PROSTATE-SPECIFIC ANTIGEN (PSA) is a sensitive

Prostate-Specific Antigen Doubling Times Are Similar in Patients With Recurrence After Radical Prostatectomy or Radiotherapy: A Novel Analysis By Bryan D. Leibman, Ozdal Dillioglugil, Peter T. Scardino, Farhat Abbas, Eamonn Rogers, Russell D. Wolfinger, and Michael W. Kattan Purpose: Some investigators have analyzed the rate of growth of prostate cancer that has recurred after definitive radiotherapy or radical prostatectomy using serum prostate-specific antigen (PSA) doubling times (DT). We examined all PSA values in recurrent patients to determine the pattern and rate of increase in PSA after radiation therapy and radical prostatectomy. Patients and Methods: Charts of 9 recurrent radical prostatectomy patients (mean age, 2.8 years; range, 47 to 7) and 42 recurrent radiation therapy patients (mean age, 7.2 years; range, 52 to 83) were reviewed. All available PSA values between the date of operation/radiation treatment and last follow-up evaluation or the initiation of second-line therapy are included. Rate of PSA DT was not assumed to be constant over time; it was instead allowed to vary. We use a piecewise linear random-coefficients model in time for log(psa), which allowed different mean models for both treatments. Results: The PSA DT in the first year after radiation therapy was - 1.17 years, which reflects the continuous decline in PSA in the average patient during the first year after radiotherapy despite eventual biochemical progression. In contrast, the PSA DT in the radical prostatectomy group was 0. in the first year. In year 2, after radiation therapy, the PSA DT was lengthy at 1.82 years, significantly longer (P =.0025) than in the radical prostatectomy group (0.7 years). After year 2, there were no significant differences between the two groups (P >.05). Conclusion: A piecewise linear random-coefficients model enables interval analysis of PSA DT. While the PSA DT after radiation therapy and radical prostatectomy are different in the first 2 years, the rate of increase in PSA appears to be similar in the two groups after year 2, which suggests the rate of growth of cancers that recur after radiation therapy and radical prostatectomy is similar. J Clin Oncol 1:227-2271. 1998 by American Society of Clinical Oncology. PROSTATE-SPECIFIC ANTIGEN (PSA) is a sensitive marker of the response of prostate cancer to definitive therapy with either radical prostatectomy or radiation therapy. Stamey et all reported PSA levels correlate with tumor volume. PSA doubling times (DTs) should therefore estimate tumor doubling times. Previous studies have examined PSA DT after radical prostatectomy 2, 3 and radiation therapy. 4-7 They found a strong association between PSA DT and pretreatment PSA level, biopsy Gleason sum, and ploidy status. 5 Also, faster DTs have been associated with aggressive tumor biology 7 and have assisted in predicting distant versus local recurrence. 2 PSA DT can thus be used to predict site of recurrence and to estimate tumor volume, and has been shown to be a strong prognostic factor for patients with biochemical evidence of progression after radiotherapy or radical prostatectomy. 2 On the other hand, an isolated PSA elevation doeý not help to distinguish local recurrence, which might benefit from irradiation to the prostatic bed, from distant metastasis that needs hormonal therapy. In this study, we compare PSA DTs for patients with recurrent disease after either radiation therapy or radical prostatectomy. Unlike previous studies, we do not assume PSA DT to be constant over time. We present a statistical model to analyze PSA DT at selected intervals, allowing variation in the event that the DT is not constant. PATIENTS AND METHODS All patients with clinically localized prostate cancer (ct1-3nxmo) initially seen in consultation in the Department of Urology who were treated with intent to cure with either definitive radiation therapy or radical prostatectomy at our hospital between June 1983 and August 1994, and who were subsequently monitored in our Urology Department (radiation therapy, n = 9; radical prostatectomy, n = 1,17), were reviewed to identify those with evidence of progression after treatment. Clinical stage distribution according to the 1992 tumor-nodemetastasis (TNM) classification system 8 for the 1,23 men in this study was as follows: Tla, 4%; Tlb, %; Tlc, 12%; T2a, 21%; T2b, 27%; T2c, 23%; T3a, %; T3b, 0.1%; and T3c, 1%. From the Matsunaga-Conte Prostate Cancer Research Center, Scott Department of Urology, and Information Technology Program, Baylor College ofmedicine, Houston, TX; and SAS Institute, Inc, Cary, NC. Submitted September 25, 1997; accepted March 1, 1998. Supported in part by Specialized Program of Research Excellence (SPORE) grant no. CA58204 from the National Cancer Institute, Bethesda, MD. Address reprint requests to Michael W. Kattan, PhD, Scott Department of Urology, Baylor College of Medicine, 535 Fannin St, F 403, Houston, TX 77030; Email mkattan@bcm.tmc.edu. 1998 by American Society of Clinical Oncology. 0732-183X/98/10-0033$3.00/0 Journal of Clinical Oncology, Vol 1, No (June), 1998: pp 227-2271 227

228 LEIBMAN ET AL Table 1. Distribution of Clinical Stage by Treatment Group: Radical Prostatectomy Versus Radiation Therapy Clinical Radical Prostatectomy Group Radiation Therapy Group Stage No. % No. % Tla 1 1 0 0 Tlb 3 3 4 10 Tic 3 3 0 0 T2a 15 1 2 5 T2b 43 45 15 12 T2c 18 19 14 T3a 11 11 13 31 T3b 0 0 2 5 T3c 1 1 10 24 NOTE. Radiation therapy patients had a higher clinical stage at presentation. Sixty percent of the radiation therapy patients had a T3 tumor v 12% in the radical prostatectomy group. Wilcoxon rank-sum, P <.001. There were 42 patients with disease progression by PSA parameter after either external-beam irradiation therapy alone (n = 34) or brachytherapy (interstitial radioactive gold-198 seed implantation) plus externalbeam therapy (n = 8).9 Treatment was directed to the prostate only, except in patients with proven pelvic lymph node metastases. There were 9 patients who progressed according to PSA after radical retropubic or radical perineal prostatectomy. Pretreatment clinical stage (International Union Against Cancer [UICC] criteria), PSA, and biopsy Gleason sum are listed in Tables 1, 2, and 3. The Wilcoxon rank-sum test was used to compare these parameters across treatments. Clinical stage was prospectively recorded according to the TNM classification system, although men treated before 1992 were retrospectively reassigned from the equivalent Whitmore-Jewett stages. 15 The mean follow-up duration for radical prostatectomy patients was 33. months (range, 47 to 7), and for radiation therapy patients, 49.4 months (range, 5 to 139). Serum PSA level was determined by the Hybritech assay (Hybritech Tandem-R; Hybritech, San Diego, CA). After radical prostatectomy, progression according to PSA was defined as a PSA measurement > 0.4 ng/ml and increasing on at least one subsequent measurement. For radiation therapy, progression according to PSA was defined as a PSA measurement > 1 ng/ml and increasing after a nadir was achieved. All patients in this study had an elevated PSA value as the first evidence of recurrence. All available PSA values between the date of treatment and last follow-up evaluation Table 2. Distribution of Preoperative Biopsy Gleason Sum by Treatment Group: Radical Prostatectomy Versus Radiation Therapy Biopsy Radical Prostatectomy Group Radiation Therapy Group Gleason Sum No. % No. % 2-4 5 5 15 5-40 42 19 4 7 40 42 10 24 8-10 10 11 15 Total 95 100 41 100 Wilcoxon rank-sum P =.43 Mean.3.0 Median 7.0.0 Range 2-9 2-8 NOTE. Both treatment groups were similar in terms of biopsy Gleason sum. Table 3. Distribution of Preoperative PSA by Treatment Group: Radical Prostatectomy Versus Radiation Therapy Preoperative Radical Prostatectomy Group Radiation Therapy Group PSA (ng/ml) No. % No. % >0-4 2 2 2 8 > 4-s 10 31 39 11 42 > 10-5 20 19 24 5 19 > 20-5 50 24 30 7 27 > 50 4 5 1 4 Total 80 100 2 100 Wilcoxon rank-sum P =.80 Mean 18.3 17.8 Median 15. 9.5 Range 1.8-88.3 1.7-84 NOTE. Both treatment groups were similar in terms of preoperative PSA. or the initiation of second-line therapy were included. Eighty-five percent of patients in the radical prostatectomy group and 90% of those in the radiation therapy group had at least four posttreatment PSA measurements, while 4% and 1%, respectively, had at least seven measurements (Table 4). Rate of PSA DT was not assumed to be constant during the follow-up period after definitive therapy. Instead, it was allowed to vary over time and was analyzed at yearly intervals. We are using a piecewise linear random coefficients model in time for log(psa), allowing different mean models for the two treatments. The log transformation is used because of the scale of the measurements and because a likelihoodbased comparison of several transformations in the Box-Cox family indicated log as the best. Because the measurements are unequally spaced and from a preliminary graphical analysis of the data, the join points for the piecewise linear mean model are selected to be at 1, 2, 3, and 7 years. The transformed data for each patient are assumed to follow a Gaussian distribution with a mean following the aforementioned piecewise linear form and variance-covariance matrix derived as follows. Each patient is assumed to possess a random intercept, a random slope for 0 to 1 years, and a random slope for 1 to 2 years, in addition to the standard residual error. The three random coefficients are added to the mean model and are assumed to have a Gaussian distribution with mean zero and an unstructured covariance matrix. The additive residual error is also assumed to have a Gaussian distribution with mean zero and unknown variance, and is independent of the random coefficients. Each patient is assumed to follow the same model Table 4. Distribution of the Total Number of PSA Measurements After Radical Prostatectomy and Radiation Therapy No. of PSA Radical Prostatectomy Radiation Therapy Measurements No. % No. % 2-3 14 15 4 10 4-38 39 12 28 7-10 22 23 17 40 11-15 19 20 14 >15 3 3 3 7 NOTE. Eighty-five percent of patients in the radical prostatectomy group and 90% of patients in the radiation therapy group had at least 4 posttreatment PSA measurements.

PSA DOUBLING TIMES (but with different realizations of the random variables), and data from different patients are assumed to be independent." The random coefficients model provides an appealing way to handle within-subject correlations. Our particular model was selected as best among models that have zero, one, two or more than three random coefficients, using restricted likelihood versions of Akaike's and Schwarz's criteria as guides." It also fits much better than an unequally spaced First-Order Autoregressive (AR[1]) model and the model that adds an unequally spaced AR(1) covariance matrix to the one generated by the random coefficients,12 both according to the same criteria. RESULTS Radiation therapy patients had higher clinical stage at presentation compared with radical prostatectomy patients (P =.001). Sixty percent of the radiation therapy group had a T3 tumor, compared with 12% in the radical prostatectomy group. Eighty percent of the radical prostatectomy patients were clinical stage T2, compared with 31% of the radiation therapy patients (Table 2). Distribution of pretreatment biopsy Gleason sum was similar in the two groups (P =.43). Mean Gleason sum in the radical prostatectomy patients was.3 and in the radiation therapy patients,.0. Median Gleason sum was 7 and, respectively (Table 3). Pretreatment PSA distribution was also similar between the two groups (P =.80) (Table 4). In the first year after radiotherapy, the PSA DT was - 1.17 years. The negative value reflects the continuing decline in PSA in most patients during the first year after radiotherapy despite eventual biochemical progression. In contrast, the PSA DT was 0. in the first year after radical prostatectomy. In year 2, after radiotherapy, the PSA DT was long, at 1.82 years, which was significantly longer (P =.0025) than the PSA DT after radical prostatectomy (0.7 years). After year 2, there were no significant differences between the two groups (P >.05) (Table 5 and Fig 1). DISCUSSION PSA is an antigen first described by Wang et al.13 It is a glycoprotein with serine protease activity, found in the cytoplasm in both benign and malignant prostate cells. PSA represents the best serum marker for prostatic carcinoma, 229 and it has the highest validity of any circulating marker for cancer today. 14 PSA is extremely useful to monitor patients for recurrence after definitive therapy for prostate cancer. Increasing serum PSA levels precede clinical recurrence detected by traditional tests such as digital rectal examination (DRE), bone scan, or other radiologic studies by 3 to years. 15 PSA progression, or biochemical failure, is therefore the most rapid means to assess results of contemporary treatment. PSA levels have been shown to correlate with tumor volume.' Schmid et a1' demonstrated a linear relationship between serum PSA levels and cancer volume. On average, one gram of cancer was shown to produce an increase in PSA of 3.5 ng/ml. The investigators therefore proposed that serial PSA determinations in the absence of any therapy should reflect the DT of the prostate cancer. They also showed that the increase in PSA in untreated patients was exponential and the DTs occurred more rapidly with higher disease stage and grade. It is not clear when to initiate additional treatment for patients with evidence of biochemical failure after radical prostatectomy or radiation therapy. Numerous factors are usually considered in this decision-making process; these include histologic grade, pathologic stage, pretreatment PSA level, time from treatment, clinical symptoms, physical findings, and radiologic abnormalities. Several studies have also touted the benefit of PSA DT in aiding in this process. 2-7 For patients with recurrent disease after radiation therapy, a short PSA DT has been shown to be associated with poorly differentiated cancers, nondiploid DNA profile, and an increased chance of distant metastasis. Zagars and Pollock 5 also noted that a faster PSA DT in radiorecurrent patients correlated significantly with high pretreatment Gleason sum and PSA level. D'Amico and Hanks 7 found a short DT correlated with the interval to clinical relapse, which suggested the potential usefulness of PSA DT to identify patients who might benefit from early second-line treatment. Pollack et al, in a linear regression analysis of PSA DT and disease relapse after radiotherapy, found a significant corre- Table 5. PSA DT by Treatment Group Year 0-1 1-2 2-3 3-7 Group PSA DT 95% CI PSA DT 95% CI PSA DT 95% CI PSA DT 95% CI Radical prostatectomy 0..89-.53.7 1.1-.3.58.77-0.47.51.1-.43 Radiation therapy -1.17 (-).93-(-)4.95 1.82 oo-.9.7 1.07-.49.2.82-.05 P.0001.0025.2531.879 NOTE. In the year immediately following radiation therapy, PSA DT was negative due to the PSA-lowering effect of radiation therapy. This resulted in a significant difference from the radical prostatectomy group. After year 2, there were no significant differences between the 2 groups. *Undefined.

2270 LEIBMAN ET AL L O G P S A 13 12 11 10 9 8 7-5- 4-3- 2-1 0- -1-2 - Fig 1. Piecewise linear randomcoefficients model in time for log(psa). -3 - -4 05 1 2 34 YEAR 7 -stimatea ppopulation curves are superinmposea. 8 9 10 11 12 lation, in which a PSA DT of 11 months predicted a disease relapse 24 months later. Their findings concur with others in suggesting that PSA DT is a strong prognostic factor for disease progression after definitive radiation therapy. After radical prostatectomy, serum PSA levels should become undetectable. For patients with biochemical evidence of failure after radical prostatectomy, important prognostic information can be gained from the relapse interval and PSA DT. With local recurrence, PSA first becomes detectable, on average, about 3 years later than with distant recurrence. 15 Most patients with an increasing PSA within the first year after surgery will manifest distant metastasis. Trapasso et a1 2 noted that the median PSA DT was 4.3 months for patients who progressed to distant metastasis, compared with 11.7 months for patients who had either clinical local recurrence or an isolated PSA elevation as sole indicator of recurrence. Stamey et al, 17 studied PSA DT in patients after radiation therapy and reported an accelerated growth rate in recurrent radiotherapy patients compared with untreated patients with prostate cancer; they suggested that this acceleration may result from tumor clonogen repopulation during radiotherapy. We examined PSA DT in recurrent patients after both radiation therapy and radical prostatectomy for comparison purposes. These two groups of patients are similar before definitive therapy when comparing biopsy Gleason sum and pretreatment PSA level. However, patients in the radiation therapy group had a higher pretreatment clinical stage. Our study analyzes PSA DT at yearly intervals and does not assume PSA DT to be constant over time. This represents a novel method to calculate PSA DT. We found PSA DT to be negative in the first year after radiation therapy in contrast to the radical prostatectomy group; this is consistent with the fact that radiation therapy is known and expected to produce declining PSA levels after treatment. Serum PSA declined and reached a nadir in the first year after radiation therapy, with a subsequent increase. PSA began to increase slowly in the radiation therapy group during the second year, but the rate was slower than that for the radical prostatectomy group in the second year (P <.05). After year 2, there were no significant differences in PSA DT for patients after radiation therapy or radical prostatectomy. This finding is consistent with data reported by Fowler et al,18 who compared PSA DT by linear regression analysis in recurrent patients after radical prostatectomy and radiation therapy. They found no significant differences between these groups, which suggests the malignant potentials of recurrent tumor after either of these therapeutic modalities are equivalent. Our results, like those of Fowler et al, differ from the earlier work reported by Stamey et al. 1 7 We believe Stamey's assumptions may be too strong. Patients who fail to respond to definitive local therapy cannot be presumed to have similar cancer characteristics as

PSA DOUBLING TIMES all patients initially diagnosed with prostate cancer. Also, they are clearly different than a group of patients with clinically organ confined prostate cancer who have elected or been selected to have no definitive treatment. Patients most commonly fail to respond to definitive therapy because they have occult metastases before treatment. When these patients fail to respond, their PSA DT will be similar to patients with known early metastatic disease. Other patients fail to respond because of local recurrence, and the more rapidly growing (poorly differentiated) cancers that recur will 2271 become apparent sooner. We know that PSA DT is shorter for patients with high-grade cancer.'" In patients monitored for the first years after definitive radiotherapy or radical prostatectomy, the detected recurrences will naturally have a PSA DT reflective of early metastatic prostate cancer or high-grade rapidly growing local tumor. Consequently, the shorter PSA DT in patients who fail to respond to radical prostatectomy or radiation therapy, when compared with untreated patients, is more likely to represent selection factors, rather than a changing biology of the tumor. 1. Stamey TA, Kabalin JN, McNeal JE, et al: Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate. II. Radical prostatectomy treated patients. J Urol 141:107-1083, 1989 2. Trapasso JG, dekemion JB, Smith RB, et al: The incidence and significance of detectable levels of serum prostate specific antigen after radical prostatectomy. J Urol 152:1821-1825, 1994 3. Partin AW, Pearson JD, Landis PK, et al: Evaluation of serum prostate specific antigen velocity after radical prostatectomy to distinguish local recurrence from distant metastases. Urology 43:49-59, 1994 4. Hanks GE, D'Amico A, Epstein BE, et al: Prostatic-specific antigen doubling times in patients with prostate cancer: A potentially useful reflection of tumor doubling time. Int J Radiat Oncol Biol Phys 27:125-127, 1993 5. Zagars GK, Pollack AP: Radiation therapy for T1 and T2 prostate cancer: Prostate-specific antigen and disease outcome. Urology 45:47-483, 1995. Pollack AP, Zagars GK, Kavadi VS: Prostate specific antigen doubling time and disease relapse after radiotherapy for prostate cancer. Cancer 74:70-78, 1994 7. D'Amico AV, Hanks GE: Linear regressive analysis using prostatespecific antigen doubling time for predicting tumor biology and clinical outcome in prostate cancer. Cancer 72:238-243, 1993 8. Beahrs OH, Henson DE, Hutter RV, et al (eds): Manual for Staging of Cancer. Philadelphia, PA, Lippincott, 1992 9. Butler EB, Scardino PT, The BS, et al: The Baylor College of REFERENCES Medicine experience with gold seed implantation. Semin Surg Oncol 13:40-418, 1997 10. Ohori M, Wheeler TM, Scardino PT: The new American Joint Committee on Cancer and International Union Against Cancer TNM classification of prostate cancer: Clinicopathologic correlations. Cancer 74:104-114, 1994 11. Littell RC, Milliken GA, Stroup WW, et al: SAS System for Mixed Models. Cary, NC, SAS Institute, 199 12. Diggle PJ, Liang KY, Zeger SL: Analysis of Longitudinal Data. Oxford, United Kingdom, Clarendon, 1994 13. Wang MC, Valenzuela LA, Murphy GP, et al: Purification of a human prostate specific antigen. Invest Urol 17:159-13, 1979 14. Gann PH, Hennekens CH, Stampfer MJ: A prospective evaluation of plasma prostate-specific antigen for detection of prostate cancer. JAMA 273:289-294, 1995 15. Frazier HA, Robertson JE, Humphrey PA, et al: Is prostate specific antigen of clinical importance in evaluating outcome after radical prostatectomy. J Urol 149:51-518, 1993 1. Schmid H, McNeal JE, Stamey TA: Observations on the doubling time of prostate cancer. Cancer 71:2031-2040, 1993 17. Stamey TA, Ferrari MK, Schmid H-P: The value of serial prostate specific antigen determinations 5 years after radiotherapy: Steeply increasing values characterize 80% of patients. J Urol 150:185-1859, 1993 18. Fowler JE, Pandey P, Braswell NT, et al: Prostate specific antigen progression rates after radical prostatectomy or radiation for localized prostate cancer. Surgery 11:302-30, 1994