Graves’ hyperthyroidism (GH) is a prevalent autoimmune thyroid disorder, primarily characterized by the overproduction of thyroid hormones and a multi-system hypermetabolic syndrome. The global prevalence of GH is estimated to be between 0.5% and 2%, with a markedly higher incidence in females compared to males, reflected in a male-to-female ratio of approximately 1:5-10 (1). This disease is most commonly seen in individuals aged 30-50, but its age distribution is wide, and it can also occur in adolescents and the elderly (2). The clinical manifestations of GH are diverse, with typical symptoms including palpitations, weight loss, excessive sweating, anxiety, tremors, and thyroid enlargement (3). Some patients may also have Graves’ orbitopathy, presenting as exophthalmos, diplopia, and visual impairment, severely affecting quality of life (4). If not treated promptly and effectively, GH can lead to a series of serious complications, such as thyroid storm, heart failure, osteoporosis, and arrhythmias, which can even be life-threatening (5, 6). Furthermore, the long-term state of hyperthyroidism has significant negative impacts on patients’ mental health and social functioning, highlighting the importance of its clinical management.

Iodine-131 (¹³¹I) therapy is one of the important treatment methods for GH, especially suitable for patients with poor efficacy, intolerance, or recurrence of antithyroid drugs (ATD) (7). The treatment principle is to selectively destroy thyroid follicular cells using the β rays released by the decay of ¹³¹I, thereby reducing the synthesis and secretion of thyroid hormones (8). Traditional dosing often involves a fixed range of 185–555 MBq (5–15 mCi), which overlooks individual patient differences, potentially leading to suboptimal outcomes or side effects (9). The dosing formula used is [Z × thyroid size (g) × 100]/24-hour iodine uptake rate (RAIU), where Z is the planned Bq or μCi per gram of thyroid tissue, ranging from 3.7 to 7.4 MBq (70-150 μCi) (10). However, these traditional methods have significant limitations. First, they highly depend on the accurate assessment of thyroid weight, while ultrasound measurement of thyroid volume has considerable inter-operator variability and measurement errors (11). Second, the existing formulas fail to adequately incorporate multiple clinical and pathophysiological factors affecting the biological effects of ¹³¹I, such as thyroid hormone levels, thyroid stimulating antibody (TSAb) titers, thyroid blood flow status, and individual metabolic differences (12). This leads to significant heterogeneity in patient outcomes after treatment, with some patients unable to achieve complete elimination (defined as the restoration of normal thyroid function), while others may develop permanent hypothyroidism, requiring lifelong thyroid hormone replacement therapy (13). Studies have shown that currently about 10%-30% of patients fail to achieve complete elimination after receiving ¹³¹I therapy, and the incidence of hypothyroidism can reach 20%-40% in the first year after treatment, increasing year by year over time (14, 15). This uncertainty in outcomes poses challenges for clinical decision-making, highlighting the urgent need for more precise dose prediction models to optimize treatment effects.

In recent years, with the rapid development of artificial intelligence (AI) technology in the medical field, machine learning (ML) algorithms have provided new solutions for complex medical prediction problems (16). Random Forest Regression (RFR), as an ensemble learning algorithm, effectively handles high-dimensional data, nonlinear relationships, and interactions between variables by constructing multiple decision trees and aggregating their prediction results, while also possessing strong anti-overfitting capabilities (17). In the medical field, RFR has been widely applied in various aspects such as disease diagnosis, prognosis prediction, and treatment response assessment (18). For example, in oncology, the RFR model successfully predicted the treatment response of Hepatocellular Carcinoma to transarterial radioembolization, achieving an accuracy rate of 79.6% (19); in the study of neurological diseases, ML models based on Random Forest (RF) showed good performance in predicting the prognosis of Leukemia, although its clinical translation still faces methodological challenges (20); in the cardiovascular field, RFR has been used to predict the risk of metabolic syndrome, with an area under the receiver operating characteristic curve (AUC) reaching 0.89 (21). These applications confirm the advantages of RFR in handling complex biomedical data.

The application of RFR in predicting the dosage of ¹³¹I treatment for GH has significant theoretical and practical implications. Firstly, RFR can integrate multidimensional predictive variables, including demographic characteristics (such as age and gender), clinical parameters (such as thyroid hormone levels, thyroid volume, and iodine uptake rate), immunological indicators (such as TSAb titer), and treatment-related factors (such as previous treatment history). By analyzing the complex relationships between these variables and treatment outcomes, the RFR model is expected to overcome the limitations of traditional formulas and achieve more personalized dosage calculations (17). Secondly, RFR has the capability to handle missing data and imbalanced datasets, which is particularly important for retrospective medical data modeling (22). In addition, the RF algorithm can assess variable importance, helping to identify key factors affecting the efficacy of ¹³¹I treatment.

It is worth noting that the development of prediction models based on RF must adhere to rigorous methodological standards, including appropriate sample size assurance, feature selection processes, model validation strategies, and performance evaluation metrics. In recent years, multiple studies have emphasized that ML models in clinical applications need to balance predictive accuracy and interpretability (23–25). For example, in the diagnostic models for acute myocardial infarction, combining interpretative AI techniques such as SHAP (SHapley Additive exPlanations) can enhance model transparency and promote clinical acceptance (26). Similarly, in predicting the dosage of ¹³¹I treatment for GH, the interpretability of the model helps clinicians understand the basis of predictions, thereby more effectively integrating model results into treatment decisions.

In summary, although ¹³¹I treatment for GH has good efficacy, the lack of precision in the dose calculation method leads to significant variability in treatment outcomes. The RFR model, as a powerful ML tool, can integrate multi-source heterogeneous data and capture the complex mapping relationship between variables and treatment response, promising more accurate individualized dose prediction. By constructing and validating a RF-based ¹³¹I treatment dose prediction model, it can not only improve the effectiveness and safety of GH treatment and reduce the occurrence of complications such as hypothyroidism, but also provide a new paradigm for precision medicine in autoimmune thyroid diseases.

This study successfully developed and validated a RFR model designed to predict the TID for patients diagnosed with GH who have achieved remission. The model demonstrated robust predictive performance, achieving an R-squared value of approximately 0.858 ± 0.05 on the validation set and 0.838 on the temporal validation set, indicating its strong capability to explain the variance in ¹³¹I dosage. Key predictive variables identified through this model included patient Gender, IDPG, FT4 levels, RAIU24h, Teff, and Thyroid weight. Furthermore, the application of SHAP values provided crucial interpretability, offering insights into how each feature contributes to the model’s predictions, thereby enhancing clinical understanding and potential for personalized treatment strategies. This interpretability is vital for gaining clinical acceptance and fostering trust in AI-driven medical decision support tools.

The findings of this study significantly advance the landscape of ¹³¹I dose prediction for GH, building upon and distinguishing itself from prior research. Traditionally, ¹³¹I dosing methods have relied on empirical formulas that primarily consider thyroid gland size and RAIU (30). While these traditional approaches offer a practical foundation, they often exhibit limitations, including variability due to operator measurement errors and an incomplete incorporation of a wide array of biological and clinical factors (31, 32). Studies utilizing such formulas often yield moderate success rates and demonstrate variability in treatment outcomes (31). For instance, a study involving 970 GH patients indicated that thyroid mass, ¹³¹I dosage, thyroid hormone levels, and the presence of thyroid murmurs independently influenced therapy efficacy, highlighting the need for personalized parameters (32). However, these methods struggle with the complex, non-linear relationships inherent in biological systems and typically cannot evaluate a large number of predictors simultaneously (33).

In contrast, the current RFR model represents a substantial methodological leap by integrating a comprehensive set of patient-specific clinical, biochemical, and immunological variables, thereby capturing the multifactorial nature of treatment response more effectively. ML algorithms, such as neural networks and support vector machines, have demonstrated their ability to process multidimensional data and model complex, non-linear relationships to improve dose prediction and outcome classification (34, 35). The superior performance of the RFR model, evidenced by its high R-squared values, aligns with recent literature advocating for the use of ensemble learning methods, particularly RF, to integrate multifaceted clinical and biochemical parameters for enhanced therapeutic dose prediction accuracy (33, 36). RF models are known for their robustness against overfitting and their capacity to handle large, complex, and heterogeneous datasets without extensive preprocessing, which is a significant advantage in medical research. Studies have shown that RF models can achieve high classification accuracy, often exceeding 90% in similar prediction tasks within hyperthyroidism patient cohorts (34). This study not only confirms the superiority of ML approaches but also provides an interpretable model, which is crucial for clinical adoption and understanding the underlying drivers of dose efficacy. The present findings strongly support and advance the viewpoint that ML, especially ensemble methods like RF, significantly enhances individualized dosimetry beyond the capabilities of classical empirical formulas, paving the way for more precise and personalized ¹³¹I therapy in GH.

Thyroid weight has long been recognized as a fundamental predictor in determining the success and dosing of ¹³¹I therapy for GH. The consistency of this factor across numerous studies underscores its central role in predicting outcomes, particularly regarding cure rates and the incidence of hypothyroidism (37–39). Recent literature, including a study on 325 GD patients, found that a smaller thyroid weight was significantly associated with successful radioiodine therapy (37). Similarly, a study involving 724 patients noted that successfully treated individuals had a smaller thyroid weight at presentation (38). Another more recent analysis confirmed thyroid volume as a significant independent predictor of radioactive iodine therapy efficacy, with smaller volumes correlating with better outcomes (40). A meta-analysis in 2022 further solidified the importance of patient characteristics, including thyroid size, in predicting ¹³¹I therapy failure in GD (41). This study reaffirms the established importance of thyroid weight as a critical determinant in ¹³¹I dosing and efficacy prediction.

RAIU24h is essential for assessing thyroid function and guiding ¹³¹I therapy, predicting treatment success and hypothyroidism risk. Lower RAIU24h levels increase early hypothyroidism risk and are the sole risk factor one year post-therapy (40, 42, 43). This study enhances its predictive role by using a RF model, capturing complex interactions with other clinical features that traditional models miss. The integration allows for a comprehensive analysis of RAIU24h’s interplay with clinical, biochemical, and immunological factors, as shown by SHAP analysis, which highlights its influence on the predicted ¹³¹I dose alongside factors like FT4 and thyroid weight.

FT4 levels are key indicators of hyperthyroidism severity and predictors of ¹³¹I therapy response. Studies show that lower FT4 levels correlate with successful radioiodine treatment and high remission rates, while higher levels suggest more severe disease and potential treatment challenges (37, 38, 44). The current study uses FT4 in a RF model to explore its complex interactions with other predictive factors, aligning with clinical insights. Unlike simpler models that view FT4 in isolation, the RFR model considers its interaction with factors like thyroid weight, RAIU, and immunological markers. In this model, FT4 influences predictions based on its numerical value: elevated FT4 levels lead to significantly higher predicted values, indicating that high FT4 levels elevate the prediction outcomes; conversely, lower FT4 levels result in decreased predicted values, suggesting that low FT4 levels adversely affect predictions. Overall, FT4 emerges as a pivotal feature within the model, exerting a significant bidirectional impact on predictions and demonstrating a positive correlation with the predicted outcomes. This integrative approach facilitates a more precise and individualized dose prediction by incorporating these elements.

Traditionally, gender has been viewed as a demographic factor rather than a predictor for ¹³¹I dosing in GH, despite its higher prevalence in females. Recent research, however, is examining sex-based differences in disease traits and treatment responses (45). While past studies often mentioned gender without recognizing it as a strong predictor, newer analyses suggest gender may influence prognosis, with factors like TPOAb affecting males differently (39). The present study distinctively integrates gender as a crucial predictive factor within its RFR model, thereby enhancing the personalization of ¹³¹I therapy. This advancement recognizes and quantifies the influence of sex-based differences on the optimal dosage of ¹³¹I, an aspect frequently neglected by previous models. The RFR model effectively captures the intricate gender-related influences on treatment by incorporating a range of clinical and immunological factors, thus facilitating more accurate dose predictions. Nevertheless, analysis of the SHAP plot reveals that the data points corresponding to gender are predominantly clustered around a SHAP value near zero, with minimal horizontal dispersion. This indicates that the average contribution of gender to the model’s output is relatively small, and its influence on predictions for individual samples is limited, both positively and negatively.

Incorporating the IDPG into advanced ML models for ¹³¹I therapy marks a significant innovation in dosimetry. Traditional dosing methods, which use fixed activity ranges or formulas based on thyroid weight and uptake, often overlook various clinical factors, leading to inconsistent outcomes. While some studies have considered IDPG in analyzing hypothyroidism risk, its use as a key predictor in ML models for determining effective curative doses is rare (37). A study highlighted ¹³¹I activity per gram of thyroid tissue” as a crucial independent predictor of ¹³¹I efficacy (40). This study’s RFR model innovatively incorporates IDPG as an input variable, categorizing it into “small” (70-90 μCi/g) and “large” (91-120 μCi/g) doses to enhance the prediction of optimal therapeutic doses based on patient-specific factors. This methodology improves the model’s capacity to discern subtle dose-response relationships, thereby enabling precise and personalized therapeutic recommendations that extend beyond conventional guidelines. By incorporating IDPG as a predictive feature, the model provides a refined, data-driven dosing strategy. It is noted that variables like IDPG and Thyroid Weight are integral to traditional dosing formulas. Therefore, the high predictive accuracy partially reflects the model’s ability to replicate the clinical decision-making process. However, the RFR model adds value by capturing non-linear interactions between these factors that linear formulas overlook.

The Teff is vital for understanding the absorbed radiation dose, combining both the radioisotope’s decay and its biological elimination. Historically difficult to measure, Teff has been underused in ¹³¹I dosing models for GH (46). Although research has aimed to optimize Teff estimation, its direct use in prediction models is rare. A study acknowledged Teff’s importance (45), and another study attempted to predict it using RAIU measurements (46). The current study innovatively includes Teff as a key feature in its RFR model, enhancing dose prediction by considering individual patient variability in radioiodine kinetics. This inclusion fills a gap in past research by integrating Teff into the main dose prediction algorithm, rather than calculating it separately. By incorporating Teff, the RFR model accounts for individual variations in iodine retention and elimination, crucial for determining the absorbed dose and therapeutic effectiveness. SHAP analysis showed Teff as a key negative factor in predicting the ¹³¹I dose, implying that a longer Teff may require a lower administered dose due to extended exposure. This precise integration of a dynamic pharmacokinetic parameter enhances the model’s ability to personalize ¹³¹I dosing, improving treatment outcomes.

Despite the significant advancements introduced by this RFR model, several limitations must be acknowledged that affect its generalizability and potential for broader clinical application. Firstly, the study predominantly utilized a retrospective cohort design. Although this approach is advantageous for assembling a substantial sample size and accessing documented follow-up data, it inherently presents risks of selection bias and incomplete data capture from existing medical records. Retrospective data may not adequately control for confounding variables or biases introduced during the data collection process over time. Furthermore, since the model was trained on patients who achieved remission, it predicts the sufficient dose for cure rather than the minimum effective dose, potentially reflecting only the historical dosing practices of the participating center. Secondly, the data sources, while from designated medical centers, may represent single or limited centers, which can restrict the model’s generalizability across diverse patient populations and varied healthcare settings. This geographical and demographic homogeneity could limit the model’s applicability to other regions or ethnic groups with different clinical practices or genetic predispositions. Thirdly, although the sample size of 975 patients is substantial, it might still be insufficient to capture the full spectrum of variability, especially for rare patient subgroups or less common long-term outcomes of ¹³¹I therapy. Furthermore, while rigorous techniques such as LASSO regression were used for variable selection, there remains a possibility that certain latent factors or unmeasured biomarkers influencing therapy outcomes were omitted from the model. Measurement errors, particularly in highly subjective assessments like thyroid volume estimation via ultrasound, can introduce inaccuracies into the model’s inputs, thereby affecting its overall predictive precision. Lastly, despite RF models generally being robust against overfitting, the risk persists, particularly when trained exclusively on retrospective clinical data that may contain specific patterns not representative of broader clinical realities. The lack of external validation across independent datasets is also a notable limitation, affecting the confidence in the model’s performance when applied to new, unseen patient cohorts.

This study successfully developed and validated a RFR model for predicting the TID in patients with GH. The model demonstrated robust predictive performance with an R-squared value of 0.838 on the temporal validation set. By identifying Gender, IDPG, FT4, RAIU24h, Teff, and Thyroid weight as key predictive variables, our RFR model offers a sophisticated approach to dose personalization. The innovative integration of these multi-dimensional features, coupled with the interpretability provided by SHAP values, allows for a more nuanced understanding of their complex interactions and individual contributions to treatment outcomes. The findings pave the way for more precise and individualized ¹³¹I therapy, potentially replicate and refine the successful dosing patterns.