Study on Interpretation of Quantitative Results of Prostate-specific Antigen Using Information Theory

Sang-Hyun Hwang; Heung-Bum Oh; Tina Pyo; Hyun-Jin Lee; Kwan Jeh Lee

doi:10.3343/kjlm.2010.30.4.357

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Hwang, Oh, Pyo, Lee, and Lee: Study on Interpretation of Quantitative Results of Prostate-specific Antigen Using Information Theory

Original Article

Korean J Leg Med 2010;30(4):357-363.

Published online: 14 January 2010

DOI: https://doi.org/10.3343/kjlm.2010.30.4.357

Study on Interpretation of Quantitative Results of Prostate-specific Antigen Using Information Theory

Sang-Hyun Hwang, M.D.^1,², Heung-Bum Oh, M.D.^3,^∗, Tina Pyo, B.S.⁴, Hyun-Jin Lee, Ph.D.⁴, Kwan Jeh Lee, Ph.D.^4,^∗

¹Department of Laboratory Medicine, School of Medicine, Busan, Korea

²Pusan National University and Medical Research Institute, Pusan National University Hospital, Busan, Korea

³Department of Laboratory Medicine, University of Ulsan College of Medicine and Asan Medical Center, Seoul, Korea

⁴Department of Statistics, Dongguk University, Seoul, Korea

Corresponding author: Heung-Bum Oh, M.D. Department of Laboratory Medicine, University of Ulsan College of Medicine and Asan Medical Center, 388-1 Pungnap-dong, Songpa-gu, Seoul 138-736, Korea Tel: +82-2-3010-4505, Fax: +82-2-478-0884 E-mail: hboh@amc.seoul.kr

Kwan Jeh Lee, Ph.D. Department of Statistics, Dongguk University, 26 Pil-dong 3-ga, Jung-gu, Seoul 100-715, Korea Tel: +82-2-2260-3222, Fax: +82-2-2267-0998 E-mail: kwanlee@dongguk.edu

^∗ This work was supported by a grant (KRF-2007-521-E00113) from the National Research Foundation of Korea funded by Ministry of Education, Science and Technology.

^∗ Heung-Bum Oh and Kwan Jeh Lee have equally contributed to this study.

Revised 1 February 201025 May 2010 Accepted 17 July 2010

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Background:

The prostate-specific antigen (PSA) is considered the most useful among tumor markers currently used. However, its quantitative results are interpreted only qualitatively for the diagnosis of prostate cancer. The recently introduced information theory enables the information of the quantitative results transformed into Shannon's entropy (S) that represents uncertainties and then “1-S” representing diagnostic certainty.

Methods:

The 882 urological patients enrolled were categorized into 2 groups: a patient group comprising 233 patients with prostate cancer and a disease control group comprising 649 patients with benign prostate disease. The level of PSA in all the patients was tested and was found to be ≥2 ng/mL. The variables like PSA level and age were modeled on logistic regression analysis to predict the probability of prostate cancer and the diagnostic certainty.

Results:

The mean (SD) of PSA levels in the patient group and the disease control group were 44.5 ng/mL (37.62 ng/mL) and 5.7 ng/mL (3.70 ng/mL), respectively. The logistic regression model fitted well when the age variable was dichotomized at the age of 55 yr. The diagnostic certainty was lowest at a PSA level of 18.90 ng/mL in the <55-yr age group, and 15.45 ng/mL in the >55-yr age group.

Conclusions:

The diagnostic certainty (1-S) of whether to diagnose prostate cancer or not at a certain PSA level could be obtained using the information theory. The methodology used in this study may help interpret the results of other quantitative tests.

Keywords: Prostate-specific antigen, Entropy, 1-S, Information theory, Diagnostic certainty, Diagnostic test

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Fig. 1.

Plot of 1-S (entropy) vs. prostate-specific antigen (PSA) level to determine the diagnostic certainty of prostate cancer.

Fig. 2.

Plot of 1-S (entropy) vs. prostate-specific antigen (PSA) level for the diagnosis of prostate cancer depending on the age groups (solid line: >55 yr; discontinuous line: <55 yr).

Fig. 3.

Predictive probability curve obtained by using the logistic regression model for the diagnosis of prostate cancer in the 2 age groups.

Table 1.

Descriptive statistics

Variable	Benign prostate disease patients (N=649)			Prostate cancer patients (N=233)			P value∗
Variable	Mean (SD)	Median	Range	Mean (SD)	Median	Range	P value∗
PSA level (ng/mL)	44.5 (37.62)	27.36	(2, >100)	5.7 (3.70)	4.57	(2, 21.1)	<0.001
Age (yr)	69.3 (7.96)	69	(47, 99)	64.7 (10.12)	66	(26, 88)	<0.001

^∗ Wilcoxon rank sum test.

Abbreviations: PSA, prostate-specific antigen.

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