Title

midas kendall -- Kendall K-plot for diagnostic test accuracy data

Syntax

midas kendall tp fp fn tn [if] [in]
[, cc(#)
xtitle(string)
ytitle(string)
title(string)
subtitle(string)
name(name)
replace
twoway_options]

tp, fp, fn, and tn are study-level 2×2 table counts:
true positives, false positives, false negatives, and true negatives,
supplied in that order.

Description

midas kendall draws a Kendall K-plot for diagnostic test accuracy
meta-analysis using study-level 2×2 table data. The command internally
computes sensitivity and specificity from the raw counts, applies a
continuity correction, transforms them to the requested link scale, and
then compares the empirical Kendall joint cumulative distribution with the
theoretical distribution under independence.

The plot contains two elements:

1. A 45-degree dashed reference line corresponding to independence.

2. The empirical Kendall cumulative curve plotted as points.

When the transformed sensitivity and specificity are approximately
independent, the points lie close to the diagonal. Systematic departures
indicate concordance (points above the diagonal), discordance (below),
or other forms of dependence. In the context of DTA meta-analysis, a
negative correlation between logit sensitivity and logit specificity —
the threshold effect — will typically produce points above the diagonal
in the upper range of the theoretical cumulative.

midas kendall complements midas chiplot and
midas bivbox: the chi-plot detects local departures from
independence study by study; the bivariate boxplot characterises the
elliptical shape and flags outliers; the Kendall K-plot characterises
the global concordance pattern relative to independence.

Options

Input transformation

cc(#) specifies the continuity correction added to the numerator
and denominator before computing sensitivity and specificity. Applied
only when at least one cell count is zero. Default cc(0.5).

Sensitivity and specificity are transformed to logit scale internally,
consistent with the bivariate normal model used throughout MIDAS.

Graph appearance

xtitle(string) and ytitle(string) specify axis titles.
Defaults are "Theoretical cumulative under independence" and
"Empirical Kendall cumulative".

title(string) and subtitle(string) specify the graph
title and subtitle. Default title is "Kendall Plot".

name(name) assigns a name to the graph.

replace permits replacement of an existing graph with the same name.

twoway_options are passed directly to twoway, allowing
control of schemes, marker options, regions, and other stylistic elements.

Returned results

midas kendall is rclass and stores:

r(n) number of studies used

r(kendall_tau) sample Kendall's τ on the transformed scale

r(cc) continuity correction used

r(input_mode) "tp fp fn tn"

Examples

Default K-plot in logit space:

. use midas_example_data, clear

. midas kendall tp fp fn tn

Custom title and graph name:

. midas kendall tp fp fn tn, title("Kendall K-plot: logit accuracy space") name(kplot1) replace

Review returned diagnostics:

. midas kendall tp fp fn tn

. return list

Comparison with related exploratory commands

midas chiplot study-by-study chi and lambda statistics;
detects local departures from independence; shows the threshold effect
study by study

midas bivbox bivariate boxplot; characterises elliptical shape,
correlation, and outliers; requires no copula assumption

midas kendall global concordance pattern; K-plot relative to
independence diagonal; sensitive to monotone dependence

References

Kendall MG. A new measure of rank correlation.
Biometrika 1938;30:81–93.
https://doi.org/10.1093/biomet/30.1-2.81

Nelsen RB. An Introduction to Copulas. 2nd ed.
New York: Springer; 2006.

Genest C, Boies J-C. Detecting dependence with Kendall plots.
The American Statistician 2003;57:275–284.
https://doi.org/10.1198/0003130032431

Reitsma JB, Glas AS, Rutjes AWS, Scholten RJPM, Bossuyt PM, Zwinderman AH.
Bivariate analysis of sensitivity and specificity produces informative
summary measures in diagnostic reviews.
Journal of Clinical Epidemiology 2005;58:982–990.
https://doi.org/10.1016/j.jclinepi.2005.02.022

Author

Ben Adarkwa Dwamena, MD

Division of Nuclear Medicine and Molecular Imaging

University of Michigan, Ann Arbor, MI

bdwamena@umich.edu

Also see

midas, midas chiplot, midas bivbox