.- help for ^concord^ (STB-43: sg84; STB-45: sg84.1; STB-54: sg84.2) .- Concordance correlation coefficient ----------------------------------- ^concord^ vary varx [weight] [^if^ exp] [^in^ range] [ ^, by(^byvar^) s^ummary ^le^vel^(^level^)^ ^g^raph^(^{^c^cc|^l^oa}^) noref reg np^saving^(^filename[^, replace^]^)^ ^snd(^sndvar[^, replace^]^)^ 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 vary and varx. Frequency weights may be specified and used. Missing values (if any) are deleted in a casewise manner. Options ------- ^by(^byvar^)^ produces separate results for groups of observations defined by byvar. ^summary^ requests summary statistics. ^level^ sets the confidence level % for the CI; default is 95%. ^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. ^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. ^npsaving(^filename[^, replace^]^)^ saves the standard normal plot generated by ^graph(loa)^. The filename is assumed to have extension gph. If filename does not exist, it is created. If filename exists, an error will occur unless ^replace^ is also specified. This option is ignored if ^graph(loa)^ is not requested. Note that the usual ^saving()^ option saves the loa plot itself when ^graph(loa)^ is specified (and the concordance plot when ^graph(ccc)^ is specified). ^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. graph_options are those allowed with ^graph, twoway^. 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, mean difference, upper confidence interval limit, data points, and 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) ------------ The following items are saved in the global ^S_^# macros and are returned in ^r()^. ^S_1 r(N)^ number of observations compared ^S_2 r(rho_c)^ concordance correlation coefficient rho_c ^S_3 r(se_rho_c)^ standard error of rho_c ^S_4 r(asym_ll)^ lower CI limit (asymptotic) ^S_5 r(asym_ul)^ upper CI limit (asymptotic) ^S_6 r(z_tr_ll)^ lower CI limit (z-transform) ^S_7 r(z_tr_ul)^ upper CI limit (z-transform) ^S_8 r(C_b)^ bias-correction factor C_b ^S_9 r(diff)^ mean difference ^S_10 r(sd_diff)^ standard deviation of mean difference ^S_11 r(LOA_ll)^ lower loa CI limit ^S_12 r(LOA_ul)^ 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: STB-43 sg84; STB-45 sg84.1