Data for this study were derived from the CHARLS, a prospective, nationally representative cohort of community-residing middle-aged and older Chinese adults. The survey utilizes a multistage probability sampling design that spans 28 provinces, 150 counties, and 450 villages, thereby ensuring broad geographic and socioeconomic diversity. The initial wave was fielded in 2011-2012, with subsequent follow-up assessments conducted at intervals of approximately two to three years^[21]. The study protocol received ethical approval from the Peking University Ethics Review Committee (IRB No. IRB00001052-11015). Written informed consent was obtained from all participants at each wave of data collection.

For the present investigation, we utilized Wave 3 (conducted in 2015) as the baseline survey for collecting predictor variables and Wave 4 (conducted in 2018) as the follow-up wave for ascertaining CKM multimorbidity. This longitudinal design enabled us to establish temporal relationships between baseline risk factors and incident CKM multimorbidity. Participants were included if they: (1) were aged 45 years or older at Wave 3; (2) had available body mass index (BMI) measurements and were classified as having overweight or obesity according to the criteria for Chinese adults (BMI ≥ 24 kg/m²)^[22,23]; (3) had no prior diagnosis of CKM multimorbidity in Wave 3; and (4) completed the Wave 4 follow-up assessment with available data for ascertaining CKM multimorbidity. Following the application of the predefined eligibility criteria, 4,244 individuals with overweight or obesity were ultimately enrolled in the final analytical sample. Supplementary Figure 1 provides a detailed flow diagram of the participant selection and exclusion process.

Candidate predictors were initially selected based on a comprehensive review of the literature and their potential association with CKM multimorbidity in individuals with overweight or obesity. These variables covered multiple domains and were derived from the CHARLS questionnaire, physical measurements, and laboratory tests. Sociodemographic characteristics included age, sex (male/female), geographic region (east/central/west), educational level (categorized as less than elementary school, elementary school, middle school, high school or above), marital status (married/others), residence (rural/urban), and self-rated living standard (poor, relatively poor, average, relatively high, very high). Socioeconomic status was constructed by combining educational level and total household wealth. Educational level was categorized as less than upper secondary education/primary (score 0), upper secondary & vocational training/secondary (score 1), and tertiary education/tertiary (score 2). Total household wealth, representing the sum of all wealth components (residence, business, vehicles, and saving accounts) excluding debts or loans, was divided into quartiles and scored from 0 (lowest) to 3 (highest). The SES score was then calculated by summing the education and wealth scores and classified into four categories: low (score 0), low-middle (scores 1-2), upper-middle (scores 3-4), and high (score 5)^[24]. Social isolation was measured using four objective criteria: not being married (including those who were separated, divorced, widowed, or had never married), residing alone, having fewer than weekly contacts with children (whether by phone, in person, or email), and engaging in no social activities during the previous month (e.g., meeting friends, playing chess or cards, or attending sports or social clubs). Each indicator scored 1 point, yielding a total score ranging from 0 to 4; participants with a score ≥ 2 were classified as socially isolated (yes/no)^[25]. Lifestyle variables included smoking status (yes/no), alcohol consumption (yes/no), sleep duration (categorized as ≤ 6 h, 6-8 h, or > 8 h), and metabolic equivalent of task (MET). MET was derived from self-reported frequency and duration of vigorous, moderate, and light physical activities, with each activity type assigned a weighting coefficient of 8.0, 4.0, and 3.3, respectively, to compute total weekly MET-minutes^[26].

Psychological status was evaluated using the 8-item Center for Epidemiologic Studies Depression Scale; a total score of 10 or higher indicated depressive symptoms (yes/no)^[27]. Dementia was identified through either self-reported physician-diagnosed memory-related diseases or the presence of both functional and cognitive impairment. Functional impairment was defined as dependency in at least one activity of daily living. Cognitive impairment was assessed using the Telephone Interview for Cognitive Status (TICS), defined as performance 1.5 standard deviations below the education-specific mean in at least two cognitive domains. Participants showing transient impairment with subsequent recovery were not classified as cases^[28]. Chronic conditions were ascertained through a combination of self-reported physician diagnoses, medication use, and laboratory or physical measurements. Hypertension was defined as self-reported physician diagnosis, self-reported use of antihypertensive medications, or measured systolic blood pressure (SBP) ≥ 140 mmHg or diastolic blood pressure (DBP) ≥ 90 mmHg^[29]. Diabetes was defined as self-reported physician diagnosis, self-reported use of glucose-lowering medications (insulin or oral hypoglycemic agents), or fasting blood glucose (FBG) ≥ 7.0 mmol/L or glycated hemoglobin (HbA1c) ≥ 6.5%^[30]. Dyslipidemia was defined as self-reported physician diagnosis, self-reported use of lipid-lowering medications, or meeting any of the following laboratory criteria: total cholesterol (TC) ≥ 240 mg/dL (6.22 mmol/L), triglycerides (TG) ≥ 200 mg/dL (2.26 mmol/L), low-density lipoprotein cholesterol (LDL) ≥ 160 mg/dL (4.14 mmol/L), or high-density lipoprotein-cholesterol (HDL) < 40 mg/dL (1.04 mmol/L)^[31]. Other chronic conditions were captured via self-reported physician diagnoses of heart disease, stroke, liver disease, kidney disease, digestive disease, memory-related disease, arthritis, menopausal status (for females: yes/no), and prostate disease (for males: yes/no). Physical function and symptoms included hearing ability (excellent, very good, good, fair, poor), visual impairment (yes/no), presence of pain (yes/no), weight change patterns (no change, only gained, only lost, first gained then lost, first lost then gained, don’t know), childhood health status (excellent, very good, good, fair, poor), and self-rated health expectation (almost impossible, not very likely, maybe, very likely, almost certain). Anthropometric measurements comprised BMI, waist circumference (WC), dominant hand grip strength (right/left/both), SBP, and DBP. Laboratory biomarkers obtained from blood samples included white blood cell count (WBC), hemoglobin, hematocrit, mean corpuscular volume (MCV), platelet count (PLT), C-reactive protein (CRP), creatinine, blood urea nitrogen (BUN), uric acid (UA), cystatin C, TC, TG, HDL, LDL, FBG, and HbA1c. Household environmental factors consisted of house type (modern, traditional, temporary, other), cooking fuel (clean fuel, non-clean fuel, other/not cooking), and perceived room temperature (very cold, cold, bearable, hot, very hot, not applicable). With the exception of self-rated living standard and weight change - both of which were obtained from the 2013 survey wave - all remaining predictor variables were taken from the 2015 wave and used to forecast CKM outcomes at the 2018 follow-up.

To reduce dimensionality and avoid overfitting, we employed a two-stage feature selection strategy combining LASSO regression with bootstrap stability analysis^[32]. First, LASSO regression with L1 penalty was applied to the training set after standardizing all continuous variables to the [0,1] range. For categorical variables, ordered factors (e.g., educational level, health expectation) were converted to integer codes preserving their natural order, while unordered categorical variables (e.g., region, house type, cooking fuel, weight change pattern) were one-hot encoded prior to LASSO regression and ML modeling to avoid introducing artificial ordinal relationships. The optimal penalty parameter λ was determined by 10-fold cross-validation, selecting the value within one standard error of the minimum deviance (lambda.1se) to enhance parsimony. Variables with non-zero coefficients at this λ were considered initially selected. Second, to address potential instability in LASSO selection, we performed bootstrap stability analysis by generating 100 bootstrap samples from the training set and repeating the LASSO procedure (with 10-fold cross-validation and lambda.1se) on each sample. Predictors that appeared in at least 90% of the bootstrap iterations were retained as the final set of features for subsequent ML modeling, ensuring that the selected variables were both relevant to the outcome and stable across data perturbations.

The primary outcome of this study was progression to incident CKM multimorbidity occurring between Wave 3 (2015) and Wave 4 (2018), defined as a binary indicator (yes/no) reflecting the coexistence of at least two of the three disease groups - cardiovascular, kidney, and metabolic diseases - within the same individual, as ascertained from the CHARLS standardized health questionnaires^[5]. CVD was defined based on two questions at Wave 4: “Have you been diagnosed with heart attack, coronary heart disease, angina, congestive heart failure, or other heart problems by a doctor?” and “Have you been diagnosed with stroke by a doctor?”. Kidney disease was defined based on the question: “Have you been diagnosed with kidney disease (except for tumor or cancer) by a doctor?”. Metabolic disease was defined as self-reported physician diagnosis of hypertension, diabetes or high blood sugar, or dyslipidemia, supplemented by physical measurements, laboratory biomarkers, and medication use to enhance diagnostic accuracy. Based on the combinations of these conditions, CKM multimorbidity was further classified into four subtypes (cardiovascular-kidney, cardiovascular-metabolic, kidney-metabolic, and complete CKM multimorbidity) for descriptive purposes; however, the primary outcome for all analyses was the binary presence versus absence of CKM multimorbidity [Supplementary Table 1]. As participants with CKM multimorbidity at baseline were excluded, and those with zero or one CKM disease group at baseline were included, the outcome represents progression from zero or one CKM condition to overt multimorbidity rather than first onset of any CKM condition. This predictor-outcome overlap is intentional: the model predicts progression from ≤ 1 to ≥ 2 CKM components, and predictors and outcomes were assessed at distinct time points (2015 vs. 2018).

To address missing data and outliers in the CHARLS cohort, we first screened continuous variables for extreme outliers using the interquartile range (IQR) rule: values below Q1 - 3 × IQR or above Q3 + 3 × IQR were considered outliers and recoded as missing to prevent undue influence on subsequent analyses. Missing data are unavoidable in large-scale longitudinal studies, arising from attrition, item non-response, or loss to follow-up; simply excluding individuals with any missing information would reduce statistical power and potentially introduce selection bias, compromising sample representativeness. For all remaining missing values (including those originally missing and those set to missing due to outlier status), we applied multiple imputation using chained equations (MICE) implemented in the R package mice^[33]. To account for imputation uncertainty, we generated five imputed datasets; all subsequent analyses were performed separately on each dataset, and results were pooled according to Rubin’s rules to obtain valid inference reflecting both within- and between-imputation variability. For continuous variables, we applied predictive mean matching; for binary variables, LR; and for unordered categorical variables, polytomous regression. To account for imputation uncertainty, five imputed datasets were generated, and all subsequent analyses were performed separately on each imputed dataset, with results pooled according to Rubin’s rules to obtain valid inference reflecting both within- and between-imputation variability. Comparisons of variable distributions before and after imputation are presented in Supplementary Figures 2 and 3. All preprocessing (imputation, scaling, feature selection) was restricted to the training set to prevent information leakage, with the outcome variable included in the imputation models. For each of the five imputed datasets, we applied the same stratified 70:30 split using a fixed random seed, ensuring reproducible and consistent partitioning. Feature selection (LASSO with bootstrap stability) was performed independently on each training set; the same nine predictors were retained across all five datasets, confirming robustness. Model tuning, training, and testing were then conducted within each split. Performance metrics [e.g., area under the curve (AUC), Brier score] were calculated on each testing set and pooled by averaging the point estimates; standard errors (95%CIs) were derived by combining within- and between-imputation variance per Rubin’s rules. Assuming missingness at random, this approach minimizes bias.

To systematically evaluate the predictive performance of different ML paradigms for incident CKM multimorbidity in Chinese adults with overweight and obesity, we constructed and compared seven algorithms representing diverse methodological approaches. These included LR, a conventional generalized linear model that estimates the probability of binary outcomes; Decision Tree (DT), which partitions data based on feature values to generate interpretable classification rules^[34]; random forest (RF), an ensemble method that aggregates multiple DT trained on bootstrap samples to reduce overfitting^[35]; extreme gradient boosting (XGBoost), a scalable tree boosting system known for its efficiency and predictive accuracy^[36]; light gradient boosting machine (LightGBM), a gradient boosting framework that uses leaf-wise tree growth to handle large-scale data with lower memory consumption^[37]; support vector machine (SVM), which constructs optimal hyperplanes in a transformed feature space to maximize class separation^[38]; and Artificial Neural Network (ANN), a multi-layer perceptron capable of capturing complex non-linear relationships through interconnected neurons^[39]. The dataset was randomly split into training and testing subsets at a 70:30 ratio, with stratification employed to maintain the original prevalence of CKM multimorbidity events in both partitions. All procedures related to model development - including feature scaling, hyperparameter optimization, and internal cross-validation within the training set - were restricted exclusively to the training set, whereas the testing set was held out and not used until the final performance evaluation [Supplementary Figure 4]. We determined the optimal hyperparameters for each algorithm using GridSearchCV paired with 5-fold cross-validation. In this framework, we partitioned the training data into five non-overlapping folds. For each iteration, we used four folds as the training subset and the held-out fold as the validation subset, cycling through all five folds. Hyperparameters were then selected by maximizing the average cross-validated AUC. The final hyperparameter configurations are summarized in Supplementary Table 2.

All statistical analyses were conducted using R (version 4.4.2; R Foundation for Statistical Computing, Vienna, Austria) and Python (version 3.10.4; Python Software Foundation). The model development workflow was implemented across both environments based on the specific capabilities of each ecosystem. Specifically, feature selection using LASSO regression with bootstrap stability analysis was performed in R via the glmnet package (version 4.1-8). The development and hyperparameter tuning of ML models - including RF, XGBoost, LightGBM, SVM, and ANN - were carried out using the scikit-learn library (version 1.2.2) in Python, with GridSearchCV and 5-fold cross-validation employed for optimization. The LR model was developed in R using the rms package (version 6.7.0). For model interpretation, SHAP analysis was executed using the fastshap package (version 0.1.1) in R, with visualizations generated via shapviz (version 0.9.0). Additional R packages utilized for preprocessing, validation, and plotting included mice (version 3.14.0) for multiple imputation, pROC (version 1.18.0) for DeLong’s tests, and ggplot2 (version 3.4.2) for general plotting. Decision curve analysis was performed using the rmda package (version 1.6). All random processes were seeded with set.seed(1234) in both R and Python [via numpy.random.seed(1234)] to guarantee complete reproducibility. Baseline characteristics were summarized separately for participants who developed incident CKM multimorbidity during follow-up and those who did not. We reported continuous data as either mean ± standard deviation or median with IQR, based on the results of the Shapiro-Wilk test for normality. Categorical variables were summarized as frequencies and percentages. For between-group comparisons, we applied independent t-tests or Mann-Whitney U tests for continuous variables (depending on distributional assumptions) and chi-square tests for categorical variables. A two-sided P value < 0.05 was regarded as statistically significant in all conventional analyses.

We comprehensively evaluated the predictive performance of all seven ML models using a variety of metrics. Discrimination ability was assessed by the AUC value, which measures the model’s capacity to distinguish between individuals who developed CKM multimorbidity and those who did not. All performance metrics were derived from predictions on the independent testing set to ensure unbiased evaluation. Model calibration was comprehensively assessed using calibration plots, which graphically compare predicted probabilities against observed outcomes across deciles of risk, along with the Hosmer-Lemeshow goodness-of-fit test and the Brier score to quantify the accuracy of probability predictions. We additionally performed decision curve analysis to assess the clinical usefulness of the models by estimating the net benefit across various probability thresholds. To enhance the clinical applicability of the LR model, a nomogram was developed as a proof-of-concept tool for research purposes, and its use in clinical practice requires external validation. To enhance clinical interpretability beyond conventional metrics, we employed Shapley Additive Explanations to elucidate the optimal model. SHAP, grounded in cooperative game theory, quantifies the marginal contribution of each feature by comparing model predictions with and without that predictor across all possible coalitions^[40]. For the best ML model, we generated multiple SHAP visualizations: a bar plot ranking feature importance based on mean absolute SHAP values, a beeswarm summary plot illustrating the distribution and directionality of SHAP values for key features, scatter dependence plots examining the marginal effects of continuous predictors, and waterfall and force plots demonstrating individual-level explanations for representative cases.

A total of 4,244 middle-aged and older adults with overweight or obesity were included, of whom 648 (15.3%) developed incident CKM multimorbidity during follow-up [Supplementary Table 3]. Compared to their non-CKM counterparts, individuals with CKM multimorbidity were significantly older, more likely to reside in central China, and had lower educational attainment. They also exhibited shorter sleep duration, lower physical activity levels, and a substantially higher prevalence of depressive symptoms. All chronic conditions assessed - including hypertension, diabetes, dyslipidemia, heart disease, stroke, kidney disease, and arthritis - were significantly more prevalent in the CKM group. Anthropometric measurements revealed higher BMI, WC, and blood pressure among CKM patients. Laboratory profiles showed elevated cystatin C, TG, and HbA1c, along with lower HDL. Additionally, use of non-clean cooking fuel was more common in the CKM group. These findings indicate that individuals with incident CKM multimorbidity present with a distinct profile characterized by adverse socioeconomic indicators, poorer cardiometabolic risk factors, and higher inflammatory burden.

Based on the two-stage feature selection strategy combining LASSO regression with bootstrap stability analysis, we identified a parsimonious set of predictors for subsequent ML modeling. In the first stage, LASSO regression with 10-fold cross-validation selected the optimal penalty parameter corresponding to the minimum deviance within one standard error (lambda.1se), yielding an initial set of 16 variables with non-zero coefficients. To enhance selection stability, we then performed bootstrap analysis with 100 resamples and retained predictors that appeared in at least 90% of the bootstrap iterations. The final selected predictors included age, depression, pain, health expectation, weight change, and four chronic conditions: dyslipidemia, hypertension, heart disease, and kidney disease [Figure 1]. Multicollinearity among the 9 selected predictors was assessed using the variance inflation factor (VIF), and all VIF values were below 5, indicating no significant multicollinearity concerns [Supplementary Table 4].

Among the seven ML models, ANN and LR demonstrated the most favorable discriminative ability in the testing set, with AUC values of 0.758 (95%CI: 0.720-0.791) and 0.757 (95%CI: 0.718-0.790), respectively [Figure 2 and Supplementary Figure 5]. In terms of calibration, ANN achieved the lowest Brier score of 0.113 (95%CI: 0.102-0.125), closely followed by LR with a Brier score of 0.114 (95%CI: 0.101-0.126), indicating acceptable calibration in the internal test set. Decision Curve Analysis (DCA) further revealed that both models provided the highest net clinical benefit across a range of threshold probabilities in the testing set. At the Youden-derived threshold, ANN and LR performed comparably (sensitivity 0.74 vs. 0.72, specificity 0.68 vs. 0.69, NPV 0.94 vs. 0.93; Supplementary Table 5). The modest positive predictive value (PPV) (~0.30) is expected given the low outcome prevalence (15.3%) and does not undermine clinical utility, as supported by DCA.

To provide a preliminary research tool for individualized risk prediction, a nomogram was constructed based on the LR model [Figure 3]. It is important to note that this nomogram requires external validation in independent cohorts before it can be recommended for routine clinical use. The nomogram integrates the selected predictors - including age, depression, pain, health expectation, weight change, dyslipidemia, hypertension, heart disease, and kidney disease - allowing for straightforward estimation of CKM multimorbidity probability by summing the points assigned to each risk factor. The calibration plot demonstrated acceptable calibration in the internal test set, with the Hosmer-Lemeshow test yielding a non-significant result, indicating no evidence of poor calibration in this internal evaluation. The nomogram is interpreted by summing the points for each predictor, then reading the corresponding predicted probability from the total points axis; its discrimination and calibration performance are reported above and are based on the testing set.

To elucidate the decision-making process of the ANN model and identify the key drivers of CKM multimorbidity risk, SHAP analysis was performed [Figure 4]. The SHAP bar plot ranks feature importance based on mean absolute SHAP values, revealing that hypertension, dyslipidemia, depression, kidney disease, and pain are the top five contributors to CKM multimorbidity risk. The beeswarm summary plot provides a comprehensive overview of SHAP value distributions for all nine key features. For categorical variables, the presence of hypertension, dyslipidemia, heart disease, kidney disease, depression, and pain consistently increased predicted CKM multimorbidity risk, while poorer health expectation (lower scores) and specific patterns of weight change (particularly weight gain or loss) were also strongly associated with higher risk. For the continuous variable age, a monotonic positive relationship with CKM multimorbidity risk was observed, indicating that older individuals faced substantially higher predicted risk. Scatter dependence plots further illustrate the marginal effect of age, confirming its linear positive association with SHAP values. SHAP analysis at the individual level revealed contrasting risk profiles: low-risk individuals were characterized by the absence of key risk factors, including hypertension, dyslipidemia, depression, and stable weight with younger age, while high-risk individuals exhibited the opposite combination.

Our parsimonious nine-predictor model demonstrated moderate performance in internal testing (AUC 0.758), aligning with recent large-scale studies while revealing important distinctions. Wang et al., using CHARLS data, reported that metabolic multimorbidity was associated with increased risks of CVD and kidney disease; our findings extend this work by showing that metabolic conditions, when combined with prior CVD and kidney disease, form a predictive signature for incident CKM multimorbidity rather than merely serving as risk factors for individual outcomes^[41]. Notably, diabetes - despite its established role - was not retained in our final model. This may reflect high collinearity with other metabolic predictors in our overweight/obese population, or that hypertension and dyslipidemia already capture substantial metabolic risk information. Formal correlation analysis [Supplementary Table 6] confirmed moderate correlations between diabetes and hypertension (r = 0.42) and dyslipidemia (r = 0.38). Clinically, this does not diminish diabetes’ importance; rather, in this population with hypertension and dyslipidemia, diabetes adds limited incremental predictive value for 3-year CKM multimorbidity. Our model should therefore be used as a screening tool to identify high-risk individuals who may benefit from further metabolic evaluation, including diabetes testing. This observation aligns with Song et al., who found that the C-reactive protein-triglyceride-glucose index outperformed individual components in predicting CKM mortality^[42].

Beyond traditional cardiometabolic risk factors, our analysis uncovered a prominent role for psychological factors - particularly depression and pain - ranking among the top five predictors. This resonates with the emerging understanding that CKM syndrome involves neuroendocrine and behavioral pathways. The inflammatory hypothesis linking depression to cardiometabolic disease is consistent with a potential mechanism: chronic low-grade inflammation, reflected by elevated CRP and pro-inflammatory cytokines, may reflect a shared pathway underlying both depressive symptoms and metabolic dysregulation^[42]. Pain may serve as a marker of musculoskeletal or neuropathic complications secondary to metabolic disease, while also contributing to physical inactivity and social isolation. Collectively, these findings suggest that comprehensive CKM risk assessment should extend beyond traditional biomedical markers to encompass psychosocial well-being^[43]. However, our observational design cannot distinguish whether depression and pain are independent drivers, proxies for systemic inflammation, or downstream consequences of early subclinical organ damage; future studies with repeated measures and longitudinal mediation analyses are needed to disentangle these pathways.

In contrast to previous studies emphasizing lifestyle factors, physical activity and sleep duration were not retained in our final prediction model, despite significant univariate differences. This may be because our study population was restricted to individuals with overweight or obesity, among whom the protective effects of physical activity might be attenuated by the predominant metabolic risk conferred by excess adiposity^[44]. Additionally, physical activity may exert effects through mediating pathways (e.g., blood pressure control, inflammation reduction) that are captured directly by disease indicators (hypertension, dyslipidemia) in our model^[45]. Third, our three-year follow-up window may be insufficient to capture cumulative protective effects of physical activity.

Another novel aspect pertains to weight dynamics. Our model retained weight change patterns - rather than baseline BMI alone - as a significant predictor, with both weight gain and loss associated with increased risk compared to stable weight. This finding aligns with the life-course perspective emphasizing weight trajectory over static adiposity^[46]. The finding that both gain and loss predicted CKM multimorbidity may reflect heterogeneity: intentional weight loss through lifestyle modification likely confers benefit, whereas unintentional loss due to underlying illness signals increased risk. Our dataset did not distinguish between these, representing an important direction for future research.

Finally, while socioeconomic and environmental factors did not emerge in our final parsimonious model, their indirect influence warrants discussion. Their effects may be mediated through retained clinical predictors (hypertension, dyslipidemia, depression) that represent the biological embedding of social adversity. Thus, although not appearing in the final model, these distal determinants remain fundamental to understanding CKM disparities and designing equitable interventions. We recognize that hypertension, dyslipidemia, heart disease, and kidney disease are both predictors and components of the outcome. This overlap reflects our design: predicting progression from ≤ 1 to ≥ 2 CKM conditions - so the model targets those with existing single-system disease, not first-onset in healthy persons.

This study has several notable advantages. To the best of our knowledge, it is the first investigation to construct ML models specifically designed for predicting CKM multimorbidity in a high-risk cohort consisting of Chinese adults with overweight or obesity. Second, our rigorous two-stage feature selection combining LASSO with bootstrap stability analysis enhances reliability and generalizability. Third, comprehensive evaluation across seven algorithms with assessment of discrimination, calibration, clinical utility, and interpretability provides a holistic understanding. Fourth, SHAP analysis enables clinically meaningful interpretation of the neural network model. Fifth, a nomogram based on LR provides a proof-of-concept tool for individualized risk prediction (pending external validation).

Several limitations warrant consideration. First, the relatively short three-year follow-up window may underestimate cumulative CKM multimorbidity incidence and limit detection of longer-latency predictors. We used Wave 3 (2015) as baseline because key biomarkers (HbA1c, lipid fractions) and consistent depression/pain measures were unavailable in Wave 1 (2011-2012); using Wave 1 would have introduced substantial missing data and biased estimates. Future studies with longer follow-up are needed to confirm our findings. Second, CKM multimorbidity ascertainment relied partly on self-reported physician diagnoses, which may introduce misclassification bias, although we supplemented with physical measurements, laboratory biomarkers, and medication use to enhance accuracy. Specifically, cardiovascular and kidney disease definitions were based on self-reported diagnoses, which may introduce recall or reporting bias. Formal sensitivity analyses using alternative diagnostic thresholds were not performed due to the absence of a gold-standard external validation cohort. Medication use during follow-up was not included as a predictor because it represents an intermediate consequence of baseline diseases rather than an independent upstream risk factor; however, differential treatment effects could influence outcomes, and future studies should examine this using time-varying approaches. Additionally, anxiety was not assessed due to CHARLS data limitations; its omission may modestly underestimate psychological risk. Third, despite comprehensive feature selection, unmeasured confounders such as dietary patterns, genetic factors, and medication adherence may influence CKM multimorbidity risk. We also acknowledge that the weight change variable conflates intentional and unintentional weight fluctuations, which may have opposed prognostic value; future studies should stratify by weight loss intentionality. Fourth, our study population was restricted to middle-aged and older Chinese adults with overweight or obesity who had zero or one CKM disease group at baseline, limiting generalizability to other populations and to prediction of first-onset CKM disease. The model is intended to predict progression from zero or one CKM condition to overt multimorbidity, not first onset of any individual CKM disease. CHARLS uses a multistage probability sampling design; our analysis did not incorporate sampling weights or design effects, as the focus was individual-level prediction. Ignoring these features may affect variance estimation and generalizability, which external validation should address. Fifth, while we employed multiple imputation for missing data, some bias may persist if data were not missing at random. Without external validation in a geographically or demographically distinct population, any claims of generalizability remain speculative, and immediate clinical translation is not warranted. Sixth, the modest improvement of ML algorithms over LR suggests that in this specific context, traditional regression may suffice for clinical application, though the SHAP insights from complex models remain valuable for understanding risk factor contributions. This near-equivalence highlights an important implementation consideration: complex models require greater computational resources and specialized expertise, whereas LR is simpler, more transparent, and readily deployed. In the absence of substantial performance gains, the choice should prioritize interpretability and ease of deployment, reserving complex ML for contexts where non-linearity is pronounced or interaction effects are strong. Seventh, and most critically, our model was internally evaluated using a train-test split rather than externally validated in an independent cohort. Therefore, our findings should be considered preliminary, and claims of generalizability remain speculative until external validation is performed.

This model is intended to predict progression from zero or one CKM condition to overt multimorbidity; it is not designed for screening completely disease-free individuals. Thus, the inclusion of baseline CKM components as predictors is appropriate for this progression-focused application. Although the model includes several established clinical predictors, its novelty lies in the inclusion of psychosocial factors and weight change dynamics, as well as the systematic comparison of ML algorithms against simple regression to quantify any non-linear advantage. For clinical practice, the identified predictor set - particularly the prominence of modifiable factors including depression, pain, and weight change alongside traditional cardiometabolic conditions - suggests that comprehensive CKM risk assessment should extend beyond conventional biomedical markers to include psychological well-being and weight trajectory. The nomogram provides an intuitive proofofconcept tool for research purposes; it is not ready for routine clinical use and requires external validation in independent cohorts. With that caveat, it may eventually help identify high-risk individuals who could benefit from intensive lifestyle interventions or closer monitoring. The comparable performance of LR to complex ML algorithms suggests that implementation in resource-constrained settings need not require sophisticated computational infrastructure. For research, our findings highlight several priority areas. First, the prominent role of psychological factors warrants investigation into whether interventions targeting depression and pain management can reduce CKM multimorbidity incidence. Second, the importance of weight change patterns over static adiposity measures suggests that longitudinal weight trajectories merit greater attention in risk prediction research. Third, future studies should examine whether predictors differ between overweight/obese and normal-weight individuals, potentially revealing distinct pathophysiological pathways. While socioeconomic and environmental factors were not retained in our final parsimonious model, their indirect influence warrants discussion; their effects may be mediated through retained clinical predictors (hypertension, dyslipidemia, depression) that represent the biological embedding of social adversity. Formal mediation analysis is needed to quantify how these distal determinants translate into proximal clinical risk markers, which would further strengthen the public health relevance of our findings. Although our study developed a static nomogram, future clinical implementation would require regular monitoring for calibration drift and predefined protocols for periodic model retraining. Practical risk thresholds and corresponding clinical actions were not pre-specified; DCA confirms net benefit over a range of probabilities, but implementation studies are needed to define optimal intervention thresholds for specific healthcare settings. Finally, external validation in independent cohorts and longer follow-up periods are essential before widespread clinical implementation to confirm generalizability and assess whether early risk signatures predict later disease trajectories.