A novel mathematical simulation modelling method to predict the probability of finding cancer in prostate biopsy on an individual basis

Evangelos Spyropoulos, Dimitrios Kotsiris, Katherine Spyropoulos, Aggelos Panagopoulos, Evangelos Chatziplis, Ioannis Galanakis, Stamatios Mavrikos


Purpose: To calculate the probability of finding cancer on prostate biopsy, we developed a prostate cancer (PCa) predictive statistical model (PCP-SMART), deriving a novel PCa-predictor (pcrdindex) and a pca-risk mathematical equation.

Subjects and methods: A total of 371 men were included. Since PCa-risk relates to tPSA, age, prostate volume[PV], fPSA, f/tPSA-ratio, PSAD and tPSA≥50ng/ml has 98.5% Positive-Predictive-Value(PPV) for PCa diagnosis, we hypothesized that correlating two variables, each consisting of three ratios/values including patient’s-tPSA, PSA50ng/ml, age, prostate volume, f/tPSAratio, could operate as a “PCa-conditions imitating-simulating model”. Linear regression derived the coefficient-of-determination(R2), termed PCRDindex. Statistics included x2-test, multiple logistic regression analysis, test-performance characteristics and AUC/ROC-curve analysis [SPSS-22(p<0.05)].

Results: Biopsy was PCa(+) in 45.1% and PCa(-) in 44.2%. PCRDindex signed(+) in 89.82% PCa(+) and negative in 91.46% PCa(-) cases (x2-test: p<0.001-RR: 10.52) [Sensitivity: 89.8, specificity: 91.5%, PPV: 91.5%, Negative-Predictive-Value(NPV): 89.8%, Positive-Likelihood-Ratio[LR(+)]: 10.5, Negative-Likelihood-Ratio[LR(-)]: 0.11 Accuracy: 90.6%]. Multiple logistic regression and AUC/ROC analysis revealed PCRDindex as independent PCa-predictor strongly (p<0.001) outperforming other clinically established while, the formulated risk-equation predicted 91% accurately the probability of finding cancer. 

Conclusions: PCRDindex effectively predicted prostate biopsy outcome, identifying correctly 9/10 men who indeed harbored cancer while, correctly ruling out PCa in 9/10 men without disease evidence. It significantly outperformed other established PCa-predictors while, the PCa-risk equation, accurately calculated the individual probability of finding cancer on biopsy.


prostate cancer; PSA testing; PCP-SMART model; PCRD-Index; prostate cancer risk mathematical equation

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Magheli A, Rais-Bahrami S, Trock JB, et al. Prostate Specific Antigen versus Prostate Specific Antigen Density as a Prognosticator of Pathological Characteristics and Biochemical Recurrence following Radical Prostatectomy. J Urol 2008; 179(5): 1780-1784.

Vickers JA, Cronin MA, Roobol JM, et.al. The relationship between prostate-specific antigen and prostate cancer risk: The Prostate Biopsy Collaborative Group. Clin Cancer Res 2010; 16(17): 437-4381.

Zhu X, Albertsen CP, Andriole LG, et.al. Risk-Based Prostate Cancer Screening. Eur Urol 2012; 61: 652-661.

Gerstenbluth ER, Seftel DA, Hampel N, et al. The accuracy of the increased Prostate Specific Antigen level (greater than or equal to20 ng/ml) in predicting prostate cancer: Is biopsy always required? J.Urol 2002; 168: 1990-1993.

Leyten G, Hessels D, Jannink AS, et al. Prospective Multicentre Evaluation of PCA3 and TMPRSS2-ERG Gene Fusions as Diagnostic and Prognostic Urinary Biomarkers for Prostate Cancer. Eur. Urol 2014; 65(3): 534-542.

Sonn AG, Chang E, Natarajan S, et al. Value of Targeted Prostate Biopsy Using Magnetic Resonance-Ultrasound Fusion in Men with Prior Negative Biopsy and Elevated Prostate-specific Antigen. Eur Urol 2014; 65(4): 809-815.

Tomlins AS. Urine PCA3 and TMPRSS2: ERG Using Cancer-specific Markers to Detect Cancer. Eur. Urol 2014; 65(3): 543-545.

Scattoni V, Lazzeri M, Lughezzani G, et al. Head-to-Head Comparison of Prostate Health Index and Urinary PCA3 for Predicting Cancer at Initial or Repeat Biopsy. J Urol 2013; 190: 496-501.

Greene LK, Albertsen CP, Babaian JR, et al. Prostate Specific Antigen Best Practice Statement: 2009 Update. J Urol 2013; 189: S2-S11.

Schroder F, Kattan WM. The Comparability of Models for Predicting the Risk of a Positive Prostate Biopsy with Prostate-Specific Antigen Alone: A Systematic Review. Eur Urol 2008; 54: 274-290.

Quentin M, Blondin D, Arsov Ch, et al. Prospective evaluation of magnetic resonance imaging guided in-bore prostate biopsy vs. systematic transrectal ultrasound guided prostate biopsy in biopsy naïve men with elevated prostate specific antigen. J Urol 2014; 192(5):1374-1379.

Shariat FS, Scardino TP, Lilja H. Screening for Prostate Cancer: An Update. Can J Urol 2008; 15(6): 4363-4374.

Gretzer BM, Partin WA. PSA markers in prostate cancer detection. Urol Clin N Am, 2003; 30: 677-686.

Hernandez JD, Han M, Humphreys BE, et al. Predicting the outcome of prostate biopsy: Comparison of a novel logistic regression-based model, the prostate cancer risk calculator and prostate-specific antigen level alone. BJU Int 2008; 103: 609-614.

Yuasa T, Tsuchiya N, Kumazawa T, et al. Characterization of prostate cancer detected at repeat biopsy. BMC Urol 2008; 8: 14. Published online 2008 November 10. doi: 10.1186/1471-2490-8-14

Roobol JM, Schroder HF, Hugosson J, et al. Importance of prostate volume in the European Randomised Study of Screening for Prostate Cancer (ERSPC) risk calculators: Results from the prostate biopsy collaborative group. World J Urol 2012; 30: 149-155.

Hansen J, Auprich M, Sascha A, et al. Initial Prostate Biopsy: Development and Internal Validation of a Biopsy-specific Nomogram Based on the Prostate Cancer Antigen 3 Assay. Eur. Urol 2013; 63: 201-209.

Karakiewicz IP, Benayoun S, Kattan M, et al. Development and validation of a nomogram predicting the outcome of prostate biopsy based on patient age, digital rectal examination and serum prostate specific antigen. J Urol 2005; 173(6): 1930-1934.

Djavan B, Remzi M, Marberger M. When to biopsy and when to stop biopsying. Urol Clin N Am 2003; 30: 253-262.

Gann HP, Fought A, Deaton R, et al. Risk Factors for Prostate Cancer Detection After a Negative Biopsy: A Novel Multivariable Longitudinal Approach. J Clin Oncol 2010; 28: 1714-1720.

Benecchi L, Pieri A-M, Melissari M, et al. A Novel Nomogram to Predict the Probability of Prostate Cancer on Repeat Biopsy. J Urol 2008; 180: 146-149.

Shariat FS, Karakiewicz IP, Roehrborn GC, Kattan WM. An Updated Catalog of Prostate Cancer Predictive Tools. Cancer 2008;

Shariat FS, Kattan WM, Vickers JA, et al. Critical review of prostate cancer predictive tools. Future Oncol 2009; 5(10): 1555-1584.

Vollmer TR. Predictive Probability of Serum Prostate-Specific Antigen for Prostate Cancer: An Approach Using Bayes Rule. Am J Clin Pathol 2006;125: 336-342.

Chung FH, de Vries SH, Raaijmakers R, et al. Ultrasonography of the prostate volume: The influence of transabdominal versus transrectal approach, device type and operator. Eur Urol 2004; 46: 352-356.

Scattoni V, Zlotta A, Montironi R, et al. Extended and Saturation Prostatic Biopsy in the Diagnosis and Characterisation of Prostate Cancer: A Critical Analysis of the Literature. Eur. Urol 2007; 52: 1309-1322.

Valdagni R., Scardino TP., Denis L., Catan WM.: Predictive Modeling in Prostate Cancer: A Conference Summary. Eur Urol 2009, 55(2):300-302.

Grimes AD, Schulz FK. Epidemiology-3: Refining clinical diagnosis with likelihood ratios. Lancet 2005; 365: 1500-1505.

Loeb S, Catalona JW.: The Prostate Health Index : A new test for the detection of prostate cancer. Ther Adv Urol 2014; 6(2): 74-77 .

Radtke PJ, Kuru HT, Boxler S, et al. Comparative analysis of transperineal template saturation prostate biopsy versus magnetic resonance imaging targeted biopsy with magnetic resonance imaging-ultrasound fusion guidance. J Urol 2015; 193(1): 87-94.

DOI: http://dx.doi.org/10.19264/hj.v29i1.108