AUA 2008 POSTER 1877, Orlando, FL, May 21 2008
lnPSA slope
Luigi Benecchi, Anna Maria Pieri, Michele Potenzoni, Andrea Prati, Roberto Arnaudi, Carmelo Destro Pastizzaro, Antonio Savino, Nicoletta Uliano, Domenico Potenzoni
Department of Urology, Fidenza Hospital, Parma, Italy
www.urologiaparma.com
urologiaparma@libero.it
ABSTRACT
OBJECTIVES To compare different tools for evaluate prostatespecific antigen (PSA) kinetics before prostate
biopsy, such as PSA velocity, PSA slope, natural logarithm PSA slope (lnPSA slope), and PSA
doubling time (PSADT).
METHODS This study was conducted involving 325 male patients evaluated with transrectal ultrasoundguided
biopsy of prostate. Patients with at least three consecutive PSA measurements taken in
at least 24 months entered in the study. We estimated PSA slope from the slope of the least
squares regression line fit to PSA versus time in years; PSA velocity was calculated as the running
average of the rate of change during at least three consecutive assays. The acceleration of PSA
(lnPSA slope) was calculated as the slope of lnPSA versus time, where ln is the natural
logarithm. PSADT was calculated using the formula: PSADT _ ln 2/(lnPSA slope).
RESULTS We found a total of 74 cancers at the ultrasound guided prostate biopsies. At the receiver
operating characteristic (ROC) analysis, lnPSA slope (area under the curve [AUC], 0.793)
evidenced better results than PSA (AUC, 0.585; P _0.001), PSA velocity (AUC, 0.734;
P _0.009), PSA slope (AUC, 0.752; P _0.043), and PSADT (AUC, 0.516; P _0.001).
CONCLUSIONS The results for PSA, PSA velocity, PSA slope, and lnPSA slope were significantly higher in
patients with prostate cancer than in controls. The results of the present study suggest that
lnPSA slope may be useful for prostate cancer diagnosis. At the ROC analyses, the lnPSA slope
AUC was better than that of PSA, PSA velocity, PSA slope, and PSADT.
INTRODUCTION
The aim of our study is to compare different tools for evaluate PSA kinetics before prostate biopsy such as PSA velocity, PSA slope, natural logarithm PSA slope (lnPSA slope) and PSA doubling time.
MATERIALS AND METHODS
Between January 2001 to June 2006, all men who underwent transrectal ultrasoundguided prostate biopsy with 6 or more cores and with at least 3 consecutive PSA measurements (done in our centralized laboratory) in 731 or more days before biopsy entered the study.
All patients were scheduled for transrectal sonography with biopsy because of abnormal digital examination findings and/or PSA levels of 4 micro/L or greater. 325 men entered the study.
For PSA velocity calculation only PSA measurements with a time interval from the previous more than 6 month were considered. We included in our study all PSA measurements if they were assayed in our centralized laboratory with the indicated technique.
PSA velocity was calculated as the increase of PSA per year from the first to the last PSA assay before prostate biopsy.
The PSA slope was calculated with the least square fit (PSA versus time) using an electronic sheet, so the line slope value and the intercept value was obtained for each patient. Specifically, we fit the equation: y=a+bx to the data of each patient, where "y" represents PSA and "a" the intercept. Parameter "b" is the slope and reflects the increase of PSA in one year ^{11}.
The "acceleration" of PSA (lnPSA slope) was calculated as the slope of lnPSA versus time, where ln is the natural logarithm.
PSADT was calculated using the formula: PSADT=ln 2 ⁄(lnPSA slope) ^{12}. Mann Wintney U test was used to assess the differences PSA between different groups (Statistica 6.0). The receiver operating characteristic (ROC) curve was generated by plotting sensitivity versus 1specificity (MedCalc 7.0). We compared results by comparing the areas under the receiver operating characteristics curve (AUC) according to Hanley and McNeil ^{13}. Stepwise logistic regression analyze was used to assess continuous variables (age, PSA, percent free PSA, PSA density, PSA velocity, lnPSA slope and PSA doubling time).
RESULTS
A total of 74 cancers were found at the ultrasound guided prostate biopsies.
PSA, PSA velocity, PSA slope, lnPSA slope were significantly higher in patients with prostate cancer than in controls. To confirm the validity of our date, in the table it is reported the significant difference also for free to total PSA, PSA density, and PSA transition zone density too.
No significant differences were found for PSA intercept, number of PSA assays and the time interval between the first and last PSA.
At the ROC analysis lnPSA slope (AUC 0.793; 95% confidence interval 0.745 to 0.836) evidenced better results than PSA (AUC 0.585; 95% confidence interval 0.530 to 0.639; p<0.001), PSA velocity (AUC 0.734; 95% confidence interval 0.683 to 0.782; p<0.009), PSA slope (AUC 0.752; 95% confidence interval 0.701 to 0.798; p<0.043) and PSADT (AUC 0.516; 95% confidence interval 0.460 to 0.571; p<0.001) (table 2).
At lnPSA slope equal to zero, the sensitivity resulted as being 95.9% with a specificity of 35.1%, a positive likelihood ratio of 1.48 and a negative likelihood ratio of 0.12. At lnPSA slope equal to 0.41 the sensitivity resulted as being 90,3% with a specificity of 50,2%.
Of the 325 patients reviewed 275 presented all clinical data (age, PSA, percent free PSA, PSA density, lnPSA slope) for multivariate logistic regression. At the multivariate logistic regression only percent free PSA (0dd Ratio 0.905) and lnPSA slope PSA (0dd Ratio 173.48) showed a statistical significance.
COMMENT
In the current study we compared different methods for evaluate PSA kinetics before prostate biopsy. Specifically PSA velocity, PSA slope and lnPSA slope were higher in patients with prostate cancer than in controls. It is interesting to note that PSADT didn't show any difference between prostate cancer patients and controls. PSADT as PSA velocity, PSA slope and lnPSA slope were analyzed as continuos variables (i.e., they could take on negative or positive values). In fact in our analyze even in men with PSA decreasing, the PSADT was easily calculated with the logarithm transformation of PSA. In previous article there was reported that PSA doubling time and log slope PSA are equivalent ^{17}, we think that PSA doubling time is related with lnPSA slope (PSADT=ln2/lnPSAslope) but they are mathematically different. PSADT correlate with tumor progression, therapeutic outcome and cancer specific mortality ^{17, 18} but in our patients showed no value as diagnostic tool for prostate cancer. In contrast with theoretically supposed advantages for screening program ^{19, 20}. PSADT is so dependent upon the baseline PSA measurement that it only works when men start out at the same baseline (such as an undetectable PSA after surgery) and doesn't work well to compare subsequent PSA rises between men starting at all different PSA levels. Recently Stephen et coll reported that PSADT was of limited utility in selecting patients for a prostate biopsy ^{21.}
For a clinical utilization of lnPSA slope it is better to use 3 or more PSA values in a period of 2 or more years. In case that the time interval is less than 2 years it is better to use the PSA slope ^{11}.
LnPSA slope permits evaluation of the "acceleration" of PSA in men with prostate cancer, in fact indicate the value of its exponential growth ^{23}.
D'Amico evaluated PSA velocity within one year before prostate cancer diagnosis in 1095 men who underwent radical prostatectomy ^{9}. D'Amico used linear regression analysis to calculate the PSA velocity, so the term PSA velocity in his work should be considered as PSA slope. Instead lnPSA slope needs more time than PSA velocity or PSA slope to evidence a pathological variation.
The major limitation of lnPSA slope is the availability of 3 or more PSA values made with the same laboratory technique in 2 or more years.
The ideal threshold for a cancer marker is at 95% of sensitivity, that for lnPSA slope corresponds to zero, but the slowgrowing and indolent nature of prostate cancer, coupled with the fact that a man will be tested again and again in his lifetime, makes a false negative test of less importance. So we promote to limit the sensitivity at 90% that corresponds to an interesting specificity of 50%. In another words, above 0.041 lnPSA slope every 2 prostate biopsies, 1 will result positive.
The potential limitations of this study must be considered. The time from first to last PSA and the number of PSA assays are different in controls than in patients (p=0.038), this because with prostate cancer diagnosis the longitudinal evaluation ends, but in controls this continues without interruption. Another limitation of our paper is the cutoff of 4.0 ng/ml of PSA used as threshold for biopsy according to our strategy at that time. We are aware that the current conventional strategy for biopsy is to reduce PSA threshold ^{2}, so we promote prospective study to confirm our analysis.
CONCLUSIONS
This is the first work about the use of natural logarithm PSA slope in prostate cancer diagnosis. PSA, PSA velocity PSA slope, lnPSA slope were significantly higher in patients with prostate cancer than in controls. The results of the present study suggest that lnPSA slope may be useful for prostate cancer diagnosis, instead PSA doubling time showed no diagnostic usefulness. At the ROC analyses the lnPSA slope AUC is better than that of PSA, PSA velocity, PSA slope, and PSA doubling time.
REFERENCES
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All 
Prostate cancers 
Controls 
P value 

N° 
Median (range) 
N° 
Median (range) 
N° 
Median (range) 

Age (yr) 
325 
65.6 (45.2  83) 
74 
64.34 (50.6  82.4) 
251 
65.8 (45.2  83) 
0.49 
PSA (ng/ml) 
325 
7.11 (0.8  52.7) 
74 
8.1 (2.12  52.7) 
251 
6.81 (0.8  35.2) 
0.025 * 
free tototal PSA (%) 
287 
17.41 (3.23  65) 
64 
11.96 (4.26  35.76) 
223 
18.4 (3.23  65) 
0.0000000012* 
Days between first and last assays 
325 
1321 (739  4581) 
74 
1245 (739  3723) 
251 
1343 (740  4581) 
0.038 
numbers of PSA assays for patient 
325 
5 (3  28) 
74 
5 (3  12) 
251 
6 (3  28) 
0.0014 
PSA velocity (ng/ml/yr) 
325 
0.392 (3.72  19.17) 
74 
0.776 (0.61  19.17) 
251 
0.189 (3.7  5.9) 
0.0000000008 * 
PSA slope (last square fit) (ng/ml/yr) 
325 
0.404 (3.28  18.07) 
74 
0.849 (0.53  18.07) 
251 
0.24 (3.2  5.8) 
0.00000000004* 
PSA intercept 
325 
5.58 (294.2  209.9) 
74 
4.096 (279  12.86) 
251 
5.9 (294  209) 
0.000022 
LnPSA slope 
325 
0.068 (0.61  0.996) 
74 
0.162 (0.074  0.99) 
251 
0.04 (0.6  0.74) 
0.00000000000002 
LnPSA intercept 
325 
639 (149  1758) 
74 
541 (149  1018) 
251 
658 (109  1758) 
0.0000853 
PSADT (yr) 
325 
4.1 (367  1758) 
74 
3.9 (59  549) 
251 
4.1 (367  1076) 
0.678 
Prostate volume (cm3) 
265 
50.8 (10  151) 
57 
35 (10  130) 
208 
53.2 (15  151) 
0.000000046 * 
PSA density(ng/ml/cc) 
265 
0.148 (0.03  1.01) 
57 
0.208 (0.055  1.01) 
208 
0.137 (0.03  0.62) 
0.0000002401* 
Transition zone volume (cm3) 
179 
33 (4120) 
41 
15.6 (5  74) 
138 
35.2 (4  120) 
0.000000595* 
PSA trasition zone density(ng/ml/cc) 
179 
0.243 (0.052  2) 
41 
0.466 (0.085  2) 
138 
0.22 (0.052  1.3) 
0.0000049 * 
Table 1) Descriptive statistics of 325 men. The last column reports p value of differences between controls and prostate cancers (Mann Wintney U test), * p<0,05.
AUC 
Std 
95% Confidence interval 

PSA 
0.585 
0.039 
0.530 to 0.639 
Free to Total PSA 
0.749 
0.031 
0.695 to 0.798 
PSA density 
0,723 
0,041 
0.665 to 0.776 
PSA trasition zone density 
0,735 
0.048 
0.664 to 0.798 
PSA velocity 
0.734 
0.036 
0.683 to 0.782 
PSA slope 
0.752 
0.035 
0.701 to 0.798 
LnPSA slope 
0.793 
0.033 
0.745 to 0.836 
PSADT 
0.516 
0.038 
0.460 to 0.571 
Table 2) ROC analyses
Example L.G 11/1/1936 T2aN0M0G7(4+3)