Development and temporal validation of a machine learning-based model for predicting renal impairment in multiple myeloma: a single-center retrospective cohort study

Abstract

Background

Multiple myeloma (MM) is a hematopoietic system malignancy characterized by clonal proliferation of abnormal plasma cells, commonly presenting with renal impairment (RI) that significantly impacts patient’s quality of life. The objective of this study was to develop a predictive model for assessing the risk of MM with RI.

Methods

This retrospective study included 1029 patients with MM, who were categorized into two groups: MM without RI group and MM with RI group. Specifically, the modeling dataset (Cohort 1) consisted of 792 patients (401 without RI and 391 with RI), and the validation dataset (Cohort 2) consisted of 237 patients (119 without RI and 118 with RI). Eight machine learning (ML) algorithms were assessed using the modeling dataset (n = 792), and model validation was conducted on the validation dataset (n = 237). The predictive performance of ML models was evaluated through the area under the receiver operating characteristic curve (AUC), calibration curve, and decision curve analysis.

Results

The optimal model among the eight ML algorithms was XGBoost. The predictive model constructed based on the XGBoost algorithm, RI-Lab6, incorporated six features: NLR, LDH, Hb, ACa, AGR and β2 microglobulin. In the modeling dataset (cohort 1), RI-Lab6 demonstrated an AUC of 0.99 (95% CI, 0.98–0.99), while in the validation dataset (cohort 2), it achieved an AUC value of 0.98 (95% CI, 0.96–0.99).

Conclusions

These results indicated that the RI-Lab6 model possessed reliable predictive value for RI risk in MM patients and facilitated early identification of RI in these individuals.

Background

Multiple myeloma (MM) ranks as the second most common hematologic malignancy, following lymphoma [1, 2]. Common clinical manifestations of MM include hypercalcemia, renal impairment (RI), anemia, and bone lesions [3–5]. RI is a frequent complication, defined as an estimated glomerular filtration rate (eGFR) below 60 mL/min/1.73 m² [6]. It is estimated that 25–50% of MM patients experience varying degrees of RI during the disease course, with 2–4% progressing to severe RI requiring dialysis, substantially impairing quality of life [7, 8]. Although therapeutic advances, such as proteasome inhibitors, autologous stem cell transplantation, and immunotherapy, have improved outcomes in MM with RI, the risk factors for RI in MM remain incompletely characterized [9]. Moreover, conventional renal biomarkers such as serum creatinine are influenced by a variety of non-renal factors, including medications, muscle mass, age, and exhibit insufficient sensitivity for detecting early-stage RI. Serum creatinine cannot be regarded as a sensitive or specific biomarker for RI [10]. Thus, there is a compelling need to identify reliable biomarkers and develop predictive tools to facilitate early detection of RI.

The expansion of medical data offers new opportunities for predictive analytics in clinical medicine [11–13]. Machine learning (ML), a subfield of artificial intelligence, has demonstrated strong capabilities in recognizing complex patterns within large-scale health data, supporting tasks such as risk prediction, diagnostics, and treatment personalization [14–17]. Within hematology, ML approaches have been increasingly applied to model disease outcomes and complications [18]. For example, Guerrero et al. developed a ML-based model to predict minimal residual disease status in MM patients after consolidation therapy and deployed it via an interactive web tool [19]. Similarly, Hussain et al. created a predictive model integrating clinical and laboratory variables to forecast onset and progression in both newly diagnosed and relapsed MM, aiding in biomarker discovery and clinical management [20]. Despite these advances, the application of ML specifically for predicting RI in MM remains underexplored.

Therefore, this study aims to develop and validate a ML-based predictive model using readily available clinical and laboratory parameters to assess the risk of RI in MM. We compare the performance of multiple ML algorithms and ultimately seek to deploy the model as an accessible online tool, with the goal of enabling early identification of high-risk patients and improving clinical outcomes.

Methods

Study design

This single-center, retrospective study utilized data from the LIS and EMR database of Xiangya Hospital, Central South University. This study has been reviewed and approved by the Ethics Committee of Xiangya Hospital, Central South University (No. 2024091167). The two cohorts were defined based on prespecified temporal periods. Cohort 1 (model development): A total of 792 adult patients newly diagnosed with MM between January 2018 and December 2022 were divided into a RI group (n = 391) and a non-RI group (n = 401). Cohort 2 (validation of the optimal model): From January 2023 to December 2023, a total of 237 adult patients newly diagnosed with MM were also divided into a RI group (n = 118) and a non-RI group (n = 119). MM was defined according to the criteria set by the International Myeloma Working Group (IMWG) standard [21]. Renal function was assessed using eGFR, derived using the Modification of Diet in Renal Disease (MDRD) formula. RI was defined as eGFR < 60 mL/min/1.73 m² [22]. Patients with baseline eGFR ≥ 60 mL/min/1.73 m² and none of the following exclusion criteria were assigned to the without RI group, indicating absolutely no RI at study entry. Exclusion criteria included: (1) a history of conditions such as hypertension, diabetes, and gout that may cause RI; (2) previous renal diseases such as nephritis, renal tuberculosis, and renal tumors; (3) presence of other factors that can cause RI such as chemotherapy, medications, and severe infections.

Clinical data collection

We retrieved demographic information and laboratory data at the time of initial diagnosis from both the LIS and EMR database. The collected data included: (1) Demographic characteristics such as age and gender; (2) Laboratory parameters including white blood cell (WBC) count, red blood cell (RBC) count, hemoglobin (Hb) level, platelet count, red cell distribution width (RDW), neutrophil-to-lymphocyte ratio (NLR), serum potassium (K) level, serum sodium (Na) level, serum chlorine (Cl) level, serum calcium (Ca) level, albumin concentration, alanine aminotransferase (ALT) level, aspartate aminotransferase (AST) level, total bilirubin level (TBiL), lactate dehydrogenase (LDH) level, serum creatinine level, β2 microglobulin concentration, and cystatin C (Cys C) concentration.

The following formula was used to calculate albumin-adjusted serum calcium (ACa): ACa (mmol/L) = serum total calcium (mmol/L) + 0.02 × (40-serum albumin (g/L)). Additionally calculated parameters included: albumin-to-globulin ratio (AGR): AGR = albumin concentration / (total protein concentration-albumin concentration) [23–25].

Model construction and evaluation

The workflow for model construction using ML algorithms is illustrated in Fig. 1. The dataset from cohort 1 was utilized to compute the coefficients of risk factors and eliminated variables with zero coefficients through least absolute shrinkage and selection operator (LASSO) logistic regression. Subsequently, the remaining variables were employed for constructing a ML model. Model evaluation and selection were carried out using five-fold cross-validation, wherein the entire dataset was divided into five folds, with four folds allocated for training the model and one fold for validation. This process was repeated five times, and the average value served as the performance metric of the model. ML algorithms applied encompass decision tree, linear support vector classification (Linear SVC), support vector machine (SVM), adaptive boosting (AdaBoost), random forest, extreme gradient boosting (XGBoost), logistic regression, and stochastic gradient descent (SGD). Model performance was comprehensively evaluated using the area under the receiver operating characteristic curve (AUC), sensitivity, specificity, accuracy, F1 score, positive predictive value (PPV), and negative predictive value (NPV). Subsequently, a nomogram was generated based on these selected variables using the “rms” package in R software. Additional evaluations included the precision-recall (PR) curve to assess predictive performance, decision curve analysis (DCA) to estimate clinical utility, and a calibration curve to examine the agreement between predicted probabilities and observed outcomes. The optimal ML model selected underwent validation using data from cohort 2.

Fig. 1.

A workflow to build the predictive model. MM, multiple myeloma; RI, renal impairment; LIS, laboratory information system; ROC, receiver operating characteristic; AUC, area under the curve; PPV, positive predictive value; NPV, negative predictive value

Statistical analysis

Statistical analysis was performed using SPSS 23.0 and R 3.6.1 software packages. The Deepwise and Beckman Coulter DxAI platforms (http://dxonline.deepwise.com) were employed for feature selection and model construction purposes. Continuous variables with a normal distribution were presented as mean±standard deviation, whereas non-normally distributed variables were represented by their median (Q₂₅, Q₇₅). Categorical variables were expressed as percentage frequencies. Between-group variable comparisons involved student’s t-test and Mann-Whitney U test where appropriate. All statistical results achieved significance at a two-sided P-value of less than 0.05.

Results

Baseline characteristics

A total of 1029 newly diagnosed MM patients were included in this study. According to the predefined cutoff of eGFR < 60 mL/min/1.73 m² for RI [22], patients were divided into two groups: the MM without RI group (eGFR ≥ 60 mL/min/1.73 m²) and the MM with RI group (eGFR < 60 mL/min/1.73 m²). Cohort 1 consisted of 792 cases, with 401 (50.63%) in the MM without RI group and 391 (49.37%) in the MM with RI group; cohort 2 consisted of 237 cases, with 119 (50.21%) in the MM without RI group and 118 (49.79%) in the MM with RI group. Table 1 summarized the baseline characteristics and routine laboratory data of all participants. In both cohorts, there were no statistically significant differences between patients with and without RI regarding age, gender, platelet count, serum K level, or serum Cl level (P > 0.05). However, patients with RI exhibited a higher likelihood of presenting anemia as well as higher WBC count, NLR ratio, and ACa level compared to those without RI. Additionally, the two groups showed significant difference in RBC count, RDW value, AGR value, serum Na level, serum creatinine level, ALT level, AST level, TBiL level, LDH level, β2 microglobulin concentration, and Cys C concentration results (P < 0.001).

Table 1.

Clinical characteristics of the study population

Characteristics	Cohort 1				Cohort 2
	Total (n = 792)	MM without RI (n = 401)	MM with RI (n = 391)	P	Total (n = 237)	MM without RI (n = 119)	MM with RI (n = 118)	P
Age (Year)	60.00 (56.00–68.00)	60.00 (55.00–67.00)	62.00 (56.00–69.00)	0.123	58.00 (52.00–65.00)	55.00 (50.50–63.00)	62.50 (53.00–67.00)	0.154
Gender				0.166				0.322
Male [n (%)]	479 (60.48)	233 (58.10)	246 (62.92)		133 (56.12)	63 (52.94)	70 (59.32)
Female[n (%)]	313 (39.52)	168 (41.90)	145 (37.08)		104 (43.88)	56 (47.06)	48 (40.68)
Male: Female ratio	1.53:1	1.39:1	1.70:1		1.28:1	1.13:1	1.46:1
WBC (109/L)	5.20 (3.90–6.60)	4.80 (3.50-6.00)	5.70 (4.30–7.25)	< 0.001	5.40 (4.30–6.10)	4.60 (3.40–5.85)	5.70 (5.20–6.40)	< 0.001
RBC (1012/L)	3.48 ± 0.87	3.76 ± 0.82	3.20 ± 0.84	< 0.001	3.49 ± 0.90	3.78 ± 0.84	3.20 ± 0.86	< 0.001
Hb (g/L)	113.00 (95.00-130.00)	125.00 (112.00-137.00)	97.00 (79.00-114.00)	< 0.001	108.00 (88.00-127.00)	121.00 (102.50–133.00)	99.00 (80.25-123.75)	< 0.001
Platelet (109/L)	206.23 ± 74.31	209.70 ± 70.78	202.70 ± 77.70	0.186	231.66 ± 82.82	240.88 ± 77.82	222.36 ± 86.92	0.085
RDW (%)	15.81 ± 2.44	16.04 ± 2.42	15.57 ± 2.44	0.006	16.02 ± 2.54	16.26 ± 2.71	15.78 ± 2.34	0.003
NLR	2.26 (1.44–3.78)	1.80 (1.13–2.26)	3.44 (2.14–4.44)	< 0.001	2.67 (1.63–4.33)	2.00 (1.35–3.41)	3.66 (2.10–5.37)	< 0.001
K (mmol/L)	3.89 (3.57–4.20)	3.72 (3.38–4.01)	4.08 (3.74–4.46)	0.126	3.73 (3.35–3.99)	3.91 (3.68–4.11)	3.45 (3.23–3.82)	0.213
Na (mmol/L)	139.90 (137.48–142.00)	140.50 (138.30-142.30)	139.20 (136.40-141.30)	< 0.001	140.90 (138.20-142.60)	141.40 (139.45–143.00)	140.00 (137.13–141.80)	< 0.001
Cl (mmol/L)	105.35 (102.80-107.70)	105.10 (103.30-107.10)	105.70 (101.90-108.20)	0.245	104.90 (102.20-107.40)	104.90 (102.40-106.90)	105.05 (101.73-107.85)	0.749
ACa (mmol/L)	2.33 (2.21–3.19)	2.24 (2.17–2.33)	3.19 (2.35–3.38)	< 0.001	2.39 (2.23–3.36)	2.26 (2.18–2.32)	3.37 (3.31–3.51)	< 0.001
AGR	1.70 (1.10–2.20)	2.20 (1.70–2.50)	1.30 (0.90–1.70)	< 0.001	1.80 (1.30–2.50)	2.40 (1.80–3.30)	1.40 (1.00-1.80)	< 0.001
ALT (U/L)	20.82 ± 12.67	18.77 ± 12.37	22.92 ± 12.64	< 0.001	28.29 ± 14.66	23.18 ± 14.69	33.45 ± 12.75	< 0.001
AST (U/L)	20.00 (15.90–26.30)	19.60 (15.30–25.80)	20.60 (16.75–26.50)	0.031	22.00 (18.20–27.00)	21.10 (17.65–25.10)	22.30 (18.73–29.53)	0.039
TBiL(µmol/L)	8.30 (5.68–11.93)	10.40 (7.10–14.30)	6.90 (4.75–9.60)	< 0.001	9.00 (6.30–13.30)	9.80 (7.60-14.15)	8.15 (5.70-11.28)	0.003
LDH (U/L)	218.50 (172.75-263.25)	181.00 (157.00-215.00)	256.00 (222.00-287.00)	< 0.001	182.00 (151.00-205.00)	171.00 (125.00-190.00)	198.00 (167.50–222.00)	< 0.001
Creatinine (µmol/L)	78.00 (57.00-171.50)	57.00 (46.00–68.00)	177.00 (96.00-363.00)	< 0.001	78.00 (66.00-119.00)	66.00 (60.00–73.00)	119.50 (90.00-243.75)	< 0.001
β2 microglobulin (mg/L)	4.42 (3.00-7.79)	3.23 (2.61–4.58)	7.66 (4.23–15.31)	< 0.001	5.07 (2.55–13.01)	2.57 (2.06–3.37)	13.04 (11.72–15.35)	< 0.001
Cys C (mg/L)	1.31 (1.04–2.30)	1.08 (0.92–1.29)	2.10 (1.40–3.91)	< 0.001	1.90 (1.05–2.53)	1.06 (0.93–1.23)	2.54 (2.30–2.95)	< 0.001

MM, multiple myeloma; RI, renal impairment; WBC, white blood cell; RBC, red blood cell; Hb, hemoglobin; RDW, red cell distribution width; NLR, neutrophil-to-lymphocyte ratio; K, potassium; Na, sodium; Cl, chlorine; ACa, albumin-adjusted serum calcium; AGR, albumin-to-globulin ratio; ALT, alanine aminotransferase; AST, aspartate aminotransferase; TBiL, total bilirubin level; LDH, lactate dehydrogenase; Cys C, cystatin C

Selection of risk factors

In order to construct a ML model for RI prediction, we focused on features that showed significant differences in cohort 1. Considering that eGFR was derived from serum creatinine levels, the evaluation excluded creatinine as a variable. Subsequently, we selected fourteen significantly different features for LASSO regression analysis. Through ten-fold cross-validation, we identified ten non-zero coefficient features that were used for ML model construction (Fig. 2A, B). These selected features include serum Na, ACa, AGR, ALT, AST, LDH, β2 microglobulin, Cys C, Hb and NLR.

Fig. 2.

LASSO regression analysis screening variables. (A) LASSO coefficient profiles of the fourteen risk factors. (B) Penalty parameter (λ) selection by LASSO adopted ten-fold cross validation

ML model establishment and evaluation

The performance of eight ML algorithms was evaluated using five-fold cross-validation. Among these, the XGBoost model demonstrated significantly superior predictive performance, achieving an AUC of 0.99 (95% CI, 0.98–0.99), sensitivity of 0.91, specificity of 0.96, PPV of 0.93 and NPV of 0.95 on the internal validation set (Table 2). Based on this algorithm, the top six features with relative weights exceeding 0.5 were used to construct a simplified risk prediction model, designated as the RI-Lab6 model. The six selected features included NLR, LDH, Hb, ACa, AGR and β2 microglobulin. The coefficients of each feature were illustrated in Fig. 3A. ROC curve analysis demonstrated the robust predictive ability of these six features for RI risk (Fig. 4).

Table 2.

Performance of eight models

Classifier	AUC [95%CI]	Sensitivity	Specificity	Accuracy	F1 score	PPV	NPV
Decision tree	0.85 [0.84–0.87]	0.87	0.95	0.91	0.91	0.92	0.89
Linear SVC	0.98 [0.97–0.99]	0.82	0.93	0.95	0.94	0.91	0.92
SVM	0.78 [0.77–0.79]	0.90	0.87	0.85	0.95	0.87	0.94
AdaBoost	0.96 [0.95–0.97]	0.91	0.94	0.95	0.95	0.83	0.93
Random forest	0.87 [0.86–0.89]	0.86	0.93	0.92	0.92	0.78	0.88
XGBoost	0.99 [0.98–0.99]	0.91	0.96	0.97	0.97	0.93	0.95
Logistic regression	0.98 [0.97–0.99]	0.90	0.95	0.95	0.94	0.91	0.92
SGD	0.88 [0.87–0.89]	0.89	0.93	0.95	0.94	0.92	0.93

AUC, area under the curve; CI, confidence interval; PPV, positive predictive value; NPV, negative predictive value; Linear SVC, Linear support vector classification; SVM, support vector machine; AdaBoost, adaptive boosting; XGBoost, extreme gradient boosting; SGD, stochastic gradient descent

Fig. 3.

Risk prediction models for MM with RI built by ML algorithms. (A) Weight of β2 microglobulin, AGR, ACa, Hb, LDH and NLR in the XGBoost model. (B) Nomogram graph of relevant factors of MM with RI. AGR, albumin-to-globulin ratio; ACa, albumin-adjusted serum calcium; Hb, hemoglobin; LDH, lactate dehydrogenase; NLR, neutrophil-to-lymphocyte ratio

Fig. 4.

ROC curve analysis of six features in MM with RI and MM without RI groups respectively. Hb, hemoglobin; NLR, neutrophil-to-lymphocyte ratio; ACa, albumin-adjusted serum calcium; AGR, albumin-to-globulin ratio; LDH, lactate dehydrogenase

Moreover, the nomogram model was constructed using these six features to estimate the probability of RI in MM patients. Each variable was assigned a specific point value, and the cumulative total score was used to predict the risk of RI (Fig. 3B). In the internal validation set, the RI-Lab6 model exhibited excellent predictive ability, achieving an AUC of 0.99 (95% CI, 0.98–0.99), a sensitivity of 0.91 and a specificity of 0.96 (Fig. 5A). Additionally, PR curve analysis, DCA analysis, and calibration curve analysis were conducted as well (Fig. 5B-D). These findings collectively indicated that the RI-Lab6 model outperformed other models in predicting RI risk.

Fig. 5.

Evaluation of the ability of the RI-Lab6 model to predict the risk for MM with RI. (A) ROC curve analysis. (B) Precision recall curve analysis. (C) Decision curve analysis. (D) Calibration curve analysis

Validation

In order to further evaluate the performance of the RI-Lab6 model, we utilized cohort 2 (n = 237) as a validation set, comprising of 119 patients without RI and 118 patients with RI. The ROC curve analysis demonstrated that the RI-Lab6 model exhibits robust and specific predictive capability for RI risk assessment, with an AUC value of 0.98 (95% CI, 0.96–0.99), sensitivity of 0.95, and specificity of 0.91 (Table 3). These findings indicated that the laboratory-based RI-Lab6 model possessed excellent potential for assessing RI risk.

Table 3.

The performance of the model in the validation cohort

RI-Lab6 model	AUC	Sensitivity	Specificity
validation cohort	0.98	0.95	0.91

AUC, area under the curve

An online tool of the prediction model

In this study, we have developed an online tool for predicting the risk probability of RI in MM patients (Fig. 6). Clinical practitioners can easily input the necessary parameters to assess the likelihood of RI occurrence among their patients. The calculated probability and results were accessible on the designated website: (https://dxonline.deepwise.com/prediction/index.html?baseUrl=%2Fapi%2 F&id=49059&topicName=undefined&from=share&platformType=wisdom).

Fig. 6.

An example of web tool usage. The risk of RI can be predicted by inputting six clinical parameters in MM patients. Hb, hemoglobin; NLR, neutrophil-to-lymphocyte ratio; ACa, albumin-adjusted serum calcium; AGR, albumin-to-globulin ratio; LDH, lactate dehydrogenase

Discussion

As a prevalent hematopoietic malignancy, the global incidence rate of MM is on the rise [26]. In 2020, approximately 117,077 deaths were attributed to MM worldwide, corresponding to a mortality rate of 1.14 per 100,000 individuals [27]. MM manifested with diverse clinical presentations, commonly involving RI as a symptom associated with bone marrow involvement [28]. Abnormal monoclonal immunoglobulins or their components secreted by MM cells can lead to various types of RI through direct deposition or indirect mechanisms [29–31]. Although eGFR and serum creatinine are widely used indicators for renal function assessment, they lack sufficient sensitivity and specificity, often leading to missed diagnoses or misclassification [32]. In this study, we employed ML algorithms to establish a model based on existing challenges that effectively predicted the risk of RI in MM patients using six commonly utilized laboratory parameters.

Rising medical demand has driven an exponential growth in medical data. Effectively leveraging this big data is essential for improving diagnostic accuracy and supporting clinical decision-making [33, 34]. However, traditional statistical methods like logistic regression and cox proportional hazards were limited by their underlying assumptions, leading to decreased predictive accuracy [35]. In contrast, ML could overcome these limitations imposed by conventional methods such as hypothesis testing due to its lower requirements and restrictions on data structure and model assumptions [36, 37]. In recent years, ML has gained increasing application for predicting and treating hematologic malignancies. For instance, Peng et al. assessed the predictive capability of six ML models for infection in patients with newly diagnosed MM. The XGBoost model demonstrated outstanding performance with an AUC of 0.971 in the training set, 0.884 in the validation set, and 0.760 in the test set [38]. Mosquera et al. integrated clinical and biochemical data with gene expression data to develop a random forest model comprising fifty variables for effective survival prediction and treatment optimization among MM patients using ML algorithms [39]. In this study, we compared eight ML algorithms regarding their data mining capabilities and performance validation; among them, the XGBoost model exhibited superior performance. Based on this algorithm, we developed the RI-Lab6 model that showed high predictive ability and clinical benefits. Additionally, we developed a user-friendly online tool to facilitate clinical assessment of RI risk in MM. By inputting routinely available laboratory indicators, clinicians can readily obtain individualized risk predictions. This tool offers a practical and efficient alternative for predicting RI risk, particularly in resource-limited settings where specialized testing may be unavailable.

Risk prediction for RI should be conducted in all MM patients during diagnosis and disease assessment. The clinical manifestations of RI in MM are highly heterogeneous, and although renal biopsy remains the gold standard for diagnosis, it is an invasive procedure associated with potential complications and prolonged recovery [6]. Although some factors related to renal complications in MM patients have been described, the specific risk factors that render MM patients susceptible to renal complications remain unclear. In this study, we developed the RI-Lab6 model based on routine laboratory tests to enable clinicians to objectively predict the risk of RI in MM patients. The model incorporated six features: NLR, AGR, LDH, Hb, ACa, and β2 microglobulin. NLR and AGR reflect systemic inflammatory status. There is growing evidence that elevated NLR may promote tumor vascular invasion leading to a local immunosuppressive microenvironment in MM and thus facilitate tumor progression. Similarly, a decreased AGR, often resulting from reduced serum albumin and elevated globulin levels, may more accurately reflect disease progression in MM [40, 41]. Zhang et al. discovered that NLR and AGR could potentially serve as prognostic biomarkers for overall survival and progression-free survival in MM with RI [25]. LDH, a predictor of malignant tumor progression, was also incorporated into the model. In MM patients, metabolic dysregulation leads to substantial release of LDH into the bloodstream. Additionally, elevated serum LDH levels often accompanied RI since it was an organ rich in LDH responsible for its excretion. Anemia caused by decreased hemoglobin is a common symptom among MM patients. Studies have indicated that 88% of MM patients with RI experience significant anemia compared to those without RI. This may be attributed to the secretion of endogenous erythropoietin in renal [42, 43]. Elevated ACa is another established prognostic factor in MM. Hypercalcemia caused constriction of glomerular blood vessels, interfered with renal blood flow, and reduced eGFR; moreover, calcium salts could deposit in the renal leading to interstitial nephropathy [2, 3]. Cheng et al. found that higher serum calcium levels were associated with an increased risk of all-cause mortality [44]. Due to abnormal immunoglobulin secretion offsetting the decrease in binding calcium caused by reduced albumin levels in MM patients, total serum calcium could not accurately reflect true blood calcium levels. Therefore, ACa formula is commonly used clinically. Furthermore, β2 microglobulin served as an important indicator for detecting RI and was included in this study’s model. As a low-molecular-weight protein, it readily passes through the glomerular filtration barrier and serves as a sensitive indicator of renal dysfunction [45].

This study has several limitations. Firstly, despite the model exhibited strong discriminatory performance across multiple metrics (e.g., AUC, sensitivity, specificity) in the current cohort, the generalizability of our model requires further validation in large-scale multicenter studies. Furthermore, the exclusion of certain disease-specific variables, such as monoclonal immunoglobulin type and ISS/R-ISS staging, due to a high rate of missing data (> 30%), may limit the comprehensiveness of the model. Future research should focus on prospectively collecting complete datasets within multicenter cohorts to develop more comprehensive predictive models. Thirdly, this study primarily focused on a single ML algorithm without considering the scalability and robustness of fusion models in large cohort disease prediction.

Conclusion

The present study developed an online portable model, RI-Lab6, based on ML algorithms to accurately predict the risk of RI in MM patients. The model incorporated six variables: NLR, LDH, Hb, ACa, AGR, and β2 microglobulin. It demonstrated robust predictive performance and clinical utility in validation cohort, thereby contributing to an improved quality of life.

Author contributions

MLZ and SSF wrote the main manuscript text. All authors reviewed the manuscript.

Funding

This study was supported by Hunan Province Key Research and Development Project (2024JK2107), and the Natural Science Foundation of Hunan Province (2022JJ30987). The funding bodies played no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.

Data availability

The datasets used and analysed during the current study available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

This study has been reviewed and approved by the Ethics Committee of Xiangya Hospital, Central South University (No. 2024091167). The adoption of a retrospective observational design by the committee obviated the need for written informed consent. The study followed the Declaration of Helsinki.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.