Evaluating Risk Factors Associating With Late Recurrence After Low‐Dose‐Rate Brachytherapy for Prostate Cancer Using Machine Learning

ABSTRACT

Background

The Phoenix definition is widely used to define biochemical recurrence (BCR) after radiation therapy for prostate cancer; however, a definitive definition of cure remains unclear. This study aimed to identify factors associated with late BCR after low‐dose‐rate brachytherapy (LDR‐BT), defined as BCR occurring ≥ 5 years after treatment among patients who remained recurrence‐free during the first 5 years, using machine‐learning methods.

Methods

We retrospectively analyzed 1419 patients who underwent LDR‐BT between 2004 and 2019. Of these, 52 (3.7%) experienced BCR within 5 years, and 244 patients did not have ≥ 5 years of follow‐up because of death or loss to follow‐up. The remaining 1123 patients were recurrence‐free at 5 years and formed the analysis cohort for late BCR (≥ 5 years). Random survival forest (RSF) and survival decision‐tree analyses were applied to identify predictive factors, and recurrence‐free survival was estimated using the Kaplan–Meier method.

Results

The 10‐year BCR‐free survival rate was 94.8%. RSF identified the 5‐year prostate‐specific antigen (PSA) value, PSA doubling time (PSA‐DT) at 5 years, primary Gleason pattern, and NCCN risk classification as the most important predictors. Optimal cutoff values were 0.93 ng/mL for PSA at 5 years and 5.3 years for PSA‐DT. Patients with lower PSA or longer PSA‐DT had significantly higher 10‐year recurrence‐free rates than those at higher risk (97.3% vs. 11.1% and 99.0% vs. 68.1%, respectively; p < 0.001).

Conclusions

PSA level and PSA‐DT at 5 years were strong predictors of late BCR after LDR‐BT. These findings suggest that follow‐up intervals may be safely extended for low‐risk patients, thereby reducing the burden of hospital visits and healthcare costs.

1. Introduction

Low‐dose‐rate brachytherapy (LDR‐BT) is established as a standard curative treatment for localized and locally advanced prostate cancer, alongside radical prostatectomy, and its excellent biochemical recurrence(BCR)‐free survival rates have been well documented [1, 2]. The Phoenix definition, which defines BCR as an increase of ≥ 2 ng/mL from the prostate‐specific antigen (PSA) nadir, is widely used as the standard criterion for recurrence after radiation therapy, including LDR‐BT [3]. Several reports have suggested that maintaining a low PSA level (< 0.1–0.5 ng/mL) at 3–5 years after LDR‐BT is associated with a reduced risk of late recurrence and may serve as a potential indicator of cure [4, 5, 6, 7, 8, 9, 10]. However, recent reports have also highlighted the occurrence of late BCR many years after LDR‐BT [11].

Although the definition of recurrence is well established, there is no consensus regarding what constitutes a cure following radiotherapy. Late recurrence can occur many years after treatment, leaving a substantial proportion of patients in an indeterminate state that is neither clearly cured nor recurrent. Consequently, these individuals require prolonged surveillance with periodic PSA assessments.

This issue is particularly burdensome for older adult patients, who must continue regular hospital visits long after completing therapy. Moreover, rising healthcare costs underscore the importance of establishing a robust definition of cure. If factors that predict late recurrence can be identified, follow‐up intensity could be tailored according to individual risks, thereby minimizing unnecessary hospital visits. Such an approach would alleviate the outpatient burden on patients and contribute to more sustainable healthcare resource allocation.

In this study, we applied machine‐learning methods to identify factors associated with late BCR after LDR‐BT for prostate cancer.

2. Materials and Methods

2.1. Patients

We included 1419 patients who underwent LDR‐BT for prostate cancer at our institution between August 2004 and November 2019. Of these, 52 patients (3.7%) experienced recurrence within 5 years after treatment. During the observation period, 138 patients died, including 12 from prostate cancer and 126 from other causes. Ultimately, 1123 patients remained BCR‐free for at least 5 years after treatment and were eligible for follow‐up beyond the 5‐year landmark. BCR was defined according to the Phoenix definition as a rise of ≥ 2 ng/mL above the post‐treatment PSA nadir.

2.2. Low‐Dose Rate Brachytherapy Treatment

In principle, patients with low‐risk disease and selected intermediate‐risk disease (Gleason Grade Group ≤ 2, clinical stage T1–2, and PSA ≤ 10 ng/mL) were treated with LDR‐BT alone without androgen deprivation therapy (ADT). Patients with other intermediate‐risk features or a large prostate volume (> 35 mL) received short‐term neoadjuvant ADT (3–4 months) before LDR‐BT. For high‐risk disease, treatment selection was based on disease characteristics. Patients with more aggressive features, including Gleason Grade Group 5 and PSA ≥ 20 ng/mL, were generally treated with combined LDR‐BT and external beam radiation therapy (EBRT), together with neoadjuvant ADT (approximately 4 months) followed by long‐term adjuvant ADT (2 years). Other high‐risk patients received short‐term neoadjuvant ADT (approximately 4 months) with concomitant ADT during EBRT, without long‐term adjuvant treatment. LDR‐BT was administered using a real‐time planning method. Preplanning was performed 3–6 weeks before treatment to determine the target volume. The prescribed dose for LDR‐BT alone was 160 Gy, whereas the prescribed dose was 110 Gy when combined with EBRT. The clinical target volume for LDR‐BT encompassed the entire prostate. For EBRT, the target volume was determined 1 month after seed implantation, and a total dose of 45 Gy (25 fractions; 1.8 Gy per fraction) was delivered using three‐dimensional conformal radiation therapy (January 2010–March 2014) or intensity‐modulated radiation therapy (after March 2014). Seed implantation was performed using the peripheral loading technique, and real‐time dynamic dose calculations were conducted with Variseed 8.0 (Varian Medical Systems, Palo Alto, CA, USA). Dosimetry analysis was performed 1 month after seed implantation.

2.3. Statistical Analyses

This study employed a 5‐year landmark design. Patients who experienced BCR within 5 years after treatment or who lacked at least 5 years of follow‐up were excluded. Subsequent analyses evaluated predictors of BCR occurring beyond the 5‐year landmark time point. To identify factors associated with late BCR after LDR‐BT, we developed a random survival forest (RSF)‐based prognostic model using R version 4.4.2 and used variable importance measures to identify key predictors. The RSF was implemented with the randomForestSRC package (version 3.4.5), growing 500 trees with a minimum terminal node size of 15. At each split, five variables (mtry = 5) were randomly selected from the 28 candidate predictors, and node splitting was performed using the log‐rank rule with 10 randomly sampled split points. Hyperparameters were optimized by minimizing the out‐of‐bag (OOB) prediction error, which is the standard validation approach for RSF.

The following variables were included in the analysis: PSA at diagnosis, total testosterone (TT) level prior to treatment, positive core rate at biopsy, total Gleason score (GS), primary and secondary Gleason patterns (GP), prostate volume (PV) at diagnosis, PSA density (PSAD), clinical T stage, the National Comprehensive Cancer Network (NCCN) risk classification, body mass index (BMI), presence of diabetes or hypertension, PV at preplanning, duration of neoadjuvant and adjuvant ADT, age at treatment, PSA and TT levels at treatment, number of needles inserted and seeds implanted during LDR‐BT, use of EBRT, dose parameters (D90 [%], V100, V150, and BED), PSA level at 4 and 5 years (4Y‐PSA, 5Y‐PSA), TT level at 5 years (5Y‐TT), and PSA doubling time (PSA‐DT) at 5 years. PSA‐DT at 5 years was calculated using the three most recent PSA measurements obtained after the 5‐year post‐treatment time point. To determine the cutoff values, the reciprocal of PSA‐DT (1/PSA‐DT) was analyzed as a continuous variable. Because PSA‐DT is not linearly distributed under these conditions, its reciprocal (1/PSA‐DT) was used to obtain a more linear relationship. However, all reported cutoff values and clinical interpretations are presented using the original PSA‐DT scale for ease of clinical application. Missing data for predictors and outcomes were handled using the built‐in missing data imputation procedure of the random survival forest algorithm.

Variable importance analysis was performed to evaluate the relative contribution of each predictor of late recurrence. Optimal cutoff values for each factor were identified using survival decision‐tree analysis. BCR‐free survival rates were estimated with Kaplan–Meier curves, and differences between groups were assessed using the log‐rank test. A two‐sided p value < 0.05 was considered statistically significant.

2.4. Ethics Statement

The study protocol was approved by the Ethics Committee of Nara Medical University (Approval No. 3867) and was conducted in accordance with the principles of the Declaration of Helsinki.

3. Results

3.1. Patients' Population

Of the 1419 patients, 52 (3.7%) experienced BCR within 5 years after treatment. The 5‐year and 10‐year BCR‐free rates for the full cohort were 96.0% and 91.1%, respectively (Figure 1).

Figure 1.

Biochemical recurrence (BCR)‐free survival after low‐dose‐rate brachytherapy (n = 1419). Among the 1419 patients, 52 (3.7%) experienced BCR within 5 years after treatment. The 5‐year and 10‐year BCR‐free rates were 96.0% and 91.1%, respectively.

During the observation period, 138 patients died, including 12 deaths due to prostate cancer and 126 deaths from other causes. Eventually, 1123 patients remained recurrence‐free for at least 5 years after treatment and were available for follow‐up beyond the 5‐year landmark.

Table 1 summarizes the clinical characteristics of the study cohort (n = 1123). The median age at LDR‐BT was 70 years (interquartile range (IQR): 65–74), and the median initial PSA level was 7.04 ng/mL (IQR: 5.26–10.34). According to the NCCN risk classification (version 4.2024), all patients were retrospectively categorized as very low‐risk (n = 28, 2.5%), low‐risk (n = 270, 24.0%), favorable intermediate‐risk (n = 309, 27.5%), unfavorable intermediate‐risk (n = 297, 26.4%), high‐risk (n = 191, 17.0%), or very high‐risk (n = 28, 2.5%). Overall, 671 patients (59.8%) received LDR‐BT alone, and 452 (40.2%) received additional external beam radiation therapy. Neoadjuvant ADT was administered to 457 patients (40.7%), adjuvant ADT alone to 4 patients (0.4%), and both neoadjuvant and adjuvant ADT to 95 patients (8.5%), as summarized in Table 1. The median follow‐up period was 108 months (IQR: 83–120). Among the 1123 patients who were recurrence‐free at 5 years (landmark cohort), the conditional 10‐year BCR‐free rate, measured from LDR‐BT, was 94.8% (Figure 2).

Table 1.

Clinical characteristics of the study cohort (n = 1123).

Variables		n = 1123
Age at diagnosis, median (IQR)		70 (65–74)
PSA at diagnosis, median (IQR) ng/mL		7.0 (5.3–10.3)
Clinical T stage	T1	475 (42.3%)
	T2	571 (50.8%)
	T3–4	77 (6.9%)
Gleason score	Grade group 1	383 (34.1%)
	Grade group 2	440 (39.2%)
	Grade group 3	147 (13.1%)
	Grade group 4–5	153 (13.6%)
Positive core rate at diagnosis, %		23.1 (10–37.5)
NCCN risk classification, %	Very low/low risk	298 (26.5%)
(NCCN guidelines version 4.2024)	Favorable intermediate risk	309 (27.5%)
	Unfavorable intermediate risk	297 (26.4%)
	High/very high risk	219 (19.5%)
Treatment	LDR‐BT as monotherapy	671 (59.8%)
	LDR‐BT + EBRT	452 (40.2%)
ADT	None	567 (50.5%)
	Neoadjuvant ADT	457 (40.7%)
	Adjuvant ADT	4 (0.4%)
	Neo ADT/adjuvant ADT	95 (8.5%)
Median prostate volume at preplan, median (IQR)		24.0 (19.0–29.6)
BED, median (IQR) Gy2		209.4 (192.0–220.3)

Abbreviations: ADT = androgen deprivation therapy, BED = biologically effective dose, EBRT = external beam radiation therapy, IQR = interquartile range, LDR‐BT = low‐dose‐rate brachytherapy, NCCN = National Comprehensive Cancer Network, PSA = prostate‐specific antigen.

Figure 2.

Biochemical recurrence (BCR)‐free survival after low‐dose‐rate brachytherapy during extended follow‐up (n = 1123). Among the 1123 patients, 48 (4.3%) experienced BCR during the extended follow‐up period. The 10‐year BCR‐free survival rate was 94.8%.

3.2. Factors for Late BCR

To identify the key factors related to late BCR, RSF models were constructed based on variable importance. Because only 48 late BCR events occurred among the 1123 patients when many predictors were included, we recognize that the model may be prone to overfitting, and the variable importance ranking should be interpreted as hypothesis‐generating rather than definitive. The RSF model demonstrated high apparent predictive performance, with a concordance index of 0.98 and an integrated Brier score of 0.06. However, given the limited number of late BCR events (n = 48) and the large number of candidate predictors, these metrics may overestimate performance and should be interpreted cautiously in the absence of external validation.

According to variable importance analysis, the most influential factors for late recurrence after LDR‐BT, in descending order of importance, were the 5‐year PSA value, PSA‐DT at 5 years, primary Gleason pattern, and NCCN risk classification (Figure 3).

Figure 3.

Key factors associated with late biochemical recurrence were identified using random survival forest models. Variable importance analysis showed that the most influential predictors of late recurrence after low‐dose‐rate brachytherapy, in decreasing order, were the 5‐year prostate‐specific antigen (PSA) level, PSA doubling time (PSA‐DT) at 5 years, primary Gleason pattern, and National Comprehensive Cancer Network (NCCN) risk classification. [Color figure can be viewed at wileyonlinelibrary.com]

Partial dependence plots illustrated the association of each factor with recurrence risk; higher 5‐year PSA and shorter PSA‐DT were consistently associated with increased recurrence risk (Figure 4A,B), while higher Gleason scores were also associated with greater risk (Figure 4C,D). In contrast, age at treatment and initial PSA (iPSA) level showed only weak associations with recurrence risk (Figure 4E,F).

Figure 4.

Partial dependence plots for late biochemical recurrence. (A) 5‐year prostate‐specific antigen (PSA) level, (B) PSA doubling time (PSA‐DT) at 5 years, (C) primary Gleason pattern, (D) total Gleason score, (E) age, and (F) initial PSA level. Higher 5‐year PSA and shorter PSA‐DT were consistently associated with increased recurrence risk, whereas higher primary Gleason patterns and total Gleason scores were also correlated with elevated risk. In contrast, age at treatment and initial PSA level demonstrated only weak associations with recurrence risk. [Color figure can be viewed at wileyonlinelibrary.com]

3.3. Cutoff Values for Factors

Survival decision‐tree analysis identified cutoff values of 0.93 ng/mL for the 5‐year PSA (Figure 5A) and 5.3 years for PSA‐DT at 5 years (Figure 5B).

Figure 5.

Optimal cutoff values for (A) 5‐year prostate‐specific antigen (PSA) level and (B) PSA doubling time (PSA‐DT) at 5 years determined by survival decision‐tree analysis. Survival decision‐tree analysis identified a cutoff of 0.93 ng/mL for 5‐year PSA level and 0.19 for the reciprocal PSA‐DT (1/PSA‐DT), corresponding to an optimal PSA‐DT cutoff of 5.3 years. [Color figure can be viewed at wileyonlinelibrary.com]

Patients with lower 5‐year PSA levels had significantly higher 10‐year BCR‐free rates than those with higher values (97.3% vs. 11.1%; p < 0.001) (Figure 6A), corresponding to substantially lower recurrence risk in the low‐PSA group. Similarly, patients with longer PSA‐DT had significantly lower recurrence rates than those with shorter PSA‐DT, with 10‐year BCR‐free rates of 99.0% versus 68.1% (p < 0.001) (Figure 6B).

Figure 6.

Comparison of biochemical recurrence (BCR)‐free survival after low‐dose‐rate brachytherapy (LDR‐BT) according to (A) 5‐year prostate‐specific antigen (PSA) levels and (B) PSA doubling time (PSA‐DT) at 5 years. Patients with lower 5‐year PSA levels had substantially lower recurrence rates than those with higher PSA levels, with 10‐year BCR‐free rates of 97.3% versus 11.1% (p < 0.001). Likewise, patients with a longer PSA‐DT had significantly lower recurrence rates than those with a shorter PSA‐DT, with corresponding 10‐year BCR‐free rates of 99.0% and 68.1%, respectively (p < 0.001). [Color figure can be viewed at wileyonlinelibrary.com]

4. Discussion

Several studies have reported that biochemical failure after radiation therapy for prostate cancer does not serve as a surrogate endpoint for overall survival [12, 13]. Conversely, other reports have demonstrated that the time to BCR correlates with prognosis [14] and that BCR is associated with distant metastasis and prostate cancer‐specific mortality [15]. In clinical practice, the presence or absence of BCR has therefore become the primary focus of post‐radiation follow‐up. A number of studies have identified risk factors for BCR after LDR‐BT, including higher clinical T stage, elevated iPSA, higher risk category, and lower local dose [16, 17, 18, 19, 20]. Among post‐treatment indicators, PSA remains the most reliable surrogate marker for BCR diagnosis, and PSA kinetics play a central role in disease monitoring [21]. Previous studies have proposed PSA cutoff levels of < 0.1 ng/mL [4], < 0.2 ng/mL [5, 6, 7, 8, 9], or < 0.5 ng/mL [10] at 3–5 years after LDR‐BT as potential definitions of “cure”. Furthermore, some reports have suggested that follow‐up may be discontinued in such patients [9].

An important consideration when interpreting our findings is whether the identified factors are truly specific predictors of late recurrence. In the overall cohort, BCR occurred throughout the follow‐up period rather than during a clearly distinct late phase. Therefore, the factors identified in this study may not represent biological mechanisms unique to late recurrence itself. Rather, they should be interpreted as predictors of subsequent recurrence among patients who had already remained recurrence‐free for 5 years after treatment. From a clinical perspective, however, this distinction is less important than the practical question faced by physicians and patients during long‐term follow‐up: which individuals who appear disease‐free at 5 years continue to harbor a meaningful risk of future recurrence? To address this question, we employed a 5‐year landmark design and specifically evaluated conditional recurrence risk beyond the 5‐year time point. Thus, our findings may provide clinically useful information for risk‐adapted surveillance, even if the underlying predictors overlap with those associated with recurrence in general.

To minimize the influence of benign PSA bounce phenomena [22, 23], we avoided evaluating PSA values within the first 3 years after treatment, when PSA bounces are most likely to occur. Accordingly, PSA values from the fourth year onward were selected as the earliest appropriate time point for analysis. We also examined PSA‐DT as a factor associated with late recurrence. The prognostic significance of PSA‐DT or PSA velocity has been reported predominantly in patients who experience BCR after radiation therapy [24, 25]. These indicators generally reflect disease progression in cases where PSA continues to rise over time. By contrast, in our cohort, PSA levels remained low or continued to decline even after 5 years post‐LDR‐BT, resulting in negative PSA‐DT values in more than half of the patients. When PSA levels continue to decline, PSA‐DT becomes negative. In this context, values close to zero (i.e., negative values with a small absolute magnitude) indicate a rapid PSA decrease and therefore reflect a more favorable trend, whereas more negative values (i.e., larger absolute magnitudes) represent a slower decline. Once PSA begins to rise, PSA‐DT becomes positive; large positive values indicate a slow increase, whereas values close to zero indicate a rapid PSA rise and thus correspond to the poorest prognosis. PSA‐DT remained informative even after transformation using 1/PSA‐DT, which better captured the gradient of PSA kinetics in our cohort. Although the reciprocal of PSA‐DT was used for model construction, clinicians can interpret the findings directly using PSA‐DT. Patients with PSA‐DT longer than 5.3 years had an extremely low risk of subsequent recurrence. These findings demonstrated that PSA kinetics remained important even before recurrence in the late phase after LDR‐BT.

In recent years, the number of studies utilizing artificial intelligence, particularly machine learning, has increased. We previously reported a predictive factor for early arteriovenous fistula failure in patients undergoing hemodialysis using machine‐learning techniques [26]. Similar approaches have been applied to predict BCR after radical prostatectomy. Sato et al. [27] developed a random survival forest model that outperformed conventional prognostic tools, whereas Zhang et al. [28] constructed interpretable models based on clinical data from robot‐assisted radical prostatectomy with good predictive accuracy. Likewise, several studies have applied machine‐learning and radiomics techniques to predict BCR after radiotherapy. Fernandes et al. [29] reported that radiomic features extracted from pre‐treatment T2‐weighted MRI modestly improved recurrence prediction beyond clinical factors, while Zhong et al. [30] demonstrated that multiparametric MRI combined with machine‐learning classifiers achieved good predictive performance after external beam radiotherapy. Janbain et al. [31] also applied machine‐learning algorithms incorporating PSMA‐PET‐derived features and clinical variables to predict biochemical control following PSMA‐guided salvage radiotherapy after prostatectomy, achieving good discriminatory performance. Although multiple machine‐learning models have been developed to predict BCR after radical prostatectomy or external beam radiotherapy, few models specifically address late recurrence following prostate brachytherapy. To the best of our knowledge, few studies have examined late recurrence after LDR‐BT using machine‐learning approaches. Our study adds to this emerging literature by focusing specifically on patients who remained recurrence‐free for 5 years and subsequently experienced late BCR.

In the present study, survival decision tree analysis identified a cutoff value of 0.93 ng/mL for 5‐year PSA as a factor associated with late recurrence. This value represents the threshold that best differentiated the risk of late recurrence in our dataset; however, it should not be interpreted as a definitive cure criterion at the individual level. Among the 1091 patients who met this cutoff, 24 (2.2%) still experienced recurrence, with the lowest 5Y‐PSA value among those who recurred being 0.033 ng/mL. If 0.033 ng/mL were used as the threshold, the recurrence‐free rate would be nearly 100%; however, this value is too low to be adopted universally in clinical practice. Thus, the 5‐year PSA level alone is insufficient to predict late recurrence. Nevertheless, for older patients or those with comorbidities who face challenges attending frequent follow‐up visits, a 5‐year PSA level below 0.93 ng/mL may serve as a practical indicator for extending follow‐up intervals. In the future, criteria for cure may become predictable through tools such as clinical applications or nomograms that integrate multiple variables, potentially including not only 5‐year PSA level, but also PSA‐DT, 4‐year PSA level, and primary Gleason pattern.

This study has several limitations. First, it was a retrospective analysis. Second, no independent validation cohort was available. Although the machine‐learning analysis identified potential predictors of late recurrence after LDR‐BT, the results were derived from a training dataset without independent validation. Therefore, the findings should be considered hypothesis‐generating, and future studies incorporating external validation are needed to confirm their robustness. Validation in an independent cohort is necessary before these findings can be applied to clinical decision‐making.

5. Conclusion

The 5‐year PSA value, PSA‐DT at 5 years, primary Gleason pattern, and NCCN risk classification were identified as key predictors of late BCR after LDR‐BT. Survival decision‐tree analysis showed that a 5‐year PSA level < 0.93 ng/mL and a PSA‐DT ≥ 5.3 years were strongly associated with a very low risk of late BCR after LDR‐BT. For patients at low risk of late recurrence, extending follow‐up intervals may help reduce the frequency of hospital visits and overall healthcare costs.

Funding

The authors have nothing to report.

Ethics Statement

Patient consent was waived because this study involved the use of de‐identified data collected during routine clinical practice. The study protocol was approved by the Institutional Review Board, and an opt‐out approach was used to provide patients with the opportunity to decline participation.

Conflicts of Interest

Nobumichi Tanaka is affiliated with an endowed chair funded by the Nihon Medi‐Physics Co. The other authors declare no conflicts of interest.

Data Availability Statement

The datasets generated and/or analyzed during the current study are not publicly available to protect study participant confidentiality, but are available from the corresponding author upon reasonable request.