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5—RELIABILITY OF PHYSICAL FINDINGS
Observer B:
Observer A:
210
90
20 80 100 20 80 100
Sample problem:
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39
agreement is also less than perfect, with κ-statistics similar to those observed with physical
signs. Even with laboratory tests, which present the clinician with a single, indisputable number,
interobserver disagreement is still possible and even common, simply because the clinician has to
interpret the laboratory test’s significance. For example, in one study of three endocrinologists
reviewing the same thyroid function tests and other clinical data of 55 consecutive outpatients
with suspected thyroid disease, the endocrinologists disagreed about the final diagnosis 40% of
the time.34 Computerized interpretation of test results performs no better: in a study of pairs of
electrocardiograms taken only 1 minute apart from 92 patients, the computer interpretation was
significantly different 40% of the time, even though the tracings showed no change.
186
By defining abnormal findings precisely, by studying and mastering examination technique,
and by observing every detail at the bedside attentively and without bias or distraction, we can
minimize interobserver disagreement and make physical diagnosis more precise. It is simply
impossible, however, to abstract every detail of clinicians’ observations of patients into exact physical signs, and, in this way, physical diagnosis is no different than any of the other tools we use to
categorize disease. So long as both the material and the observers of clinical medicine are human
beings, a certain amount of subjectivity always will be with us.
Appendix. Calculation of the κ-statistic
e observations of two observers who are examining the same N patients independently are
customarily displayed in a 2 × 2 table, similar to that in Fig. 5.1. Observer A finds the sign to
be present in w1 patients and absent in w2 patients; observer B finds the sign to be present in y1
Fig. 5.1 Interobserver agreement and the κ-statistic. Top half: Conventional 2 × 2 table displaying data for
calculation of κ-statistic. Bottom half: A sample case, in which observed agreement is 80%, chance agreement is 74%, and the κ-statistic is 0.23 (see Appendix for discussion).
Sign +
Sign +
Sign −
Observed agreement Chance agreement
15 75
a
c
y
55 10
Sign −
b
d
1
90
y
2
w
1
w
2
N
72
40
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2—UNDERSTANDING THE EVIDENCE
patients and absent in y2 patients. e 2 observers agree the sign is present in a patients and absent
in d patients. erefore, the observed agreement (PO) is:
PO = (a + d)/N
Calculation of the κ-statistic first requires calculation of the agreement that would have occurred
by chance alone. Among all the patients, observer A found the fraction w1/N to have the sign;
therefore, by chance alone, among the y1 patients with the sign according to observer B, observer
A would find the sign in (w1/N) times y1 or (w1y1/N) patients (i.e., this is the number of patients in
which both observers agree the sign is present, by chance alone). Similarly, both observers would
agree the sign is absent by chance alone in (w2y2/N) patients. erefore, the expected chance agreement (PE) is their sum, divided by N:
()wy wy
+
PE=
11 22
2
N
is equation shows that agreement by chance alone (PE) approaches 100% as both w1 and y1
approach 0 or N (i.e., both clinicians agree that a finding is rare or that it is very common).
e κ-statistic is the increment in observed agreement beyond that expected by chance (PO–PE),
divided by the maximal increment that could have been observed had the observed agreement
been perfect (1–PE):
(1Po P
−
)
κ =
E
P
−
()
E
For example, Fig. 5.1 depicts the observations of two observers in a study of 100 patients with
dyspnea. Both agree the third heart sound is present in 5 patients and absent in 75 patients; therefore, simple agreement is (5 + 75)/100 or 0.80. By chance alone, they would have agreed about
the sound being present in (10 × 20)/100 patients (i.e., 2 patients) and absent in (90 × 80)/100
patients (i.e., 72 patients); therefore, chance agreement is (2 + 72)/100 patients or 0.74. e
κ-statistic for this finding becomes (0.80–0.74)/(1–0.74) = (0.06)/(0.26) = 0.23.
References may be accessed online at Elsevier eBooks for Practicing Clinicians.
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