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J Clin EpidemiolVol. 44, No. 11, pp. 127S-1283, 1991
Pergamon Press plc
Printed in Great Britain
Letters to the Editors TRICHOTOMOUS DECISIONS DO NOT IMPLY TRICHOTOMOUS TESTS
In his recent editorial rumination [l], Feinstein suggests that a diugnostic test measured on a continuous scale should be considered trichotomous. This is inappropriate for two reasons. First, it is the medical decision after getting the test result that is trichotomous. Second, forcing tests into 3 categories may throw away valuable information. We now consider each of these in turn. Medical decision analysts use the 3 zones: “no treatment” (and no more tests), “further tests”, and “treatment without further tests”. The 3 zones are separated by “no treatment-test” and “test-treatment” thresholds [2,3]. The position of the thresholds is based on the risks and benefits of the alternative actions. This decision trichotomy is not a necessary feature of a diagnostic test, but rather a feature of the probability of disease after the diagnostic test result is obtained (post-test probability of disease). As the post-test probability of disease depends upon pre-test probability, Feinstein’s view that a diagnostic test should have a fixed “inconclusive” zone seems inappropriate. The following simple example using the CK likelihood ratios from Feinstein’s Table 2 and con-
ventional Bayesian methods [2] demonstrates this issue: (see Table 1, below). Imagine that the medical decision “no-treatment/further test” threshold probability was 5% and the “further test/treatment threshold” was 50%. The “no-treatment” zone is above and left of the upper dotted line in Table 1 and the “treatment” zone below and right of the lower dotted line. The “further testing” zone lies between the two dotted lines. Using the trichotomy Feinstein suggests in the text under his Table 3 would “lump” the 40-79 and the 80-279 group into his “inconclusive” category when in fact the table shows that the optimal decision may differ if the extra information obtained by keeping them separate is used. For example, if the pretest probability is lo%, further testing is warranted if the CK is 80-279, but not if it is 40-79. If the pretest probability is 20%, further testing is warranted if the CK is 40-79 but unnecessary if it is over 80. Thus the “inconclusiveness” of the test depends on the pre-test probability and the CK result, here divided into 4 categories. In this example, the use of 4 categories has provided more information than 3. The ideal
Table 1 Post-test probability (%) Pre-test Probability (%) 10 Don’t treat
CK = l-39 0.1
90 Treat
3 __________~
+
20 Consider further Tests (inconclusive) -
I I
0.3
.
CK = 40-79
, I
8 _______A 1279
7 I ;
73
80-279
I
33 _______’
1 I I I
> 280
;
86
52
93
98
100
1280
Letters to the Editors
would be to use test results as a continuum, or at least 5-7 categories [4] should be used to obtain likelihood ratios and extract the maximum information content from the test. LEs IRWIG PAUL GLASZIOU Department of Public Health University of Sydney, New South Wales Australia 2006
1. Feinstein AR. Editorial Rumination: The inadequacy of binary models for the clinical reality of three-zone diagnostic decisions. J Clln Epidemlel 1990; 43: 109-l 13. 2. Sox HC, Blatt MA, Higgins MC, Marton K. Medical DecisionMaking. Boston, MA: Butterworths; 1988. 3. Pauker SG, Kassirer JP. The threshold approach to clinical decision making. N Engl J Med 1980; 302: 1109-1117. 4. Ri&in RD. Maximum Shannon Information Content of diagnostic medical testing (Including application to multi$e non-independent kts). Med Deds Making 1985; 5: 179-W.
Response My “rumination” was intended to point out the inadequacy of a binary model for describing the results and usage of diagnostic tests. After a test, clinicians decide that the disease is present, absent, or inconclusive, i.e. a definite decision cannot be reached from the result. The clinician’s subsequent decisions and actions will then depend on many factors that are not included in isolated reasoning about numerical values for the diagnostic test itself. Despite what may have been learned from the writings of “medical decision analysts”, the comments by Irwig and Glasziou suggest that they are not familiar with the way clinicians actually order or use the tests. Rather than trying to untangle all of the jargon and numbers in the comments, however, I shall simply respond by saying:
(1) The pattern of clinical reasoning I described is what actually happens in reality. Like many other clinical realities, it may not conform to attractive but abstract mathematical models.
(2) I did not demand a “fixed ‘inconclusive’ zone”. The boundaries and location of that zone will obviously vary in different clinical situations. (In fact, the theoretical castle built on foundations of Bayes diagnostic theorem has been destroyed by the eventual “discovery” of reality. Contrary to the mathematical model, the values of sensitivity and specificity are not constant and will vary greatly in different clinical situations.) (3) I agree that 4 categories can provide “more information than 3”, and that “at least 5-7 categories” can provide more than 4. My main point was that the customary 2 Bayesian categories are not enough. For pragmatic clinical decisions, however, the rest of the additional categories will usually constitute ordinal layers in the inconclusive zone. ALVAN R. FEINSTEM Yale University School of Medicine New Haven, CT 06510 U.S.A.
J Clin EpidemiolVol. 44, No. 11, pp. 127S-1283, 1991
Pergamon Press plc
Printed in Great Britain
Letters to the Editors TRICHOTOMOUS DECISIONS DO NOT IMPLY TRICHOTOMOUS TESTS
In his recent editorial rumination [l], Feinstein suggests that a diugnostic test measured on a continuous scale should be considered trichotomous. This is inappropriate for two reasons. First, it is the medical decision after getting the test result that is trichotomous. Second, forcing tests into 3 categories may throw away valuable information. We now consider each of these in turn. Medical decision analysts use the 3 zones: “no treatment” (and no more tests), “further tests”, and “treatment without further tests”. The 3 zones are separated by “no treatment-test” and “test-treatment” thresholds [2,3]. The position of the thresholds is based on the risks and benefits of the alternative actions. This decision trichotomy is not a necessary feature of a diagnostic test, but rather a feature of the probability of disease after the diagnostic test result is obtained (post-test probability of disease). As the post-test probability of disease depends upon pre-test probability, Feinstein’s view that a diagnostic test should have a fixed “inconclusive” zone seems inappropriate. The following simple example using the CK likelihood ratios from Feinstein’s Table 2 and con-
ventional Bayesian methods [2] demonstrates this issue: (see Table 1, below). Imagine that the medical decision “no-treatment/further test” threshold probability was 5% and the “further test/treatment threshold” was 50%. The “no-treatment” zone is above and left of the upper dotted line in Table 1 and the “treatment” zone below and right of the lower dotted line. The “further testing” zone lies between the two dotted lines. Using the trichotomy Feinstein suggests in the text under his Table 3 would “lump” the 40-79 and the 80-279 group into his “inconclusive” category when in fact the table shows that the optimal decision may differ if the extra information obtained by keeping them separate is used. For example, if the pretest probability is lo%, further testing is warranted if the CK is 80-279, but not if it is 40-79. If the pretest probability is 20%, further testing is warranted if the CK is 40-79 but unnecessary if it is over 80. Thus the “inconclusiveness” of the test depends on the pre-test probability and the CK result, here divided into 4 categories. In this example, the use of 4 categories has provided more information than 3. The ideal
Table 1 Post-test probability (%) Pre-test Probability (%) 10 Don’t treat
CK = l-39 0.1
90 Treat
3 __________~
+
20 Consider further Tests (inconclusive) -
I I
0.3
.
CK = 40-79
, I
8 _______A 1279
7 I ;
73
80-279
I
33 _______’
1 I I I
> 280
;
86
52
93
98
100
1280
Letters to the Editors
would be to use test results as a continuum, or at least 5-7 categories [4] should be used to obtain likelihood ratios and extract the maximum information content from the test. LEs IRWIG PAUL GLASZIOU Department of Public Health University of Sydney, New South Wales Australia 2006
1. Feinstein AR. Editorial Rumination: The inadequacy of binary models for the clinical reality of three-zone diagnostic decisions. J Clln Epidemlel 1990; 43: 109-l 13. 2. Sox HC, Blatt MA, Higgins MC, Marton K. Medical DecisionMaking. Boston, MA: Butterworths; 1988. 3. Pauker SG, Kassirer JP. The threshold approach to clinical decision making. N Engl J Med 1980; 302: 1109-1117. 4. Ri&in RD. Maximum Shannon Information Content of diagnostic medical testing (Including application to multi$e non-independent kts). Med Deds Making 1985; 5: 179-W.
Response My “rumination” was intended to point out the inadequacy of a binary model for describing the results and usage of diagnostic tests. After a test, clinicians decide that the disease is present, absent, or inconclusive, i.e. a definite decision cannot be reached from the result. The clinician’s subsequent decisions and actions will then depend on many factors that are not included in isolated reasoning about numerical values for the diagnostic test itself. Despite what may have been learned from the writings of “medical decision analysts”, the comments by Irwig and Glasziou suggest that they are not familiar with the way clinicians actually order or use the tests. Rather than trying to untangle all of the jargon and numbers in the comments, however, I shall simply respond by saying:
(1) The pattern of clinical reasoning I described is what actually happens in reality. Like many other clinical realities, it may not conform to attractive but abstract mathematical models.
(2) I did not demand a “fixed ‘inconclusive’ zone”. The boundaries and location of that zone will obviously vary in different clinical situations. (In fact, the theoretical castle built on foundations of Bayes diagnostic theorem has been destroyed by the eventual “discovery” of reality. Contrary to the mathematical model, the values of sensitivity and specificity are not constant and will vary greatly in different clinical situations.) (3) I agree that 4 categories can provide “more information than 3”, and that “at least 5-7 categories” can provide more than 4. My main point was that the customary 2 Bayesian categories are not enough. For pragmatic clinical decisions, however, the rest of the additional categories will usually constitute ordinal layers in the inconclusive zone. ALVAN R. FEINSTEM Yale University School of Medicine New Haven, CT 06510 U.S.A.
