1849
A Neurocomputational Model for Prostate Carcinoma Detection Pankaj Kalra, M.D.1 Joanna Togami, M.D.1 Gaurav Bansal, B.S.1 Alan W. Partin, M.D.2 Michael K. Brawer, M.D.3 Richard J. Babaian, M.D.4 Lawrence S. Ross, M.D.1 Craig S. Niederberger, M.D.1 1
Department of Urology, University of Illinois at Chicago, Chicago, Illinois.
2
The Johns Hopkins Medical Institution, The James Buchanan Brady Urological Institute, Baltimore, Maryland.
3
Northwest Prostate Institute, Northwest Hospital, Seattle, Washington.
4
The University of Texas M. D. Anderson Cancer Center, Houston, Texas.
Supported in part by Grant P01 HD36289 from the National Institutes of Health. Drs. Brawer, Niederberger, and Babaian serve as consultants with honoraria for Bayer Corporation. Drs. Brawer and Niederberger receive research support from Bayer Corporation. Dr. Partin serves as an investigator with Bayer Corporation. Address for reprints: Craig S. Niederberger, M.D., Department of Urology, University of Illinois at Chicago, 840 S Wood St, M/C 955, Chicago, IL 60612-7316; Fax: (360) 838-1823; E-mail:
[email protected] Received April 23, 2003; revision received July 18, 2003; accepted August 1, 2003. © 2003 American Cancer Society DOI 10.1002/cncr.11748
BACKGROUND. Current guidelines for prostate carcinoma screening rely primarily on the digital rectal examination (DRE) and prostate specific antigen (PSA). Well described patient risk factors for prostate carcinoma also include age, ethnicity, family history, and complexed PSA. However, due to the nonlinear relation of each of these variables with prostate carcinoma, it is difficult to predict reliably each patient’s risk based on linear univariate analysis. The authors investigated a neural network to model the risk of prostate carcinoma by seven readily available clinical features. METHODS. The database for the current study comprised 3268 men recently evaluated for the early detection of prostate carcinoma. The seven clinical features evaluated included age, race, family history, International Prostate Symptom Score (IPSS), DRE, and total and complexed PSA. Three hundred forty-eight subjects in the dataset included men with determined prostate biopsy outcomes and for whom at least 6 of 7 features were available. The dataset was divided randomly into a training set (60%) and a test set (40%), with n1/n2 cross-validation used to evaluate model accuracy, and was modeled with linear and quadratic discriminant function analysis and a neural computational system. After a model with acceptable goodness of fit was achieved, reverse regression analysis using Wilks’s generalized likelihood ratio test was performed to evaluate the statistical significance of each input variable. RESULTS. The receiving operating characteristic (ROC) area for the neural computational system in the test set was 0.825, whereas total PSA and complexed PSA alone had ROC areas of 0.678 and 0.697, respectively. The ROC area of logistic regression in the test set was 0.510, linear discriminant function analysis was 0.674, and quadratic discriminant function analysis was 0.011. All were significantly less than the ROC area of the neural computational model (all Ps ⬍ 0.002). Reverse regression based on Wilks’s generalized likelihood ratio test demonstrated each input feature to be highly significant to the model (all Ps Ⰶ 0.000001). CONCLUSIONS. The authors modeled a combination of well described patient risk factors for prostate carcinoma using a neural computational system with acceptable goodness of fit. They demonstrated that each of the seven variates on which the model was based was critically significant to model performance. The authors presented this model for clinical use and suggested that clinicians use it in deciding to perform prostate biopsy. Cancer 2003;98:1849 –54. © 2003 American Cancer Society. KEYWORDS: prostate carcinoma screening, detection, neural network, neurocomputer, prostate specific antigen.
W
ith the introduction of the prostate specific antigen (PSA) assay into clinical practice in the late 1980s, the incidence of localized disease initially increased substantially, and has since shown signs of significant decline.1 The incidence of metastatic prostate carcinoma
1850
CANCER November 1, 2003 / Volume 98 / Number 9
and the death rate have also progressively diminished.1 Currently, T1c (nonpalpable, PSA detected) prostate carcinoma represents the most prevalent clinical stage of disease.2 Despite these favorable statistics, however, there remains controversy surrounding the clinical use of PSA and of early detection for this disease.3 Perhaps the strongest opposing argument for PSA remains the lack of a randomized trial directly linked to a reduction in prostate carcinoma mortality with PSA testing.4 In addition, investigators have debated the specificity of the current PSA threshold, generally accepted to be 4.0 ng/mL.5 Currently, only 25% of patients with a PSA level between 4.0 and 10.0 ng/mL who undergo a prostate biopsy receive a diagnosis of prostate carcinoma.6 Other studies suggested that this PSA cutoff point also has a low sensitivity because approximately 20% of prostate carcinomas are found in men with PSA values less than 4 ng/mL.7 Another limitation of the sole use of total PSA as a tumor marker is that considerable overlap exists in values between patients with prostate carcinoma and individuals with benign prostatic processes. Total PSA elevations may originate from a variety of confounding factors, such as urologic manipulations, urinary retention, benign prostatic hyperplasia (BPH), and prostatic inflammation.8,9 For this reason, numerous adjunctive techniques have been studied to better assess the risk of prostate carcinoma for men undergoing a biopsy. These methods include the use of PSA density, velocity, age-specific PSA cutoff points, free PSA, and the use of predictive nomograms and models.10 Many researchers have evaluated the utility of free and complexed PSA to serve as more specific biomarkers of prostate carcinoma.11,12 Identified by immunoassay, serum PSA exists as complexed (bound) and uncomplexed (free) forms. In the complexed form, PSA is bound primarily to alpha1-antichymotrypsin, an endogenous protease inhibitor.13 Catalona et al.14 reported that the clinical use of percent-free PSA reduced the number of unnecessary biopsies by 20%, while maintaining a 95% cancer detection rate in men with PSA levels in the range 4 –10 ng/mL. The potential benefit of percent-free PSA is notable, but prospective clinical trials have yet to demonstrate an improvement in cancer detection compared with total PSA alone. Although many investigators have suggested methods to improve the diagnostic accuracy of PSA, no single test has emerged as a definitive alternative. Nevertheless, investigators in clinical practice have observed certain well established patient characteristics that correlate with the risk for prostate carcinoma. These features include patient age,15 race,16,17 family
history,18 and urinary tract symptoms.19 Although none of these variables alone may accurately predict prostate carcinoma, we investigated whether a combination of these factors may best determine a patient’s risk for disease using the nonlinear mathematic modeling approach of neural computation. Briefly, neural computation is a computational system that simulates the physiology of the biologic neuron. Training patterns are presented to a nodal system in which each node applies a transfer function to its presenting information and presents its outcome to other nodes in a well defined topography. A “learning” algorithm is iteratively applied to the system, which minimizes the error derived from the network’s output state and the presented outcomes data, in this case, prostate biopsies described as cancerous or not. Input features included age, ethnicity, family history, International Prostate Symptom Score (IPSS), digital rectal examination (DRE), and total and complexed PSA (Bayer Diagnostics). After a model with acceptable goodness of fit was found, we employed a statistical method, Wilks’s generalized likelihood ratio test (GLRT), to determine which input features were significant to the model’s outcome. Essentially, we performed a reverse regression analysis.20,21 We deployed the model in the javascript language for ready availability on the worldwide web (Fig. 1). The clinician enters the patient’s data using the formsbased interface and the model reports the odds of prostate carcinoma. (For readers familiar with neural computation, the outcome of a model using a sigmoidal transfer function and the cross-entropy error function is the probability, p, that the outcome is 1— defined in the current study as cancer—and the odds are expressed as p/(1⫺p).20) Currently, the model may be found at URL: www.urocomp.net
MATERIALS AND METHODS We wrote a suite of C⫹⫹ programs, named “neUROn” (neural computational environment for UROlogic numericals), to implement neural computational and statistical algorithms, which are cross compiled using Microsoft Visual C⫹⫹ version 6 (Microsoft, Redmond, WA) and GNU C⫹⫹ (Cygwin port) version 2.95. The training method was canonical off-line backpropagation with weight decay, with the weight decay term lambda chosen to be 5e-05.20 All transfer functions were sigmoidal, allowing for odds ratios to be computed easily at the output node, and the error function was chosen to be cross-entropy for feature extraction using Wilks’ GLRT. The archival serum samples were obtained during screening before prostatic manipulation or biopsy was
Prostate Ca Neurocomputer/Kalra et al.
FIGURE 1. Example of neural computational model Javascript implementation. IPSS: International Prostate Symptom Score; PSA: prostate specific antigen.
performed. The samples were tested retrospectively at six sites, including the Northwest Prostate Institute (NWP; Seattle, WA), the University of Washington (UW; Seattle, WA), the Johns Hopkins Hospital (JH; Baltimore, MD), Memorial Sloan-Kettering Cancer Institute (MSK; New York, NY), Brigham and Women’s Hospital (BWH; Boston, MA), and The University of Texas, M. D. Anderson Cancer Center (MDA; Houston, TX).22 A total of 3268 men were enrolled to this protocol from the six sites. Data were obtained at each institution after approval was granted by the institutional review board and in conformance with the Health Insurance Portability and Accountability Act of 1996 (HIPAA) regulations. Participants with a personal history of prostate carcinoma or symptoms of acute prostatitis and/or current urinary tract infection were excluded from the current study. Of these 3268 men, 363 men underwent a transrectal ultrasound- guided prostate needle sextant biopsy (NWP, 42; UW, 92; JH, 85; MSK, 30; BWH, 73; MDA, 42). The indication to perform a biopsy was either a PSA level greater than or
1851
equal to 4.0 ng/mL and/or an abnormal DRE. Each institution performed its biopsies according to its standard of practice at the time. However, the sextant strategy was the minimum. Of these 363 men, 9 were excluded because of incomplete sample collections. Consequently, 354 men were eligible for the current study. They had a median age of 66 years (range, 50 – 84 years). A blood sample was drawn and analyzed at each institution to measure total and complexed PSA using the Bayer Technicon Immuno 1 PSA method (Bayer Diagnostics, Tarrytown, NY). All serum samples were drawn no more than 1 month before enrollment DRE, or at a time point greater than or equal to 1 week, but less than 1 month after DRE. Within 24 hours of collection, all samples were centrifuged and stored at ⫺70 °C. The study population comprising 354 patients with known prostate biopsy outcomes was used to construct the dataset. Patients with prostatic intraepithelial neoplasia were excluded from the current study. The resulting dataset, which was comprised of 348 subjects, was modeled using the neUROn software environment. The output node represented the result of the prostate biopsy, which was encoded as a binary variable (cancer or benign). Each outcome was mapped with the corresponding patient characteristics (i.e., age, ethnicity, family history, IPSS, DRE, and total and complexed PSA). The dataset was divided randomly into a training set of 218 subjects and a test set of 144 subjects. The proportion of positive biopsy outcomes was constrained to be similar in both sets using a randomization algorithm that maintained equal frequencies of outcomes. The test set was excluded from training and only used for cross-validation (the n1/n2 method). Multiple random sets of initial conditions (connection weights) were derived and the training set was applied iteratively to the neural computational system. When overlearning was observed by divergence of training and test set errors, hidden nodes were removed to reduce network topology. A 1-hidden node layer with three hidden nodes was determined to represent an optimal topology that maintained acceptable goodness of fit without overlearning. We considered the network to be trained to completion when the error was observed to be oscillating at a local error minimum. We employed Wilks’s GLRT to determine which input features were significant to the model’s outcome in a reverse regression analysis.20 We also modeled the dataset using logistic regression and linear and quadratic discriminant function analysis (LDFA and QDFA) to compare the nonlinear computational method of neural computation with traditional linear
1852
CANCER November 1, 2003 / Volume 98 / Number 9
TABLE 1 Receiver Operating Characteristic Areas in the Test Set Method
ROC area
P value
Neural computational system Logistic regression Total PSA Complexed PSA QDFA LDFA
0.825 0.510 0.678 0.697 0.011 0.674
0.0001 0.0007 0.002 0.0001 0.0002
ROC: receiver operating characteristic; PSA: prostate specific antigen; QDFA: quadratic discriminant function analysis; LDFA: linear discriminant function analysis.
statistical modeling tools.23 We computed receiver operating characteristic (ROC) curve areas statistically where possible using the statistical method described by Wickens,24 and compared ROC areas statistically according to the method described by DeLong et al.25
RESULTS Table 1 shows the ROC curve areas for the neural computational system observed to have the highest goodness of fit (Kolmogorov–Smirnov P ⬍ 1e-11, by comparison for logistic regression, P ⫽ 0.11), for the logistic regression model and for the linear statistical tools LDFA and QDFA, and for total and complexed PSA alone in the test set. Briefly, the ROC curve area is calculated by plotting the sensitivity versus (1 ⫺ specificity) for all possible thresholds and computing the area under the curve. As common computational techniques for determining the ROC area such as integrating using a trapezoidal method may be inaccurate, we chose to use the statistical technique described by Wickens whenever possible.24 The P values in Table 1 represent the probability that the ROC curve area is significantly different from that of the neural computational system, using the method of DeLong et al.25 Figure 2 shows the ROC curves for logistic regression, LDFA, and the neural computational model. After an acceptable goodness of fit was observed (the ROC curve area for the neural computational system in the test set was ⬎ 0.8), reverse regression was employed using Wilks’ GLRT. To use Wilks’ GLRT for feature extraction, the full network was trained to a strict local error minimum and the cross-entropy error was calculated. Subtracting each input node sequentially created feature-deficient networks. These subnetworks were retrained to a strict local error minimum and the cross-entropy error for each subnetwork was recorded. The probability, P, that the modeler can reject the null hypothesis that the full network and feature-deficient networks are the same follows a chisquared probability distribution with degrees of free-
FIGURE 2. Receiver operating characteristics curves for logistic regression, linear discriminant function analysis (LDFA), and the neural computational model.
dom equal to the number of nodal connections removed by generating the feature-deficient subnetwork.20 All observed probability values (P Ⰶ 0.000001) indicated that all variates were highly significant to the model.
DISCUSSION The prediction of prostate carcinoma using known patient characteristics is a concept familiar to the urologist. Urologists use well established guidelines to recommend patients to undergo a prostate biopsy. However, because of the limitations of the PSA and DRE alone, individual urologists generally take other clinical features into account in formulating a recommendation. Neural computation represents a field in which mathematical models are derived from algorithms based loosely on the physiologic function of the biologic neuron. Investigators have used this nonlinear computational modeling technique to solve a variety of complex cognitive clinical problems. Greater than 400 biomedical applications of artificial neural networks are reported in computational, engineering, biologic, and medical journals. In this application, the neural computational method clearly outperformed traditional linear modeling tools such as LDFA and QDFA and unimodal diagnostic techniques such as total or complexed PSA alone.
Prostate Ca Neurocomputer/Kalra et al.
After training the model, we performed feature extraction (statistical regression) to evaluate the contribution of each variable to the model’s outcome. The current analysis demonstrated that all variates (age, ethnicity, family history, IPSS, DRE, total and complexed PSA) were of critical significance in this well conditioned multivariate model. This finding is not surprising when these features are evaluated on an individual basis, with emphasis on their already well established correlations with prostate carcinoma. Age is a known risk factor for prostate carcinoma. The prevalence of prostate carcinoma increases with age. After the age of 50 years, both the incidence and the mortality from prostate carcinoma increase at a near exponential rate.26 Ethnicity was also highly significant to the outcome of the model. This finding reinforces epidemiologic observations of a higher risk for prostate carcinoma among African-American men. Although to our knowledge the exact etiology of this disparity is unknown, various investigators attribute this observation to genetic, nutritional, and hormonal factors, as well as to differences in access to health care and cultural conceptions of the disease.27,28 Family history was found to be of critical significance to the model’s outcome. Many investigators reported that the risk of prostate carcinoma is increased if other family members are affected.18,29,30 These studies demonstrated an approximately twofold increase in risk if a first-degree relative has the disease. The molecular mechanisms underlying the oncogenesis and progression of prostate carcinoma are still unclear.31 Statistical regression of the model also identified the degree of urinary bother as measured by the IPSS to be highly significant to model outcome. As prostate carcinoma is generally asymptomatic, and benign conditions such as BPH and chronic prostatitis are symptomatic, it follows our clinical judgment that the model found IPSS to be significant in determining the risk of cancer. In addition, a DRE was found to be an important feature to the model. Before the advent of PSA, DRE alone was the principal method of cancer detection.32 DRE has been reported to have low reproducibility and depends on the experience of the examiner.33 However, this examination is, nevertheless, indispensable as an adjunct for diagnosing prostate carcinoma. Screening program studies have reportedly identified 18% of cancer in men with PSA values less than 4 ng/mL as detected by abnormal DRE.34 Investigators also reported higher cancer detection in screening when DRE and PSA are performed together.34,35 Many researchers have investigated the role of free, complexed, and total PSA in prostate carcinoma screening.13,14,36,37 Free PSA has been suggested as an
1853
adjunctive modality in men with moderately elevated PSA values (4 –10 ng/mL).38 Serum PSA is complexed to the enzyme inhibitor, alpha1-antichymotrypsin, and investigators reported that this moiety comprises a greater proportion of the total PSA in men with cancer.39 Thus, it is not surprising that total and complexed PSA were both critical to the model and that neither could be omitted without significantly degrading model performance. In the current study, we built a well conditioned neural computational model to predict prostate carcinoma on transrectal biopsy using seven clinical features (i.e, patient age, race, family history, IPSS, DRE, and total and complexed PSA). This nonlinear mathematical model was cross-validated using a test set that was not used in its construction. We found it to be significantly more accurate (the ROC area in the test set was 0.825) than the linear statistical modeling methods of logistic regression, LDFA and QDFA, and the unimodal use of PSA alone. We suggest that clinicians consider reporting the outcome of the model as the odds of harboring prostate carcinoma to patients. For example, for a hypothetical 52-year-old white male with a total PSA level of 4.5 ng/mL, a complexed PSA of 3.2 ng/mL, IPSS 22, no family history of prostate carcinoma, and a normal DRE, the model’s odds of cancer is 1 to 5. Given these odds, some patients may sensibly choose a biopsy, whereas others may not.
REFERENCES 1.
2.
3. 4.
5.
6.
7.
8.
Mettlin CJ, Murphy GP, Ho R, Menck HR. The National Cancer Database report on longitudinal observations on prostate cancer. Cancer. 1996;77:2162–2166. Pound CR, Partin AW, Epstein JI, Walsh PC. Prostate-specific antigen after anatomical radical retropubic prostatectomy. Patterns of recurrence and cancer control. Urol Clin North Am. 1997;24:395– 406. Wilkinson S, Chodak G. Informed consent for prostate-specific antigen screening [editorial]. Urology. 2003;61:2– 4. Carter HB, Pearson JD. Prostate-specific antigen testing for early diagnosis of prostate cancer: formulation of guidelines. Urology. 1999;54:780 –786. Catalona WJ, Smith DS, Ratliff TL, et al. Measurement of prostate-specific antigen in serum as a screening test for prostate cancer. N Engl J Med. 1991;324:1156 –1161. Arcangeli CG, Ornstein DK, Keetch DW, Andriole GL. Prostate-specific antigen as a screening test for prostate cancer. The United States experience. Urol Clin North Am. 1997;24: 299 –306. Catalona WJ, Smith DS, Ornstein DK. Prostate cancer detection in men with serum PSA concentrations 2.6 to 4.0 ng/ml and benign prostate examination. Enhancement of specificity with free PSA measurements. JAMA. 1997;277:1452–1455. Nadler RB, Humphrey PA, Smith DS, Catalona WJ, Ratliff TL. Effect of inflammation and benign prostatic hyperplasia on elevated serum prostate-specific antigen levels. J Urol. 1995; 154:407– 413.
1854 9.
10.
11.
12.
13.
14.
15. 16.
17.
18.
19.
20. 21.
22.
23. 24. 25.
CANCER November 1, 2003 / Volume 98 / Number 9
Deliveliotis C, Alivizatos G, Stavropoulos NJ, et al. Influence of digital examination, cystoscopy, transrectal ultrasonography and needle biopsy on the concentration of prostatespecific antigen. Urol Int. 1994;53:186 –190. Polascik TJ, Oesterling JE, Partin AW. Prostate specific antigen: a decade of discovery—what we have learned and where we are going. J Urol. 1999;162:293–306. Cheli CD, Levine RL, Cambetas DR, Kolker JD, Roberts SB. Age-related reference ranges for complexed prostate-specific antigen and complexed/total prostate-specific antigen ratio: results from East Texas Medical Center Cancer Institute screening campaign. Urology. 2002;60(4 Suppl 1):53–59. Miller MC, O’Dowd GJ, Partin AW, Veltri RW. Contemporary use of complexed PSA and calculated percent free PSA for early detection of prostate cancer: impact of changing disease demographics. Urology. 2001;57:1105–1111. Lilja H, Christensson A, Dahle´n U, et al. Prostate-specific antigen in serum occurs predominantly in complex with alpha 1-antichymotrypsin. Clin Chem. 1991;37:1618 –1625. Catalona WJ, Partin AW, Slawin KM, et al. A multicenter clinical trial evaluation of free PSA in the differentiation of prostate cancer from benign disease [abstract]. J Urol. 1997; 157:111. Wingo PA, Tong T, Bolden S. Cancer statistics. CA Cancer J Clin. 1995;45:8 –30. Morgan TO, Jacobsen SJ, McCarthy WF, Jacobson DJ, McLeod DG, Moul JW. Age-specific reference ranges for prostatic-specific antigen in black men. N Engl J Med. 1996; 335:304 –310. Moul JW, Sesterhenn IA, Connelly RR, et al. Prostate-specific antigen values at the time of prostate cancer diagnosis in African-American men. JAMA. 1995;274:1277–1281. Steinberg GD, Carter BS, Beaty TH, Childs B, Walsh PC. Family history and the risk for prostate cancer. Prostate. 1990;17:337–347. Lepor H, Owens RS, Rogenes V, Kuhn E. Detection of prostate cancer in males with prostatism. Prostate.1994;25:132– 140. Golden RM. Mathematical methods for neural network analysis and design. Cambridge, MA: MIT Press, 1996. Wilks SS. The large sample distribution of the likelihood ratio for testing composite hypotheses. Ann Math Stat. 1938; 9:60. Okihari K, Cheli CD, Partin AW, et al. Comparative analysis of complexed prostate specific antigen, free prostate specific antigen and their ratio in detecting prostate cancer. J Urol. 2002;167:2017–2023; discussion 2023–2024. Duda RO, Hart PE. Pattern classification and scene analysis. New York: John Wiley & Sons, 1973. Wickens TD. Elementary signal detection theory. New York: Oxford University Press, 2002. DeLong ER, DeLong DM, Clarke-Pearson DL. Comparing the areas under two or more correlated receiver operating
26.
27. 28.
29.
30.
31. 32.
33.
34.
35.
36.
37.
38.
39.
characteristic curves: a nonparametric approach. Biometrics. 1988;44:837– 845. Pienta KJ. Etiology, epidemiology, and prevention of carcinoma of the prostate. In: Walsh PC, Retik AB, Vaughan ED, Wein AJ, editors. Campbell’s urology. Philadelphia: W.B Saunders Company, 1998:2489 –2496. Powell IJ. Prostate cancer and African-American men. Oncology. 1997;11:599 – 605; discussion 606 – 615. Wu AH, Whittemore AS, Kolonel LN, et al. Serum androgens and sex hormone-binding globulins in relation to lifestyle factors in older African-American, white, and Asian men in the United States and Canada. Cancer Epidemiol Biomarkers Prev. 1995;4:735–741. Spitz MR, Currier RD, Fueger JJ, Babaian RJ, Newell GR. Familial patterns of prostate cancer: a case-control analysis. J Urol. 1991;146:1305–1307. Carter BS, Beaty TH, Steinberg GD, Childs B, Walsh PC. Mendelian inheritance of familial prostate cancer. Proc Natl Acad Sci USA. 1992;89:3367–3371. Latil A, Lidereau R. Genetic aspects of prostate cancer. Virchows Arch. 1998;432:389 – 406. Gerber GS, Thisted R, Chodak GW, Thompson IM. Diseasespecific survival following routine prostate cancer screening by digital rectal examination: corrected patient classification. JAMA. 1993;269:61– 64. Smith DS, Catalona WJ. Interexaminer variability of digital rectal examination in detecting prostate cancer. Urology. 1995;45:70 –74. Catalona WJ, Richie JP, Ahmann FR, et al. Comparison of digital rectal examination and serum prostate specific antigen in the early detection of prostate cancer: results of a multicenter clinical trial of 6,630 men. J Urol. 1994;151: 1283–1290. Carvalhal GF, Smith DS, Mager DE, Ramos C, Catalona WJ. Digital rectal examination for detecting prostate cancer at prostate specific antigen levels of 4 ng/ml or less. J Urol. 1999;161:835– 839. Christensson A, Bjo¨rk T, Nilsson O, et al. Serum prostatespecific antigen complexed to alpha 1-antichymotrypsin as an indicator of prostate cancer. J Urol. 1993;150:100 –105. Catalona WJ, Smith DS, Wolfert RL, et al. Evaluation of percentage of free serum prostate-specific antigen to improve specificity of prostate cancer screening. JAMA. 1995; 274:1214 –1220. Catalona WJ, Partin AW, Slawin KM, et al. Use of the percentage of free prostate-specific antigen to enhance differentiation of prostate cancer from benign prostatic disease: a prospective multicenter clinical trial. JAMA. 1998;279:1542– 1547. Brawer MK, Meyer GE, Letran JL, et al. Measurement of complexed PSA improves specificity for early detection of prostate cancer. Urology. 1998;52:372–378.
