cmd:loa()} may also be specified with other options, which should normally
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be options of {helpb scatter}. For example,
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the reference line of perfect average agreement was generated as
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{cmd:loa(yline(0, lstyle(refline)) yscale(range(0)) ylabel(0, add))}.
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{p 4 8 2}
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{cmd:qnormd} requests a normal plot of differences.
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{p 8 8 2}
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{cmd:qnormd()} may also be specified with options, which should
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be options of {helpb scatter}. For example,
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{cmd:qnormd(title(Normal plot of differences))} adds a title to the graph.
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{title:Comments}
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{p 4 4 2}
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Lin (2000) reported typographical errors in his original 1989 paper
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that affected calculation of the standard error of rho_c. These corrections
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were included in {cmd:concord} in version 2.2.7 (January 2002) when the erratum
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was brought to the attention of the program authors by Dr. Benjamin Littenberg.
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We thank Dr. Littenberg.
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{p 4 4 2}Kevan Polkinghorne pointed out a problem with {cmd:loa()}.
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Mark Marshall pointed out a problem with {cmd:by()} under Stata 9.
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{p 4 4 2}
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Dunn (2004) contains a bibliography on related work.
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Cox (2004) discusses other graphical approaches to this and related
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problems. Cox (2006) discusses concordance correlation and
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other numerical and graphical methods for assessing agreement
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with various scientific examples.
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{title:Saved results}
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{p 4 4 2}
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The following items are returned in {cmd:r()}, if the {cmd:by()} option was
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not used:
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{p 8 18}{cmd:r(N)}{space 9}number of observations compared{p_end}
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{p 8 18}{cmd:r(rho_c)}{space 5}concordance correlation coefficient rho_c{p_end}
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{p 8 18}{cmd:r(se_rho_c)}{space 2}standard error of rho_c{p_end}
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{p 8 18}{cmd:r(asym_ll)}{space 3}lower CI limit (asymptotic){p_end}
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{p 8 18}{cmd:r(asym_ul)}{space 3}upper CI limit (asymptotic){p_end}
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{p 8 18}{cmd:r(z_tr_ll)}{space 3}lower CI limit (z-transform){p_end}
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{p 8 18}{cmd:r(z_tr_ul)}{space 3}upper CI limit (z-transform){p_end}
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{p 8 18}{cmd:r(C_b)}{space 7}bias-correction factor C_b{p_end}
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{p 8 18}{cmd:r(diff)}{space 6}mean difference{p_end}
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{p 8 18}{cmd:r(sd_diff)}{space 3}standard deviation of mean difference{p_end}
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{p 8 18}{cmd:r(LOA_ll)}{space 4}lower loa CI limit{p_end}
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{p 8 18}{cmd:r(LOA_ul)}{space 4}upper loa CI limit{p_end}
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{p 8 18}{cmd:r(rdm)}{space 7}correlation between difference and mean{p_end}
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{p 8 18}{cmd:r(Fdm)}{space 7}F from Bradley-Blackwood test{p_end}
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{title:Examples}
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{p 4 8 2}
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{cmd:. concord rater1 rater2}
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{p 4 8 2}
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{cmd:. concord rater1 rater2 [fw=freq]}
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{p 4 8 2}
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{cmd:. concord rater1 rater2, summary ccc}
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{p 4 8 2}
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{cmd:. concord rater1 rater2, summary ccc(noref)}
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{p 4 8 2}
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{cmd:. concord rater1 rater2, level(90) by(grp)}
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{p 4 8 2}
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{cmd:. concord rater1 rater2, loa(regline noref)}
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{p 4 8 2}
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{cmd:. concord rater1 rater2, qnormd(title(Normal plot))}
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{title:Authors}
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{p 4 4 2}
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Thomas J. Steichen, Winston-Salem, NC, USA, steichen@triad.rr.com
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{p 4 4 2}
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Nicholas J. Cox, Durham University, UK, n.j.cox@durham.ac.uk
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{title:References}
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{p 4 8 2}
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Bland, J. M., and D. G. Altman. 1986. Statistical methods for assessing
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agreement between two methods of clinical measurement. {it:Lancet} I:
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307{c -}310.
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{p 4 8 2}
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Bradley, E. L., and L. G. Blackwood. 1989. Comparing paired data:
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a simultaneous test for means and variances. {it:American Statistician}
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43: 234{c -}235.
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{p 4 8 2}
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Cox, N. J. 2004. Graphing agreement and disagreement.
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{it:Stata Journal} 4: 329{c -}349.
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{p 4 8 2}
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------. 2006.
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Assessing agreement of measurements and predictions in geomorphology.
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{it:Geomorphology} 76: 332{c -}346.
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{p 4 8 2}
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Dunn, G. 2004.
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{it: Statistical Evaluation of Measurement Errors: Design and Analysis of Reliability Studies.}
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London: Arnold.
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{p 4 8 2}
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Hsu, C. T. 1940. On samples from a normal bivariate population.
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{it:Annals of Mathematical Statistics} 11: 410{c -}426.
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{p 4 8 2}
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Krippendorff, K. 1970. Bivariate agreement coefficients for reliability of data.
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In Borgatta, E.F. and G.W. Bohrnstedt (eds)
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{it:Sociological Methodology}. San Francisco: Jossey-Bass, 139{c -}150.
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[a.k.a. {it:Sociological Methodology} 2: 139{c -}150]
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{p 4 8 2}
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Lin, L. I-K. 1989. A concordance correlation coefficient to evaluate
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reproducibility. {it:Biometrics} 45: 255{c -}268.
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{p 4 8 2}
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------. 2000. A note on the concordance correlation coefficient.
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{it:Biometrics} 56: 324{c -}325.
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{p 4 8 2}
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Pitman, E. J. G. 1939. A note on normal correlation.
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{it:Biometrika} 31: 9{c -}12.
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{p 4 8 2}
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Reynolds, M., and T. G. Gregoire. 1991. Comment on Bradley and Blackwood.
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{it:American Statistician} 45: 163{c -}164.
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{p 4 8 2}
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Snedecor, G. W., and W. G. Cochran. 1989. {it:Statistical Methods.}
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Ames, IA: Iowa State University Press.
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{title:Also see}
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{p 4 13 2}
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STB: STB-43 sg84; STB-45 sg84.1; STB-54 sg84.2; STB-58 sg84.3
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{psee}
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SJ:{space 3}SJ2-2 st0015; SJ4-4 st0015_1; SJ5-3: st0015_2; SJ6-2: st0015_3
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{p_end}
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