PSA density of the lesion: a mathematical formula that uses clinical and pathological data to predict biochemical recurrence in prostate cancer patients

ABSTRACT A main challenge in the clinical management of prostate cancer is to identify which tumor is aggressive and needs invasive treatment. Thus, being able to predict which cancer will progress to biochemical recurrence is a great strategy to stratify prostate cancer patients. With that in mind, we created a mathematical formula that takes into account the patients clinical and pathological data resulting in a quantitative variable, called PSA density of the lesion, which has the potential to predict biochemical recurrence. To test if our variable is able to predict biochemical recurrence, we use a cohort of 219 prostate cancer patients, associating our new variable and classic parameters of prostate cancer with biochemical recurrence. Total PSA, lesion weight, volume and classic PSA density were positively associated with biochemical recurrence (p<0.05). ISUP score was also associated with biochemical recurrence in both biopsy and surgical specimen (p<0.001). The increase of PSA density of the lesion was significantly associated with the biochemical recurrence (p=0.03). Variables derived from the formula, PSA 15% and PSA 152, were also positive associated with the biochemical recurrence (p=0.01 and p=0.002 respectively). Logistic regression analysis shows that classic PSA density, PSA density of the lesion and total PSA, together, can explain up to 13% of cases of biochemical recurrence. PSA density of the lesion alone would have the ability to explain up to 7% of cases of biochemical recurrence. In conclusion, this new mathematical approach could be a useful tool to predict disease recurrence in prostate cancer.

of the University of São Paulo (under the number: 1.955.609).
Initially, 372 male patients, aged between 43 and 81 years, from a private clinic of a single surgeon (CCP), operated between September 2009 and June 2019 were evaluated.However, 76 patients were excluded because they were regularly followed up according to the protocol.Another 64 patients were excluded because they did not present an exact description of the weight of the lesion or the weight of the prostate in the pathological exam.Thirteen patients were excluded for having hormonal block prior to surgery.Thus, the population of the present study was composed of 219 patients.
The PSA density of the lesion of all the patients was calculated and at the end, this calculation was correlated with the presence of tumor recurrence.We have considered biochemical recurrence the finding of PSA values greater than 0.2ng/dL in two consecutive postoperative samples.The first postoperative PSA measurement occurred eight weeks after the operation.
Patients with values greater than or equal to 0.2ng/dL underwent a new confirmatory dosage 7 .

Evaluation of the PSA density of the lesion
To analyze the density of the PSA we used anatomopathology information.We estimated the weight of the primary neoplastic lesion as well as the multicentric lesions using the method standardized by the College of American Pathologists.This method defines that the specimen from radical prostatectomy can have its neoplasia percentage quantified by: careful visualization, being complemented by objective data such as measures of tumor dimensions and; the number of blocks involved by the tumor in relation to the number of total blocks.It is important to highlight that the pathology analysis of the samples was not necessarily performed by the same pathologist 8,9 .
We calculated the difference between the weight of the prostate (WP) and the weight of the neoplastic lesion (WL Firstly, we calculated the weight of the nonneoplastic (benign) portion of the prostate (BP) with the data obtained from the complete anatomopathology examination of each patient (which systematically reports the prostatic weight and the estimated percentage of the prostatic volume represented by tumor tissue).
Differences between the weight of the prostate (WP) and the weight of the neoplastic lesion (WN), were assessed according to the following formula: BP = WP -WN.
Then, we performed the calculation of the PSA produced only by the benign portion of the prostate (PSABP).We considered the PSA density of 15% as the cutoff to estimate PSA production by the non-neoplastic portion of the prostate.This value of 0.15 is based on the cutoff of the predictor called classic prostate PSA density, traditionally used as a predictor for patient selection for prostate biopsy and as a parameter for the management of patients under active surveillance.This value is obtained by dividing the total PSA value and the prostate volume, then the following formula was used: PSABP = 0.15 x BP [3][4][5] .Subsequently, we calculated the PSA produced by the neoplastic portion (PSA of the lesion), using the formula: PSA of the lesion = total PSA -PSABP.
After calculating the PSA of the lesion, a correction factor was added, since there is a possibility that the PSA calculation value of the lesion is negative.patient model with a potential small aggressive lesion that could induce the production of a large amount of PSA per gram of injury.Therefore, this is a profile of a patient with a greater possibility of biochemical recurrence, susceptible to being neglected by current predictors (Figure 1A).

Detailed calculations of example 1:
Example 2: patient with total PSA of 6.0ng/ dL, prostate with a volume of 34cm 3 , prostate weight of 35g and 10% of the prostate volume occupied by the neoplasm, classic PSA density of 0.17  The study was approved by the local ethics committee under the number 64119817.6.0000.0065.

Statistical analysis
We calculated a post hoc sample power, using the G Power 3.1 program based the determination Junqueira PSA density of the lesion: a mathematical formula that uses clinical and pathological data to predict biochemical recurrence in prostate cancer patients coefficient (r 2 ) obtained from the models generated from the multiple Logistic Regression.We considered the sampling error of 5% and a 95% confidence interval, and the minimum significant sample for the study was Regarding continuous variables, analyzes were performed using Student's t and Mann-Whitney tests.In order to explore the contribution of continuous and categorical exploratory variables under the postoperative outcome, multiple logistic regression was performed using the conditional step-forward method.In all analyzes, the level of significance adopted was 5% (p<0.05).

RESULTS
The patients' clinical variables are shown in Tables 1 and 2. The average age was 62.51± 7.60 years.
We observed a biochemical recurrence rate of 18.3%.The new developed PSA density of the lesion was assessed, and we found that the increase of this variable was significantly correlated with the biochemical recurrence (p=0.03).PSA 15% and PSA 15 2 were also positively associated with the biochemical recurrence (p=0.01 and p=0.002 respectively) Additionally, the ISUP score between the group with or without biochemical recurrence (Figure 2) was evaluated, and the increase in the ISUP score was associated with the biochemical recurrence in both biopsy and surgical specimens of PC samples (p<0.001).
Finally, the multiple logistic regression (Table 4) indicated that the classic variables as PSA density, PSA density of the lesion and total PSA, together, can explain up to 13% of cases of biochemical recurrence.PSA density of the lesion, according to this model, would have the ability to explain up to 7% of cases of biochemical recurrence.

DISCUSSION
The curative treatment for PCa has highly been carried out in recent decades 10 .Robotic radical prostatectomy is certainly one of the greatest advances.
However, treatment is not free from adverse effects and there is always the possibility of an unfavorable outcome despite the use of the best available methods.
Overtreatment is a real problem for PCa, thus being able to predict those patients who need invasive treatment, and those who have an indolent disease is highly necessary 11 .
In addition, the indiscriminate use of PSA levels has been associated with a high rate of overdiagnosis and excessive treatment [12][13][14] .
Normally, after treatment, the PSA levels of PCa patients drop to zero.Biochemical recurrence is a phenomenon in which the PSA increases again, indicating the disease recurrence 15 .Therefore, being able to predict biochemical recurrence is a great strategy to early identify aggressive tumors.
In  of this new parameter would be for the selection of patients with a higher risk of biochemical recurrence.
For these patients, adjuvant treatments would be considered more seriously instead of waiting for the patient to present biochemical recurrence to administer rescue therapies.Junqueira PSA density of the lesion: a mathematical formula that uses clinical and pathological data to predict biochemical recurrence in prostate cancer patients The pathology graduation according to the ISUP criteria showed a positive association when the outcome of biochemical recurrence was considered.Other authors have also identified the pathology graduation as a predictor of biochemical recurrence 16 .In a recent study, the rate of biochemical recurrence in 1,754 men who underwent radical prostatectomy and concluded that ISUP score was assessed as the most important predictor for biochemical recurrence in high-risk patients 15 .Our data are in agreement with the literature in this topic.
The total PSA value was confirmed as an independent predictor of biochemical recurrence, both in the univariate analysis and in multiple logistic regression, which is widely supported by the literature [17][18][19] .The classic density of PSA also showed a statistically significant correlation and this is in agreement with what we found in our literature review 17,18 .In a series of 784 patients undergoing robotic radical prostatectomy, it was identified that the density of PSA is an independent predictor of biochemical recurrence in patients undergoing treatment with a curative purpose 20 .
We analyzed the potential correlation of the prostate weight provided by the pathology examination and did not find any significant association.When we considered the prostate volume measured by preoperative ultrassonograpy and tried to correlate it with the outcome of biochemical recurrence, we did not find any statistically significant values.In contrast, other authors have already demonstrated the association between biochemical recurrence and prostate volume 19 .Evaluating 5,637 patients who underwent radical prostatectomy, a the authors concluded that intermediate-risk patients with lower-volume prostates are more likely to develop biochemical recurrence, which indicates that the relationship between volume and biochemical recurrence may be more complex than it is thought 21 .
In the present work, we set out to test the capacity of a new predictor of biochemical recurrence which is the PSA Density of the lesion.Other authors had already tried to use derivations of the PSA density.
However, we did not find studies that used the same criteria of our study to predict biochemical recurrence 22 .

Figure 1 .
Figure 1.Illustration of the prostate models.The larger ellipse represents the entire prostate and the smaller ellipse represents the neoplastic lesion.The blue tone estimates the increase of produced PSA (the lighter, the lower the PSA production) by the fabric in question.A) Small lesion with high DNL.B) Larger lesion with low DNL.C) Lesion with very low DNL.
(considered high, predictor of aggressiveness) and DNL of 0.46 (new parameter, considered low, with a possible predictor of little aggressiveness).The patient in question did not present biochemical recurrence.It is a patient model that presents a potential little aggressive lesion that could induce the production of a small amount of PSA per gram of lesion.Therefore, this is a profile of a patient with less chance of biochemical recurrence, susceptible to being treated with unnecessarily adjuvant therapy, based on currently available predictors (Figure 1B).

Example 3 :
patient with total PSA of 3.1ng/ dL, prostate with a volume of 40cm 3 , prostate weight of 40g, 10% of the prostate volume occupied by the neoplasia, classic PSA density of 0.07 (considered low, predictor of low aggressiveness) and DNL of 1.32 (new parameter, considered high, bearing a possible predictor of aggressiveness).The patient in question evolved with biochemical recurrence.This is a patient model with a likely aggressive injury that could cause little or no increase in PSA levels per gram of injury.Therefore, this is a profile of a patient with a greater possibility of biochemical recurrence, susceptible to being neglected by current predictors (Figure1C).
68 patients.The collected data were initially plotted on a spreadsheet using the Microsoft Excel software (2013) and later analyzed with the aid of the SPSS software (23.0).The characterization of the patient's profile was performed by absolute (n) and relative (%) frequency for categorical variables.Mean, standard deviation, median, minimum, maximum and interquartile range for continuous variables were considered.In this study, the normality was tested by the Shapiro-Wilk test.The comparison of the postoperative outcomes with categorical exploratory variables was performed using the Pearson chi-square and Post hoc chi-square test.The agreement between ISUP in surgical specimen and ISUP in biopsies was made using the Kappa test (data no shown).

Figure 2 .
Figure 2. Comparison ISUP score between biopsy and surgical specimens in patients with or without biochemical recurrence.*Mann-Whitney test.

Table 1 .
Characterization of continuous exploratory variables.

Table 2 .
Characterization of categorical exploratory variables.
JunqueiraPSA density of the lesion: a mathematical formula that uses clinical and pathological data to predict biochemical recurrence in prostate cancer patients The presented results reveal that the proposed new parameter has a statistically significant correlation with the outcome, both in univariate analysis and in multiple logistic regression.The clinical applicability

Table 3 .
Result of biochemical recurrence comparison with continuous exploratory variables.

Table 4 .
Result of multiple logistic regression models using the Backward-LR method.