OJMI  Vol.8 No.4 , December 2018
The Specificity of a Diagnostic FDG-PET Study Is a Function of the Patient and the Location
Author(s) Michael L. Goris
ABSTRACT
The present paper is based on the observations that 1) there is reported variation in the specificities according to the type of tumor targeted (target) by FDG PET and 2) that while one can posit that the sensitivity of the tracer depends on the avidity for glucose and the plasma supply of the target, even so that the targeting cannot influence the avidity of unrelated tissues or lesions. The hypothesis to be tested is twofold: 1) patients imaged for different types of lesions could have a different prevalence of FDG avid tissues or lesions different from the target and 2) that the target lesions could be generally located in body location (sites) more likely to contain unrelated foci of increased uptake. Variance analysis shows that the sensitivity varies according to the target (p = 0.022), but not according to the location (p = 0.34); the specificity varies with the location (p = 0.0012) and the target (p = 0.05). Specificities are significantly different in different primary targets and target locations. The former is assumed to be due to different comorbidities in patients with different targets, the latter to the different locations of unrelated glucose avid organs or structures. Conclusion: When specificities are recorded or defined, the patient population characteristics and the organ or pathology of the false positives should also be described.

1. Introduction

In 2001 Sam Gambhir et al. published a supplement to the Journal of Nuclear Medicine reviewing the operating characteristics of Positron emission tomography with fluorine-18 Fluorodeoxyglucose (FDG-PET) in oncology. The article [1] is organized around tumors in large categories (e.g. Lung cancer rather than NSCLC, colorectal cancer); each in a tabulated form. In each table, for each cancer surveyed, the reference of the reviewed paper is given in column 1. Column 3 specifies the context (e.g. diagnose masses or nodules) and eventually a specific location (e.g. Mediastinum or lung or lymph nodes). The relevant columns for this paper are columns 8 and 10 which were the reported sensitivity and specificity of the FDG PET in the reference is noted. All quoted references do not necessarily have both sensitivities and specificities, and in that case the reference is not used.

The present paper is based on the observation that 1) there is a variation in the specificities according to the type of tumor targeted (target); 2) that while one can posit that the sensitivity of the tracer depends on the avidity glucose and the plasma flow to the target, and 3) that the targeting cannot influence the avidity of unrelated tissues or lesions. Why then the variations in specificity according to the target?

The hypothesis to be tested is twofold that: 1) patients imaged for different types of lesions could have a different prevalence of FDG avid tissues or lesions different from the target and 2) the target lesions could be generally located in body location more likely to contain unrelated foci of increased uptake. In short, one can show that specificities are significantly different in different primary targets and target locations, but not as a function of the nature of the target.

In a lapidary term, the injected FDG does not know what the target is. The expectations are that:

1) Even if the FDG is in general use for cancer detection, the sensitivities would generally be high (by selection) and variable as a function of the target.

2) Specificities could be different for different targets either because certain targets are associated with a higher prevalence of other lesions, or because some locations contain more structures (normal or abnormal) with high FDG uptake.

2. Method

The plan was to review the survey paper (1) and look at the first five tumors reviewed. Lymphoma was not included because of the wide range of phenotypes in lymphomas and specific locations could not be deduced (see below). In addition, we included the first ten references from the top of the tables that included both sensitivity and specificity. In this way we reviewed: Lungs [2] - [9] , Colon [10] [11] [12] [13] [14] , Melanoma [15] - [24] , Head and Neck (H & N) [25] - [32] , and Breast cancer [33] - [38] for the data on the targets.

Second, from all the references above we deduced the site scanned e.g. the site for a colon cancer recurrence was assumed to be the colon. For this step we broke the rule in the case of melanomas because to collect 3 defined sites we had to reach to the second page of the table. The sites are: Breast [33] - [38] , Colon [10] [11] [12] [14] , H & N [27] [29] [31] , Liver [10] [12] [14] , Lung [2] [3] [4] [5] [7] [8] [9] [13] [14] , Lymph nodes [13] [16] [19] [23] [25] [26] [28] - [38] and Mediastinum [2] [6] [8] .

The analysis of variance (ANOVA) compares the sensitivities and specificities for specific targets (tumor type Table 1 & Table 2) and sites (locations Table 3 & Table 4)

In ANOVA the variation (within) specific targets or locations is compared to the variation between groups (targets or sites).

3. Results

In the type of target (tumor), the lowest sensitivity is for the H&N cancers (80%), but the range is narrow (94 - 80 Table 1). The difference between groups (targets) is significant at the p = 0.022 levels. The specificities vary between 74% and 94% (Table 2), and there is a weak but significant difference between targets (p = 0.052). However, patient specific prevalence’s of lesions or tissues in different patient types, that could be (falsely) positive are not likely to be very high, even if variable for different types of patients.

For the sites, the sensitivity range is narrow (Table 3) and location (site) has no effect on the sensitivities (p = 0.39), but a strong one (Table 4) for the specificities (p = 0.0012).

4. Discussion

The operating characteristics of diagnostic tests (sensitivity and specificity) are generally synoptically reflected in Bayes theorem expressed as1:

Table 1. Sensitivities by targeted tumors.

The table shows the number of observations included in each target group. The analysis of variance shows that the differences in sensitivity between different targets (between), are significantly larger (p = 0.022) than within identical targets.

Table 2. Specificities by targeted tumors.

The table shows the number of observations included in each target group. The analysis of variance shows that the differences in specificitiy between different targets (between), are significantly larger (p = 0.056) than within identical targets.

Table 3. Sensitivities by location.

The differences of sensitivities between the inspected site or organ is not significantly greater (p = 0.39) than within locations.

Table 4. Specificity by location.

The differences of specificities between different locations (site or organ) is significantly greater (p = 0.0012) than within locations.

P ( D + | S + ) = P ( S + | D + ) P ( D + ) P ( S + | D + ) P ( D + ) + P ( S + | D ) P (D−)

The denominator in the equation is the prevalence of positive symptoms in the population tested (P(S+)). This expression is misleading, because it assumes that the world is binary; it is not. An abnormal ejection fraction response to exercise could indicate ischemia, but also valvular disease. Gallium 67 citrate imaging is positive for multiple benign lung diseases [39] .

A better expression for P(S+) would be i = 1 i = n P [ D i ] P ( S | D i ) , where S is the symptom (e.g. positive FDG uptake) for the lesion “i” and P(Di) represents the prevalence of all the possible lesions or structures that could lead to the symptom. P ( S | D i ) then represents the sensitivity of a positive finding for lesion “i”. Written in this way the equation points out to the fact that the non-specificity (and therefore the positive predictive value), is the function of the prevalence of lesions or tissues that could come out positive either in the patient or at the imaged site.

The proper expression for Bayes’ theorem should then be:

P ( D m + | S + ) = P ( S | D m + ) P ( D m + ) i = 1 i = n P [ D i ] P ( S | D i ) where S is the general symptom (e.g. FDG uptake) and D m + is the targeted disease. P ( S | D i ) is the sensitivity of the test for all (including the targeted lesions) or tissues from i to n and P [ D i ] is their prevalence (including the targeted lesions).

5. Conclusion

The thesis of this paper is that the prevalence of falsely positive findings varies with the targeted disease, because of the association with comorbidities, and with the search location because of adjacent structures, and not because of the differences in target. Publications reviewing operating characteristics should be encouraged to give information on the population with the targeted disease, with the location and nature of positive but non-target lesions.

Appendix: Deriving Bayes’ Theorem

B = B (1)

B A × A = B (2)

B C × C = B (3)

B A A = B C C (4)

B A × A U = B C × C U (5)

1) Is a tautology, since B on both sides is the same area.

2) In effect, B is multiplied by A/A, which is 1.

3) In effect, B is multipled by C/C, which is 1.

4) This only rewrites 1.

5) Both sides are divided by U.

In this representation U represents all the patients the universe of patients. A is the set of patients who have a particular symptom (e.g. high FDG uptake in a location where there should not be high uptake). C is the set of patients who have the disease one is looking for (e.g. a lung cancer). B is the set of patients who have the symptom and the disease. Redefining the terms, A/U is the prevalence of the symptoms or the prevalence of the symptom in the general population [P(S+)]. C/U is the prevalence of the disease in this population [P(D+)]. In the same way, B/A is the conditional probability of having the disease if one has the symptom [P(D+|S+)] and B/C is the conditional probability of having the symptom, if one has the disease[P(S+|D+)]. P(D+|S+) is the positive predictive value and P(S+|D+) is the sensitivity.

Rewriting Equation (5):

P ( D + | S + ) P ( S + ) = P ( S + | D + ) P ( D + ) (6)

P ( D + | S + ) = P ( S + | D + ) P ( D + ) P ( S + ) (7)

NOTES

1 P ( D + | S + ) is the positive predicted value, P ( S + | D + ) is the sensitivity, P ( D + ) is the prevalence , P ( S + | D ) is the non-specificity and P ( D ) = 1 P ( D + ) is the prevalence of no disease.

Cite this paper
Goris, M. (2018) The Specificity of a Diagnostic FDG-PET Study Is a Function of the Patient and the Location. Open Journal of Medical Imaging, 8, 102-110. doi: 10.4236/ojmi.2018.84013.
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