The purpose of the current study was to evaluate modeling strategies using sextant core prostate biopsy specimen data that would best predict biochemical control in patients with localized prostate carcinoma treated with permanent prostate brachytherapy (PPB).
One thousand four hundred seventy–seven patients underwent PPB between 1992 and 2000. The authors restricted analysis to those patients who had sextant biopsies (n = 1073). A central pathology review was undertaken on all specimens. Treatment consisted of PPB with either I-125 or Pd-103 prescribed to 144 Gy or 140 Gy, respectively. Two hundred twenty–eight patients (21%) received PPB in combination with external radiotherapy and 333 patients (31%) received neoadjuvant hormones. In addition to clinical stage, biopsy Gleason sum, and pretreatment prostate specific antigen (pretx-PSA), the following detailed biopsy variables were considered: mean percentage of cancer in an involved core; maximum percentage of cancer; mean primary and secondary Gleason grades; maximum Gleason grade (primary or secondary); percentage of cancer in the apex, mid, and base; percent of cores positive; maximum primary and secondary Gleason grades in apex, mid, and base; maximum percent cancer in apex, mid, and base; maximum Gleason grade in apex, mid, and base; maximum primary Gleason grade; and maximum secondary Gleason grade. In all, 23 biopsy variables were considered. Four modeling strategies were compared. As a base model, the authors considered the pretx-PSA, clinical stage, and biopsy Gleason sum as predictors. For the second model, the authors added percent of cores positive. The third modeling strategy was to use stepwise variable selection to select only those variables (from the total pool of 26) that were statistically significant. The fourth strategy was to apply principal components analysis, which has theoretical advantages over the other strategies. Principal components analysis creates component scores that account for maximum variance in the predictors.
The median followup of the study cohort was 36 months (range, 6–92), and the Kattan modification of the American Society for Therapeutic Radiology and Oncology (ASTRO) definition was used to define PSA freedom from recurrence (PSA-FFR). The four models were compared in their ability to predict PSA-FFR as measured by the Somers D rank correlation coefficient. The Somers D rank correlation coefficients were then corrected for optimism with use of bootstrapping. The results for the four models were 0.32, 0.34, 0.37, and 0.39, respectively.
Several prognostic models to predict outcome in patients treated for prostate carcinoma have been developed which include risk stratification and nomograms.1–3 These models are almost all universally based on three important prognostic factors: pretreatment prostate specific antigen (PSA) value, Gleason grade, and clinical stage. Recently, it has been suggested that the addition of the percent of positive core specimens enhances the predictive ability of risk stratification.4 Nonetheless, most patient biopsy specimens contain a myriad of information, such as the individual Gleason grade, location of positive specimens, and either the measurement or the percentage of tumor in each positive specimen. The purpose of the current study was to address whether detailed pathologic data improve the predictive power over simpler models and to assess which modeling approach is best for doing so.
MATERIALS AND METHODS
Patient Selection and Pathology Data
One thousand four hundred seventy-seven consecutively treated patients with clinically localized prostate carcinoma underwent permanent prostate brachy therapy (PPB) at Memorial Sloan Kettering Cancer Center at Mercy Medical Center between June 1992 and June 1999 (Table 1). All patients had biopsy proven adenocarcinoma, and all patients were staged with history and physical examinations according to the 1997 American Joint Committee on Cancer standards.5 Only patients with sextant core biopsies were included in the current study. Central pathology review was performed on all specimens by R.P. or S.B., and all final reports included primary or secondary Gleason grade, percent of each core involved, and core location for each positive core specimen.
Table 1. Patient Characteristics
n = 1073 (%)
D90: minimum dose that covers 90% of the target (prostate) structure; NAAD: neoadjuvant androgen ablation; PSA: prostate specific antigen; XRT: external radiation therapy.
Addition of XRT
All patients underwent transrectal ultrasound (TRUS) to assess prostate size, and those with glands greater than 60cc received three to four months of hormone therapy to reduce prostate volume before undergoing an implant (n = 340). Treatment generally followed the standards suggested by the American Brachytherapy Society, whereby patients presenting with a PSA ≤ 10, Gleason sum 2–6, and clinical Stage T1-T2a were considered low risk and treated with brachytherapy alone.6 Patients with a PSA > 10, Gleason sum 7–10, or clinical Stage T2b were considered to have intermediate to high risk of prostate carcinoma and were generally offered a combination of external beam radiation therapy (EBRT) and PPB.
Implant Technique and Dosimetry
Preplanning for PPB was performed using the prostate dimensions as measured on TRUS. The required isotope activity to achieve the prescribed dose was determined from an isotope activity nomogram. The implant procedure has been previously described.2 In brief, with patients placed in an exaggerated dorsal lithotomy position, the implant was performed, the biplane ultrasound probe (B&K, Marlborough, MA) with needles placed using weighted peripheral loading and urethral sparing. Individual seeds were placed in the prostate with an interstitial gun applicator (Mick Nuclear, Bronx, NY). The prescribed dose for patients implanted with I-125 was 144 Gy (TG43) and 140 Gy (NIST-99) for Pd-103. Despite changes in dosing I-125 and Pd-103 based on the TG-43 and National Institute Standard of Technology (NIST) 99 standards throughout the study period, our prescribed dose was modified in order to maintain a clinically consistent delivered dose. When EBRT was added, the prescribed implant dose for I-125 was 110 Gy (TG43) and 105 Gy for Pd-103. The EBRT doses were 41.4 Gy to 45 Gy at 1.8 Gy per fraction.
Table 2. Evidence of Failure Information from the Entire Cohort
First evidence of failure
n = 1073
PSA: prostate specific antigen.
Death from disease
Median (maximum) months of followup for censored patients
Total number of PSA values obtained at followup
In addition to clinical stage, biopsy Gleason sum, and pretreatment-PSA, the following detailed biopsy variables were considered: mean percentage of cancer across all cores; maximum percentage of cancer in any core; mean primary Gleason grade across all cores; mean secondary Gleason grade across all cores; maximum Gleason grade (primary or secondary) in any core; percentage of cancer in the apex, mid, and base across all cores; percent of cores positive; maximum primary Gleason grade in apex, mid, and base in all cores; maximum secondary Gleason grade in apex, mid, and base cores; maximum percent cancer in apex, mid, and base cores; maximum Gleason grade in apex, mid, and base cores; maximum primary Gleason grade in any core; and maximum secondary Gleason grade in any core. In all, 23 biopsy variables were considered. Four modeling strategies were compared. As a base model, we considered the pretreatment-PSA, clinical stage, and biopsy Gleason sum as predictors (Model 1). For the second model, we added the percent of cores positive. The third modeling strategy was to use stepwise variable selection to select only those variables (from the total pool of 26) that were statistically significant.9 The fourth strategy was to apply principal components analysis.10 Principal components analysis creates component scores that account for maximum variance in the predictors regardless of their individual significance. We used as many principal components as possible while maintaining 10 events per model degree of freedom.10 This nomogram was evaluated using bootstrapping11 to obtain relatively unbiased estimates of expected future performance. This is a procedure whereby the data set is repeatedly sampled and the nomogram regenerated and tested. Although there are several measures of predictive accuracy, we chose to use Somers D rank correlation between predicted and observed failure times based on the arguments made by Harrell et al.12 In this measure, a correlation coefficient of 0 represents no discriminating ability and a value of 1 represents perfect discrimination. It can be converted to a concordance index by dividing by 2 and then adding 0.5.
The median followup based on our modification of the ASTRO consensus panel was 36 months (range, 4–91). The Kaplan-Meier five year freedom from biochemical recurrence was 82.1% (Fig. 1). The univariate prediction for each variable is presented in Table 3. The four models were compared in their ability to predict PSA-FFR as measured by the Somers D rank correlation coefficient. The Somers D rank correlation coefficients were then corrected for optimism with use of bootstrapping. The results for the four models were 0.32, 0.34, 0.37, and 0.39, respectively (Table 4). Model 4 used three principal components.
Table 3. Univariate Analysis for Each of the 26 Variables Examined
PSA: prostate specific antigen.
Mean percentage of cancer in an involved core
Maximum percentage of cancer
Mean primary Gleason grade
Mean secondary Gleason grade
Maximum primary Gleason grade
Percentage of cancer at the apex
Percentage of cancer at the midgland
Percentage of cancer at the base
Percentage of positive cores
Maximum primary Gleason at apex
Maximum primary Gleason at the midgland
Maximum primary Gleason at base
Maximum secondary Gleason at the apex
Maximum secondary Gleason at the midgland
Maximum secondary Gleason at the base
Maximum Gleason sum at the apex
Maximum Gleason sum at the midgland
Maximum Gleason sum at the base
Maximum percent in the apex
Maximum percent in the midgland
Maximum percent in the base
Maximum primary Gleason
Maximum secondary Gleason
Maximum Gleason sum
Table 4. Somers D rank Correlation Coefficients Corrected for Optimism with Use of Bootstrapping
PSA: prostate specific antigen.
Model 1 (PSA, Gleason, and stage)
Model 2 (Model 1 + % positive cores)
Model 3 (stepwise analysis)
Model 4 (principal components)
Use of nomograms that avoid discrete risk assignments have been identified as offering better predictive discrimination than use of traditional risk group assignments.1, 13, 14 Nonetheless, contemporary nomograms do not fully exploit the wealth of data provided in pathology reports. This current retrospective study found that the additional information contained in pathology reports predicts biochemical freedom from disease better than using just the original three factors as well as the addition of the percent of cores positive.
Further, the current study shows that principal components analysis was a better model than stepwise analysis.
Models using prognostic factors for predicting biochemical outcome in patients with localized prostate carcinoma have been developed.1–3, 13–16 Most of these models use various combinations of prognostic factors grouped by discrete values into stratification schemes. Almost all series use the pretreatment PSA value, Gleason sum, and clinical stage for the purposes of this predictive modeling. Recently, the addition of percent positive biopsy data appears to offer additional predictive power.4 Nevertheless, there are concerns about these schemes, as it appears they were generally constructed logically, using reasonable cut points for stage, grade, and PSA. Therefore, these models may not represent the optimal grouping for prognostic discrimination. Shipley et al. developed an empiric risk stratification scheme by analyzing the pretreatment variables and outcome results in a large multi-institutional cohort of patients treated with 3D conformal radiotherapy.16 It is not clear that the scheme reported by D'Amico et al.15 which adds the percent of positive core variable, though easier to remember, is as accurate as Shipley's. Furthermore, while the benefits of such stratification schemes to better identify patients who may be eligible for either more or less aggressive therapy are intuitive and easy to comprehend, they are nonetheless not the best models to use for this purpose.
Another approach at risk estimation is the use of prognostic nomograms that compute continuous probabilities of an outcome.1, 3, 14 Their advantage over the risk stratification prediction systems is likely associated with the use of continuous risk scales for relevant parameters, rather than condensing sections of the risk spectra into heterogeneous risk groups. Such nomograms have been developed for prostate carcinoma treated with radical prostatectomy, 3-dimensional radiation therapy, and brachytherapy. Due to improved accuracy, these nomograms may provide benefit for the purposes of patient counseling, where more accurate prediction should translate into better treatment decision making and reduced likelihood of treatment choice regret.17–19
One weakness associated with all these model schemes is based on the limits of available variables that can be incorporated. As has been shown by D'Amico et al., it appears that the percentage of positive core biopsies provides additional prognostic information beyond what is conveyed by the three standard predictor variables: pretreatment PSA value, Gleason sum, and clinical stage.4 Nonetheless, the pathology information is not limited only to these variables but includes additional data that may contribute to modeling. In the current study, we utilized comprehensive pathology data from each patient, increasing from 3 or 4 variables per patient to 26 predictor variables per patient. A comparison of the four tested modeling schemes identified that the principal components model, which incorporates comprehensive pathology data, predicts best.
Model 1, which uses the pretreatment PSA value, Gleason sum, and clinical stage, is identical in scope to the published brachytherapy nomogram. Model 2 adds a single additional variable, the percent of positive cores, which expands upon the risk stratification scheme of D'Amico's by using continuous variable values and which in fact does have an improved predictability as compared to Model 1.
Models 3 and 4 utilize the additional information supplied by each patient's pathology record. Stepwise analysis (Model 3) predicts better than the first two models, implying that more information may lead to improved accuracy of the nomogram. However, stepwise analysis is limited to only a subset of the predictors and produces variable coefficients, which are potentially biased. Even the data from an insignificant predictor can contribute to the nomogram construction. An example of this can be shown by assessing those insignificant factors in Table 3. Is the exclusion of the percentage of cancer in the base compared with the percentage of cancer at the midgland and apex more a reflection of the current data, or the disease itself? The advantage of principal components analysis is including all factors, ranked by significance into component groups, but not excluding those insignificant factors, as is done by the stepwise method. The fact that principal component analysis predicted best may be a reflection of this, and thus it should be used for future nomogram construction (Model 4).
Principal components analysis is a variable reduction procedure. A principal component can be defined as a linear combination of optimally weighted observed variables. The weights produced for each component score can be regarded as optimal because they account for as much variance from all the observed variables as possible. Conceptually, there are as many principal components as there are observed variables; however, based on the number of events in the current data set, we chose to consider the first three. These three, nonetheless, are the highest-ranking component groups in terms of variance explained. It may be helpful to think of a principal component variable as the prediction obtained from a linear regression equation using all the biopsy measures as predictor variables. Thus, in Model 4, we took all the biopsy variables, made three linear regressions from them, and used these linear regression predictors as new variables, replacing all the original biopsy measures. In the current study, the use of these three components produced the best model to predict biochemical freedom from disease in men treated with brachytherapy having prostate carcinoma. It is our intention to test this model by developing a validated nomogram for brachytherapy and other treatment methods.
One difficulty associated with nomogram use is that it is does not allow for intuitive or subjective responses without actually calculating the nomogram score. Nonetheless, nomograms can easily be constructed on paper that allows for such computations. Since the addition of each of the 26 variables improves upon the original nomogram, the addition of these variables would vastly complicate the nomogram on paper and is not easily accomplished. An alternative for using such a nomogram is via a database or palm-type application (e.g., www.nomograms.org) where the data is elementary and the result instantaneous.
One limitation of the current study was that we only included patients with sextant samples. It was our intention to initially explore which model best predicts outcome with an appropriate sample size. With standards changing to include 10 or 12 core biopsy specimens, additional modeling using the principal components analysis is needed to include patients with either more or fewer biopsy specimens. While this may create an additional level of complexity to the modeling, it will allow for additional data use that should add power to the predicting outcome model. Further, variability of the number of core specimens also seems to be best evaluated by principal components analysis, where many pieces of data can be evaluated without bias as to individual significance. Another limitation of the current study is the use of the Somers D rank correlation coefficient as a measure of discrimination ability. While it is appropriate for this type of data, it is difficult to interpret in a meaningful way other than as a range from 0 to 1, where 0 is useless and 1 is perfect. Another way to interpret this measure is to divide it by 2, then add 0.5. This yields an interpretation similar to an area under the receiver operator characteristic curve. It is the probability that, given two randomly selected patients, the patient who fails first has the higher predicted probability of failure.
In conclusion, the current analysis evaluated the addition of detailed pathology data to assess its value for predicting outcome following brachytherapy for localized prostate carcinoma. Not only did the addition of multiple pathology factors improve upon prognostic models that are already established, but the variable reduction approach via principal components analysis also produced the most accurate predictive model for biochemical freedom from recurrence. This novel approach can be incorporated into predictive nomograms for patients treated with radical prostatectomy or external beam, in addition to those treated with brachytherapy.