g
-Rate–based machine learning model to predict overall survival (OS) in patients with metastatic prostate cancer (mPC) while on treatment.
Authors: Leuva Harshraj , Wang Jieqiong , Azzam Mohamed , Zhou Mengxi , Teply Benjamin A. , Bergan Raymond C. , Bates Susan Elaine , Fojo Antonio Tito 
Published: February 2025

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Background:
Dynamic biomarkers to predict OS while a pt is on treatment are unavailable in mPC. We have developed
g
-rate method which can estimate tumor growth (
g
) and decay (
d
) rates using PSA values. This has been validated to show a robust inverse correlation with OS using 13 clinical trials and real-world data from the US Veterans. We now explore the
g
-rate method in developing a multimodal machine learning (ML/AI) tool to serve as a dynamic biomarker predicting OS while a pt is on treatment.
Methods:
We have created a comprehensive VA database with more than 20,000 pts to assess drug efficacy in mPC.
g
and
d
rates are calculated using PSA values while on treatment via the TUMGr package for R. All available variables such as age at the start of treatment, race, treatment setting (rural vs urban), gleason score, charleson comorbidity index (CCI), hormone sensitivity, line of treatment, serial PSA, and
g
-rate while on treatment. The histogram-based gradient boosting tree ML algorithm is used to build the classifier. This algorithm is optimized to handle large data (records > 10,000). Sample reweighting is used to account for data imbalance by adjusting weights inversely proportional to class frequencies in the training data. Permutation importance is used to assess the significance of features in the resulting model. A binary classifier is used to predict the survival status. Shapley additive explanations (SHAP) were used to evaluate the contribution of individual features.
Results:
We utilized data from 25641 treatment records from 22958 unique pts; 20475 records were used for training and 5166 were used for testing ML algorithm. We identified 16 features, including demographic, CCI, baseline PSA, baseline CBC, and PSA-based g-rate for the model. The resulting model yielded an accuracy of 77%, a precision of 89.7%, a sensitivity/recall of 79%, a specificity of 73%, and an F1-score of 84%. The area under the receiver operating characteristic (ROC) curve (AUC) was 0.83. The classification results were statistically significant (p<10
-6
).The mean absolute SHAP values revealed that starting PSA and
g
-rate were 2 most influential features in predicting pt survival. The model showed concordant results amongst White, Black, Hawaiian, and American Indian races, but not for Asian pts (Table).
Conclusions:
g
-rate-based ML/AI model can accurately, consistently and reliably predict pt survival while being treated for mPC across different races as soon as 3 months once the
g
-rate is calculated after starting treatment. Future incorporation of this model into clinical trials may identify opportunities for early intervention for those with poor prognoses.

Race
Records
Accuracy
AUC score
Precision

White
3520
0.78
0.83
0.9

Black
1387
0.76
0.83
0.9

Native Hawaiian
44
0.80
0.96
1

American Indian
27
0.85
0.93
0.9

Asian
20
0.65
0.69
0.7

Unknown
168
0.77
0.86
0.9

All
5166
0.77
0.83
0.9