Data from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database(mimic.mit.edu/) was utilized in the present study, developed by Beth Israel Deaconess Medical Center (19). The MIMIC-IV database contains de-identified clinical data from >400,000 ICU admissions, encompassing comprehensive records such as patient demographics, diagnoses, treatments and medications. All data is rigorously anonymized in compliance with privacy regulations to ensure patient confidentiality. The present authors completed the required training course for MIMIC-IV and were granted access to the database. As the database contains only de-identified information, the requirement for informed consent was waived for the present analysis.

A total of 65,346 patients with their first ICU admission were initially identified. From this cohort, 8,451 patients with a diagnosis of malignancy were selected based on the Charlson Comorbidity Index (CCI) (20,21). The following exclusion criteria were subsequently applied: i) Patients aged under 18 years (n=0); ii) those with an ICU length of stay <24 h (n=1,710); and iii) patients lacking lactate or albumin measurements on the first day of ICU admission (n=5,107). This resulted in the exclusion of 6,817 patients. Consequently, a final cohort of 1,634 critically ill patients with malignancy was included in the analysis. These patients were further stratified into three groups according to their LAR values: Tertile 1 (T1; n=539), tertile 2 (T2; n=556) and tertile 3 (T3; n=539; Fig. 1).

All data for the present study were extracted from the MIMIC-IV database using PostgreSQL software (version 17.4, postgresql.org/). The extracted data pertained to the first 24 h of ICU admission and included: i) Baseline demographic information; ii) vital signs; iii) severity-of-illness scores, including the Sequential Organ Failure Assessment (SOFA) and Logistic Organ Dysfunction System (LODS) score; iv) history of chronic comorbidities (such as coronary artery disease, congestive heart failure, cerebrovascular disease, chronic lung disease, liver disease, diabetes or hypertension); v) laboratory parameters measured within 24 h of ICU admission (including red blood cell count, white blood cell count, platelet count, sodium, potassium, calcium, glucose, lactate, albumin, anion gap, blood urea nitrogen (BUN), creatinine, international normalized ratio (INR), prothrombin time (PT), activated partial thromboplastin time (APTT) and urine output); and vi) details regarding medication administration and treatment regimens (such as epinephrine, norepinephrine, mechanical ventilation and continuous renal replacement therapy). Data regarding hospitalization-associated outcomes were also collected, encompassing hospital and ICU length of stay, as well as 30-day and 360-day all-cause in-hospital mortality. Baseline laboratory data were defined as the first measurements obtained within 24 h of ICU admission (rather than the highest or lowest values) to reflect the initial physiological status and minimize the influence of subsequent therapeutic interventions.

In the present study, different strategies were employed to handle missing data. For variables with a percentage of missing values <20%, multiple imputation was applied to fill the gaps. Specifically, the multiple imputation method was used to generate several imputed datasets, thereby reducing the potential bias associated with single imputation and ensuring the accuracy and robustness of the imputed data (22). By contrast, variables with >20% missing values were excluded from the subsequent analysis to prevent their influence on the findings.

LAR, as the exposure of interest, was calculated using the following formula: LAR=lactate (mmol/l)/albumin (mg/dl). The values for both lactate and albumin were obtained from the first 24 h following ICU admission. The primary outcome of the present study was 30-day all-cause mortality. The secondary outcome was 360-day all-cause mortality. Follow-up for all outcomes commenced from the first day of hospital admission, aiming to assess both in-hospital and post-discharge long-term mortality risk.

Normality of all continuous variables was assessed using the Shapiro-Wilk test. Variables conforming to a normal distribution are presented as the mean ± SD and group comparisons were performed using an independent sample t-test. Non-normally distributed variables are summarized as the median with interquartile range (IQR) and the Mann-Whitney U test was employed for group comparisons. Categorical variables are expressed as frequency and percentages (%), and differences were assessed using the χ2 test, unless any expected cell frequency was less than 5, in which case Fisher's exact test was used.

Survival rates across groups were visualized and compared using Kaplan-Meier curves and the log-rank test, respectively. Kaplan-Meier curves were used to plot survival rates for different groups, allowing a visual comparison of patient survival across groups. Differences between groups were assessed using the log-rank test to determine whether significant differences existed among the survival curves. To identify risk factors, univariate Cox proportional hazards regression was initially performed. In the present study, univariate Cox regression analysis was first performed to identify potential risk variables. Variables with a significance level of P<0.05 from the univariate analysis, along with those considered clinically relevant, were subsequently incorporated into a multivariate Cox regression model. This model was used to evaluate the independent predictive value of the LAR for both 30-day and 360-day all-cause mortality. Multivariate Cox regression analysis was initially performed in the crude model without adjusting for any confounding factors. Subsequently, potential confounders including sex, race, age and weight were progressively incorporated into the adjusted models. Further adjustments included clinical variables such as norepinephrine use, continuous renal replacement therapy, heart rate, systolic blood pressure, respiratory rate, potassium, anion gap, BUN, INR and urine output. The covariate selection was guided by a pre-defined clinical framework, consistent with established principles of confounder selection in epidemiological research, rather than a purely data-driven approach (23). CCI was included to account for baseline comorbidity burden, while the SOFA score was incorporated to reflect the severity of acute illness at ICU admission. Given that LAR is derived from lactate and albumin, both of which are closely associated with shock severity, inflammatory response, nutritional status and liver function, a multicollinearity assessment was further performed. All included variables exhibited Variance Inflation Factor (VIF) values <5, indicating the absence of significant multicollinearity and supporting the stability and reliability of the model estimates.

The potential nonlinear association between LAR and mortality risk was explored using a Restricted Cubic Spline (RCS) model with four knots. To explore nonlinear associations between the variables and 30-day and 360-day all-cause mortality, RCS with three knots were employed. Furthermore, interaction tests were conducted to assess the heterogeneity of the LAR effect across different pre-specified subgroups. Interaction tests were also performed to assess differences in the effect of the variables across subgroups. Specifically, subgroup analyses were conducted based on age (<65 years and ≥65 years), sex (female and male), chronic lung disease (absent and present), liver disease (absent and present), diabetes (absent and present) and hypertension (absent and present).

To develop machine learning models, the present study first split the dataset into a training set and a test set at a ratio of 7:3. On the training set, the Boruta algorithm (version 8.0.3) was employed in R software (version 4.4.1) for feature selection to identify the most useful variables for predicting the risk of mortality. Subsequently, based on the selected variables, a number of machine learning models were constructed, including Ridge regression, Elastic Net (ENet), support vector machine (SVM), K-nearest neighbors (KNN), random forest (RF) and XGBoost. After model construction, the performance of these models was evaluated using the test set. The evaluation metrics for model performance included the receiver operating characteristic (ROC) curve, precision-recall (PR) curve, calibration curve and decision curve. These metrics enabled a comprehensive assessment of each model's performance in predicting 30-day all-cause mortality among patients with malignancy in the ICU, thereby facilitating the selection of the optimal predictive model. All statistical analyses were performed using R software (version 4.5.1; Posit Software, PBC). A two-tailed P<0.05 was considered to indicate a statistically significant difference for all tests.

A total of 1,634 patients was included in the final analysis. The median age of the cohort was 67.77 years (IQR: 60.20–76.46). The overall median LAR was 0.75 (IQR: 0.46–1.26). The present study population was stratified into tertiles based on LAR values. Comparison of baseline characteristics across these LAR tertiles revealed statistically significant differences in key clinical and physiological parameters, including vital signs (heart rate, systolic and diastolic blood pressure, and respiratory rate), severity-of-illness scores (LODS and VIF), and the prevalence of chronic comorbidities such as congestive heart failure, cerebrovascular disease, chronic pulmonary disease and liver disease (Table I; all P<0.05).

Kaplan-Meier survival curves were plotted for patients stratified by LAR tertiles and compared using the log-rank test. The results demonstrated statistically significant differences in mortality among the LAR tertiles at both 30-day and 360-day follow-ups (Fig. 2; P<0.05). Patients in T1 exhibited the most favorable prognosis, whereas those in T3 demonstrated the worst prognosis. These findings indicated that elevated LAR levels were associated with poorer short-term and long-term outcomes in critically ill patients with malignancy.

Variables for the multivariate Cox regression models were selected based on both univariate Cox regression analysis (P<0.10) and established clinical evidence regarding mortality predictors in critically ill patients with cancer. Covariates with recognized clinical relevance and biological associations with mortality, including organ dysfunction assessed by the Sequential Organ Failure Assessment (SOFA) score and major comorbidities, were prioritized for adjustment (24,25). In addition, the variable selection strategy followed the principle of integrating statistical significance with clinical relevance, which is widely recommended in prognostic modeling studies to improve model interpretability and clinical applicability (26). The multivariate Cox regression models were then used to assess the associations of continuous LAR values and LAR tertiles with 30-day and 360-day all-cause mortality (Table II). For 30-day mortality, the continuous LAR remained a significant predictor of mortality risk in the fully adjusted model (model 3), with a HR of 1.13 (95% CI: 1.04–1.22; P=0.004). Analysis using LAR tertiles revealed that patients in the highest tertile (T3) continued to exhibit a significantly increased risk compared with the reference group (T1), with an HR of 1.29 (95% CI: 1.01–1.64; P=0.040). With regard to 360-day mortality, the continuous LAR was also a significant independent predictor in model 3 (HR=1.15; 95% CI: 1.07–1.23; P<0.001). Similarly, the tertile analysis determined that the T3 group was associated with a significantly elevated mortality risk (HR=1.26; 95% CI: 1.06–1.49; P=0.010).

To evaluate the incremental clinical value of LAR, a comparative analysis with the SOFA score was then performed. The results showed that the SOFA score alone had limited discriminative ability for predicting 30-day mortality [area under the curve (AUC)=0.540], whereas incorporation of LAR significantly improved the model performance, increasing the AUC to 0.622 (DeLong's test, P<0.001; Fig. S1A). LAR remained an independent predictor after adjustment for the SOFA score, indicating its prognostic robustness across different acute clinical settings. ROC curve analysis was also performed, identifying the optimal cut-off value of the LAR for predicting 30-day mortality as 0.760, with a sensitivity of 62.2% and a specificity of 56.2% (Fig. S1B). In clinical practice, this cut-off may serve as an additional tool for identifying patients with cancer who are at increased risk despite relatively stable conventional organ dysfunction scores, such as the SOFA score. Elevated lactate levels are associated with occult tissue hypoperfusion and metabolic stress (27), whereas hypoalbuminemia reflects systemic inflammation and impaired nutritional reserve (25). By integrating these pathophysiological dimensions, the LAR may provide complementary prognostic information beyond conventional organ dysfunction assessment and improve clinical risk stratification (28). Consequently, patients with elevated LAR values may warrant closer monitoring and more comprehensive clinical evaluation in critical care settings.

RCS was employed to assess the potential non-linear association between LAR and both 30-day and 360-day all-cause mortality. The results indicated no significant deviation from linearity for the association between LAR and mortality at either time point (nonlinearity P>0.05; Fig. 3). However, a significant overall positive association was observed, demonstrating a linear increase in mortality risk with rising LAR levels. Furthermore, subgroup analyses revealed no significant interaction effects, demonstrating the consistent association between elevated LAR and increased mortality risk across all predefined patient subgroups. While liver disease can influence both lactate metabolism and albumin synthesis, the present interaction analysis indicated that LAR remained a robust predictor of mortality irrespective of hepatic comorbidity, reinforcing its utility as a simple, integrated risk marker in the present heterogeneous population.

Subgroup analysis revealed no significant interaction effects between LAR and any pre-specified subgroups for both 30-day and 360-day all-cause mortality (all interaction P>0.05; Fig. 4). This indicated that the positive association between elevated LAR and increased mortality risk was consistent and independent of the subgroup factors examined. Specifically, stratified and interaction analyses were performed according to liver disease status, which exhibited a non-significant interaction effect (interaction P=0.375; Table III), supporting the consistency of LAR across different hepatic conditions.

Based on the selected variables, machine learning models were developed on the training set, including Ridge regression, ENet, SVM, KNN, RF and XGBoost. During model development, grid search was employed for hyperparameter tuning. Grid search is a systematic approach that considers all parameter combinations within a specified subset of the hyperparameter space to identify the configuration that maximizes model performance, thereby mitigating the risk of overfitting during the tuning process (29).

On the test set, the area under the ROC curve (ROCAUC) results for each model were as follows (Fig. 5A): Ridge regression was 0.7968 (95% CI: 0.7564–0.8372), ENet was 0.7900 (95% CI: 0.7489–0.8312), KNN was 0.7478 (95% CI: 0.7028–0.7928), RF was 0.7902 (95% CI: 0.7492–0.8313), XGBoost was 0.7832 (95% CI: 0.7423–0.8242) and SVM was 0.7974 (95% CI: 0.7571–0.8377).

On the test set, the area under the precision-recall curve (PRAUC) results for each model were as follows (Fig. 5B): Ridge regression was 0.6376 (95% CI: 0.5548–0.7121), ENet was 0.6161 (95% CI: 0.5333–0.6915), KNN was 0.5561 (95% CI: 0.4652–0.6291), RF was 0.6186 (95% CI: 0.537–0.6978), XGBoost was 0.6019 (95% CI: 0.5176–0.6874) and SVM was 0.5997 (95% CI: 0.5197–0.6812). These results indicated that the Ridge regression model achieved the best PRAUC performance on the test set, with the highest PRAUC value (0.6376), whereas the KNN model exhibited a relatively poorer PRAUC performance. Following comparisons of calibration curves and decision curves on the test set, the SVM was ultimately identified as the optimal model, demonstrating favorable predictive value (Fig. 5C and D).