A Validation Study of New Rules for Interpretation of Prostate Cancer Biopsy Results, Based on Gland Volume and Number of Positive Cores.

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1 A Validation Study of New Rules for Interpretation of Prostate Cancer Biopsy Results, Based on Gland Volume and Number of Positive Cores. Gerald O. Ogola, Nicolas Delongchamps 2, and Robert Serfling 3 Institute for Health Care Research and Improvement, Baylor Health Care System, Dallas, Texas. 2 Department of Urology, Cochin Hospital, Paris Descartes University, Paris, France. 3 Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas. Corresponding author: Robert Serfling, Ph.D. Professor, Department of Mathematical Sciences, University of Texas at Dallas Richardson, Texas (Voice) (FAX) serfling@utdallas.edu Conflicts of Interest: None of the authors have conflicts of interest to report Abstract word count = 25 Manuscript word count = 825 Running Head: Validation of prostate-volume-based decision rules Page of

2 ABSTRACT Purpose: To test on a prostatectomy dataset a new decision rule derived by probability modeling of the number of positive cores, for deciding insignificant versus significant prostate cancer (CaP), based on prostate volume, Gleason score, tumor lengths in biopsy cores, and number of positive cores. Materials and Methods: A prostatectomy dataset of 59 patients aged 42 to 92 years with prostate volumes 22 to 95 cc is used. Clinically insignificant CaP is defined as Gleason sum < 7, total tumor volume <.5 cc, and sufficiently small tumor lengths in the cores. For prostate volumes 2-3, 4, 5, 6-7, and 8- cc, and numbers of biopsy cores 6, 2, and 8, separate counts of Significant versus Insignificant by both the decision rule and the actual data are obtained. These yield specificity, sensitivity, and concordance values, by prostate volume and number of cores, for evaluation of the efficacy of the decision rule. Results: The model-based rule yields SP from 83 to, SE from 62 to, and concordance from 78 to. Being model-based, the rule and these results apply generally. Also, the findings compare favorably with currently used study-based rules and their individually fitted SP and SE, which, however, differ across studies. Conclusions: Our model-based decision rule performs well with this prostatectomy dataset, confirming its practical feasibility and its potential to help reduce over- and under-treatment. However, additional validation studies with other datasets including higher prostate volumes are desired for possible further calibration and improvement of the model-based rule. KEY WORDS: Prostate, cancer, biopsy, decision, validation Page 2 of

3 INTRODUCTION Planning for effective prostate cancer (CaP) biopsy sessions and interpreting marginally positive biopsy results is challenging. With millions of CaP biopsies performed annually, avoiding overtreatment poses a world-wide dilemma of large scale. To avoid over-treatment, one needs to distinguish between insignificant and significant CaP with sufficiently high specificity (SP), and this requires assigning some marginally positive cases to watchful waiting. How to select such candidates? To avoid under-treatment, decision-making with sufficiently high sensitivity (SE) is required, and this entails increasing the number of biopsy cores as prostate volume increases, keeping in mind the burden on the patient. In what manner should this increase proceed? Addressing these questions, a probability model,2 for the number of positive cores in a biopsy session, as a function of prostate gland volume, tumor nodule volumes, and number of cores, was recently developed and applied to construct favorable prostate-volume-specific decision rules for insignificant versus significant CaP on the basis of Gleason score, tumor lengths in the cores, and the number of positive cores. By favorable is meant a favorable tradeoff between SP and SE, prioritizing on high SP, among available options. In particular, for prostate volumes through 2 cc and number of cores 6, 2, 8, and 24, model-based SP and SE were evaluated and examined for decision rules of form Decide insignificant CaP if D < x, for specified x with D the number of positive cores. Initially setting aside Gleason score and tumor lengths in cores, insignificant CaP" is defined simply as total tumor volume T <.5 cc. For this purpose, model-based SP and SE are defined, respectively, as the conditional probability of deciding insignificant CaP when CaP is truly insignificant, and the conditional probability of deciding significant CaP when CaP is truly significant. For SP a total tumor volume T below the clinically significant threshold.5 cc is selected, in particular T =.25 cc, defining SP(x n, V) = P(D x n, V, T =.25 cc) = P(D = x n, V, T =.25 cc), and for SE we choose T above.5 cc, in particular T = 2. cc, defining SE(x n, V) = P(D > x n, V, T = 2. cc) = P(D = x n, V, T = 2. cc). Based on the derivations of (SP, SE) in previous work 2, favorable choices considered here are displayed in Table. Page 3 of x x= min {k,n} x=x +

4 Biopsy results yield not only D but also tumor lengths (or % CaP) in the cores and Gleason score. We therefore embed our model-based rules within fully structured rules,2 incorporating this additional data, as follows. For Gleason sum 7 or higher, immediately conclude Significant CaP. Otherwise, consider tumor lengths and if % CaP is sufficiently large in sufficiently many cores, then conclude Significant CaP. Otherwise, finally, apply the appropriate model-based rule to decide insignificant versus significant CaP. This fully structured rule, exhibited in Table 2, has the same SP as for the model-based rule, but higher SE. In the present study, the fully structured rule is validated using a prostatectomy dataset, supplied by the 2 nd author, consisting of 59 patients aged 42 to 92 years with prostate volumes from 22 to 95 cc. Biopsy data is from an 8-core biopsy scheme for 47 patients and from a 36- core scheme for 2 patients. Figure displays the biopsy protocol diagram labeling the biopsy needle locations. Available data elements include prostate volumes, number of biopsy cores, number of positive cores, positive core locations, core lengths, tumor lengths, percent of tumor involvement in cores, tumor volumes (index and total), and Gleason scores. Using this data, the fully structured rule is validated for prostate volumes through 9 cc and numbers of biopsy cores 6, 2, and 8, by extracting 6-core and 2-core biopsies from the actual 8- and 36-core biopsies, extracting 8-core biopsies from the 36-core biopsies, and also using the 8-core biopsies as is. We obtain SP, SE, and concordance for the fully-structured rule, by prostate volume and number of biopsy cores. As a matter of interest, we obtain these also for just the model-based rule comprising Step 3 of the fully structured rule. These results, given in Table 3, show that the SP and SE of the fully structured rules with this particular data set are highly competitive with those of rules in current practice and also are consistent with those in Table for the model-based component. These findings confirm with this data set that the fully structured rule based on probability modeling, if judiciously applied in practice, can be effective in lessening both over- and under-treatment. MATERIALS AND METHODS Model-based decision rules. The decision rule developed in earlier work,2 and to be validated here consists of the fully structured rule in Table 2 incorporating the model-based rules in Table. Our main focus is the fully structured rule based not only on the number of positive cores but also on the Gleason score and tumor lengths, but in passing we also examine the performance of the model-based component rules alone. Validation data. From the data set of 59 patients, we use the following data elements: prostate volumes (22 to 95 cc), number of biopsy cores (6-8), number of positive cores, positive core Page 4 of

5 locations, core lengths, tumor lengths, percent of tumor involvement in cores, tumor volumes (index and total), and Gleason scores. From the 8-core biopsy data on 47 patients, we extract in addition 6-core and 2-core biopsies. From the 36-core schemes used with 2 patients, we extract 6-core, 2-core, and 8-core biopsies. The 6-core biopsies use locations labeled to 6, the 2-core biopsies locations -6 and 3-8, and the 8-core biopsies locations -8, in Figure. Although the model-based rules also include the case of 24-core biopsies, and we could have extracted 24-core biopsies 36-core biopsies, the rule under study recommends 24 cores only as a possibility for prostate volumes above cc, which are lacking in the present dataset. Because of the small numbers of cases for some volumes, we combine into groups as needed, resulting in the following prostate volume groups and number of cores subgroups: 2-3 cc (with 6 cores), 4 cc (with 6, 2, and 8 cores), 5 cc (with 6, 2, and 8 cores), 6-7 cc (with 2 and 8 cores), and 8- cc (with 2 and 8 cores). Validation approach. Separately by available prostate volumes and numbers of cores, we determine the empirical SP, SE, and concordance of both the fully structured rules and the model-based components. In particular, for each combination of prostate volume and number of cores, we classify the corresponding validation data into a table of form Prostatectomy Result Rule Decision Significant Insignificant Significant A [a] B [b] Insignificant C [c] D [d] where A, B, C, D are the counts using the fully structured rule and a, b, c, d are those using just the model-based component based only on the number of positive cores. For each such table, SP, SE, and concordance values are reported using the formulas SP = D/(B+D), SE = A/(A+C), and concordance = (A+D)/(A+B+C+D), and similar formulas with the a, b, c, d counts. High values of SP, SE, and concordance reflect strong performance. RESULTS Table 3 provides the SP, SE, and concordance values for both the fully structured rule and the component using number of positive cores only, for each combination of prostate volume (or prostate volume range) and number of biopsy cores. For example, for 4 cc prostate volume, this table gives for the fully structured rule: (SP, SE, concordance) = (, 86, 9), (,, ), and (,, ) for number of cores = 6, 2, 8, respectively. The corresponding Page 5 of

6 values for the component using number of positive cores only have comparable SP but lower SE and lower concordance. It is seen that the SP values range from 83 (a singular low) to, the SE values from (a singular low) to 5, and the concordance values from 78 to. Also, as an overall summary, the table also provides (SP, SE, concordance) for the group of 6-core biopsies combining the counts for the separate prostate volumes, and likewise for the 2- and 8-core biopsies. These (SP, SE, concordance) values are (, 84, 92), (9, 88, 89), and (, 88, 94), respectively.. DISCUSSION The findings from this work show that the fully structured decision rule with a model-based component performs very well with the present prostatectomy dataset. For the 6-core biopsies, which were used only for prostate volumes 2-5, the SP is in all cases and the SE ranges from 75 to 87. For the 2-core biopsies, used for volumes 4-, the SP ranges from 83 to and the SE is in all cases except for one (62). For the 8-core biopsies, used for volumes 4-, the SP is in all cases and the SE is in all cases except one (62). Looking at all cases together for the 6-core, 2-core, and 8-core biopsies, the corresponding (SP, SE) values are (, 84), (9, 88), and (, 88), respectively. This favorable finding supports the fundamental design of the fully structured rule, which prioritizes on SP in order to avoid overtreatment, uses more cores with larger prostates to obtain reasonable SE in order to avoid under-treatment, and includes a component based on the number of positive cores as data. It is also seen from Table 3 that by itself the latter component is similar in SP but lower in SE, as expected. Being derived using a probability model, rather than from a particular dataset, this rule possesses generality of potential application. It is reassuring to see that it performs well with this particular data set, the only one investigated to date, and this suggests going forward with validation studies using other available data sets, including prostate volumes -2 cc. For comparison with other methods in current practice, a review of leading methods 3 indicates (SP, SE) such as (, 4), (99, 7), (99, 34), (98, 53), (98, 52), (98, 23), (97, 67), (96, 5), (96, 27), (95, 56), (89, 33), (78, 7), and (75, 77), the two in bold including prostate volume as an input. These are derived, typically, by fitting logistic regression models to particular data sets, but the optimal fitted models differ across the data sets of patients, making it problematic to decide which to use with a patient. Also, these concern a range of 6 to 2 biopsy cores. In Page 6 of

7 contrast, the fully structured rule not only compares well in (SP, SE) but also, very importantly, properly adjusts for prostate volume. The following guideline follows from Table. Prostate Volume (cc) Number of cores 6 6, 2, or 8 2 or 8 8 or 24 CONCLUSIONS The model-based fully structured decision rule performs very well when validated with actual prostatectomy data and is consistent with model-based expectations. This suggests the value of the rule in judicious practical application, along with additional modeling and validation studies for possible further calibration and improvement of the decision rule. ACKNOWLEDGMENT The authors gratefully thank Dr. Gabriel Haas, M.D., and Dr. G. L. Thompson, Ph.D., for very helpful remarks and encouragement. REFERENCES. Serfling R and Ogola GO: Probability modeling of the number of positive cores in a prostate cancer biopsy session, with applications. Submitted. Available at 2. Ogola GO and Serfling R: Planning of prostate cancer biopsies and interpretation of biopsy results, using rules based on gland volume and number of positive cores, with favorable model-based specificity and sensitivity. Submitted. Available at 3. Anast JW, Andriole GL, Bismar TA et al: Relating biopsy and clinical variables to radical prostatectomy findings: can insignificant and advanced prostate cancer be predicted in a screening population? Urology 24; 64: Delongchamps, NB, de la Rosa G, Jones R et al: Saturation biopsies on autopsied prostates for detecting and characterizing prostate cancer. BJUI 28; 93: 49. Page 7 of

8 TABLES AND FIGURES Table. Model-based specificity (SP) and sensitivity (SE) for selected insignificant CaP thresholds (x ), by prostate volume (V) and number of biopsy cores (n). Favorable cases in bold prioritize on high SP and offer n versus SE tradeoffs. n V x (SP, SE) x (SP, SE) x (SP, SE) x (SP, SE) 2 (67, 93) (95, 53) 2 (47, ) (89, 73) 3 (6, 9) (95, 45) 4 (69, 8) (97, 29) (47,) (88, 8) 2 (75, 97) (96, 68) 5 (75, 7) (98, 2) (55, 96) (92, 65) 2 (82, 9) (98, 5) 6 (6, 9) (94, 5) 2 (87, 83) (99,39) 7 (66, 85) (96, 4) (52, 98) (9, 72) 8 (69, 8) (97, 34) (57, 95) (92, 62) 9 (72, 75) (97, 28) (6, 9) (94, 53) (75, 7) (98, 24) (64, 87) (95, 46) (67, 84) (96, 4) (58, 94) (92, 6) 2 (69, 8) (96, 35) (6, 9) (94, 54) 3 (72, 77) (97, 3) (64, 88) (94, 49) 4 (73, 74) (97, 28) (66, 85) (95, 44) 5 (75, 7) (98, 25) (68, 83) (96, 4) 6 (76, 68) (98, 22) (69, 8) (96, 36) 7 (78, 65) (98, 2) (7, 78) (97, 33) 8 (79, 63) (98, 8) (72, 75) (97, 3) 9 (8, 6) (74, 73) 2 Page 8 of (98, 7) (8, 58) (99, 5) (97, 28) (75, 7) (98, 26)

9 Table 2. Fully Structured Decision Rule for Insignificant versus Significant CaP.. Check Gleason sum. If 7 or higher, conclude Significant CaP. Otherwise proceed to next step. 2. Check tumor lengths in the positive biopsy cores. If At least core contains >. cm tumor (or 67%), Or at least 2 cores each contain >.8 cm tumor (or 53%), Or at least 3 cores each contain >.7 cm tumor (or 47%), Or at least 4 cores each contain >.65 cm tumor (or 43%), conclude Significant CaP. Otherwise proceed to next step. 3. Apply model-based decision rules based on number of positive cores, for given prostate volume and number of biopsy cores. Conclude either Significant CaP or Insignificant CaP. Page 9 of

10 Table 3. Validation Results for Fully Structured Decision Rule [for Model-Based Component Only] Prostate Number Rule Prostatectomy Result Volume (cc) of Cores Decision Significant Insignificant (SP,SE) Concordance Significant 3 [] [] (, 75) Insignificant [3] 8 [8] [(, 25)] 92 [75] 6 Significant 6 [] [] (, 86) Insignificant [7] 3 [3] [(, )] 9 [3] 4 2 Significant 7 [2] [] (, ) Insignificant [5] 3 [3] [(, 27)] [5] 8 Significant 7 [] [] (, ) Insignificant [6] 3 [3] [(, 4)] [4] 6 Significant 7 [3] [] (, 87) Insignificant [5] 6 [6] [(, 37)] 93 [64] 5 2 Significant 8 [4] [] (83, ) Insignificant [4] 5 [5] [(83, 5)] 93 [64] 8 Significant 8 [4] [] (, ) Insignificant [4] 6 [6] [(, 5)] [7] Significant 5 [4] [] (9, 62) 78 [72] Insignificant 3 [4] 9 [9] [(9, 5)] 8 Significant 5 [4] [] (, 62) 83 [78] Insignificant 3 [4] [] [(, 5)] 8-2 Significant 2 [] [] (,) Insignificant [] 3 [3] [(, 5)] [8] 8 Significant 2 [] [] (,) Insignificant [] 3 [3] [(, 5)] [8] 6 Significant 6 [4] [] (, 84) Insignificant 3 [5] 7 [7] [(, 2)] 92 [58] All 2 Significant 22 [] 2 [2] (9, 88) Insignificant 3 [4] 2 [2] [(9, 44)] 89 [66] 8 Significant 22 [] [] (, 88) Insignificant 3 [5] 22 [22] [(, 4)] 94 [68] Page of

11 Figures Figure. The saturation biopsy scheme: cores 8, extended biopsy protocol; cores 6, MPZ; cores 7 2, LPZ; cores 3 8, CZ; cores 9 36 (in red) are additional cores; 9 24, MPZ; 25 3, LPZ; 3 36, CZ. Reprinted with permission from Dr. Nicolas Delongchamps. Page of