This study retrospectively included psoriasis patients who were hospitalized for the first time from the MIMIC-IV (Medical Information Mart for Intensive Care IV) database for clinical research. The MIMIC-IV database is a comprehensive dataset developed and maintained by the Massachusetts Institute of Technology Laboratory for Computational Physiology. It encompasses medical information related to patients admitted to the intensive care unit of Beth Israel Deaconess Medical Center (https://physionet.org/content/mimiciv/3.0/).

Inclusion criteria for patients were as follows: (1) patients diagnosed with psoriasis based on ICD-9 codes (6960, 6961) and ICD-10 code (L40) in the MIMIC database; (2) patients admitted to the hospital for the first time. Exclusion criteria included: (1) patients with missing laboratory test results; and (2) patients without recorded survival time ( Figure 1 ). The diagnosis of sepsis was based on the Sepsis 3.0 diagnostic criteria. Patients were required to have a concurrent infection and a Sequential Organ Failure Assessment (SOFA) score of ≥ 2 (18, 19). It is worth noting that, due to the limitations of the database, the autoimmune diseases and sepsis involved in this study were defined using ICD - 10 - CM diagnostic codes and the free - text information in patients’ discharge summaries and previous published studies were referred to (20).

Included patients were classified into sepsis and non-sepsis groups based on the occurrence of sepsis. One of the authors of this study, Zheng, successfully completed the “Data or Sample Research” training program (CITI) and passed the examination (Record ID: 39635575), subsequently obtaining access to the dataset. Considering that the MIMIC-IV database is publicly accessible and consists of de-identified patient data, this study did not require informed consent or ethical approval.

Data extraction was performed using the Decisionlinnc1.071 software (https://www.statsape.com). In this study, the clinical parameters extracted from the MIMIC database included age, sex, hematocrit, hemoglobin, platelet count, red cell distribution width, red blood cell count, white blood cell count, anion gap, serum total calcium, chloride concentration, glucose levels, potassium concentration, sodium concentration, creatinine levels, blood urea nitrogen levels, body mass index (BMI), and histories of hypertension, type 2 diabetes, coronary artery disease, chronic obstructive pulmonary disease (COPD), chronic kidney disease (CKD) and acute kidney injury (AKI). These parameters encompass hematological indices, electrolyte balance, metabolic status, and chronic disease history, aiming to provide a comprehensive assessment of the patients’ prognosis and their potential impact on the risk of sepsis. The diagnosis of sepsis was based on the Sepsis-3 criteria, identifying patients with infection and a Sequential Organ Failure Assessment (SOFA) score of ≥2 after admission (21). In the cross-sectional study section, laboratory parameters were extracted from the first biochemical analysis results obtained after patient admission. The patients’ routine blood tests were performed on the first day post - admission. The time of the first biochemical examination occurred within 7 days after admission. For the longitudinal study of serum calcium, data were collected from the first measurement taken upon admission, as well as subsequent measurements up to day seven.

The primary outcome of this study was the incidence of sepsis in hospitalized patients with concomitant psoriasis. The secondary outcomes included the all-cause mortality rate within 90 days post-admission and the mortality rate within 365 days post-admission.

Using the occurrence of sepsis as the outcome event, patients were randomly divided into a training set (780 cases) and a validation set (520 cases) in a 6:4 ratio ( Supplementary Table S1 ). The survival time was defined as the time from admission to the occurrence of all-cause mortality, with follow-up time points set at 90 days and 365 days post-admission. A Cox proportional hazards model was established. Initially, in the training set, independent risk factors influencing the development of sepsis in patients were identified using the Least Absolute Shrinkage and Selection Operator (LASSO) regression model. Variables with non - zero coefficients in the results of LASSO regression were selected to construct the subsequent nomogram prediction model. The nomogram prediction model was constructed using logistic regression. The model’s predictive accuracy was assessed in both the training and validation sets using the Receiver Operating Characteristic (ROC) curve. The model’s discriminative ability was validated through calibration curves, and clinical decision curves were plotted to evaluate the potential benefits to patients. Furthermore, using the feature variables selected from the training set, the Shapley Additive Explanations (SHAP) values were calculated utilizing a machine learning random forest algorithm. The SHAP is a method used to explain the prediction results of machine learning models. The basic principle of this method lies in calculating the incremental impact of each feature on the model output, enabling the interpretation of the model’s behavior at both the global and local levels. The importance of the feature variables was visualized using a beeswarm plot, allowing for the further identification of clinical indicators that contribute most significantly to the occurrence of sepsis for additional analysis (22). To further refine the predictive model, we compared the predictive capabilities of five machine learning algorithms—Decision Tree, K-Nearest Neighbors (KNN), Logistic Regression, Random Forest, and XGBoost—in predicting the occurrence of sepsis within the overall sample.

This study utilized R software (http://www.R-project.org; version 3.4.3) for data processing. The Shapiro-Wilk test was employed to assess the normality of the data. For normally distributed continuous variables, results are presented as means ± standard deviation, and intergroup comparisons were conducted using the Student’s t-test. Categorical data were described using frequencies and percentages, with intergroup comparisons made using the Chi-square test or Fisher’s exact test. For the features selected by LASSO regression, the SHAP values were referenced to further identify the most contributive variables, leading to the construction of three distinct regression models. Model 1 served as a basic model without any adjustments for covariates. Model 2 adjusted for age and sex as covariates to eliminate potential confounding effects related to demographics. Model 3 further expanded upon Model 2 by incorporating additional features identified through LASSO regression. The regression models included both logistic regression for sepsis occurrence and Cox regression for all-cause mortality at 90 days and 365 days. Subgroup analyses were conducted to evaluate the impact of feature variables on the study outcomes across different subpopulations. Additionally, restricted cubic splines (RCS) were used to analyze the nonlinear relationships between the most contributive feature variables and the occurrence of sepsis as well as all-cause mortality. Mediation analysis was performed to assess potential mediating pathways through which feature variables influence sepsis and all-cause mortality. After establishing the impact of feature variables on sepsis and all-cause mortality in hospitalized psoriasis patients, a Group-Based Trajectory Model (GBTM) was employed to identify potential trajectories of feature variables, with sepsis occurrence as the outcome measure. The selection of the optimal number of groups involves an iterative process. A polynomial function is applied to the trajectories to determine the number of groups, with the model ranging from 1 group (indicating no significant trajectories) to 5 groups. The evaluation of model fitting criteria is considered from the following aspects: (1) Focus on evaluating the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC); (2) Require that each trajectory group includes at least 5% of the population; (3) The average post - hoc assignment probability (Avepp) with a value greater than 0.7; (4) The simplicity and clinical interpretability of the model (23, 24). Logistic regression was used to analyze the effects of different trajectories on the incidence of sepsis. Finally, two sensitivity analyses were conducted. The first one was to exclude potential biases that might be introduced during the data imputation process. This step involved deleting all samples with missing laboratory values or containing outliers, and then re - analyzing the impact of characteristic variables on the incidence of sepsis and all - cause mortality. The second step was to further remove patients with comorbid CKD and those using immunosuppressants based on the previous step, and then evaluate the impact of characteristic variables. In terms of missing value processing, the threshold for missing laboratory values was set at 5% ( Supplementary Table S2 ), and for laboratory indicators with missing rates below 5%, multiple imputation was performed using the Predictive Mean Matching method. After imputation, the complete measurement data were assessed for potential outliers using Z-scores. Values with a Z-score greater than 3 or less than -3 were considered to be outlier (25). Subsequently, the outliers identified by the Z - score method were converted to “NA”, and the K-Nearest Neighbors (KNN) method was employed for imputation (26). A two-sided p-value of < 0.05 was considered statistically significant.

A total of 1,300 hospitalized patients with psoriasis were included in this study, of which 213 patients (16.38%) were classified into the sepsis group, while 1,087 patients were in the non-sepsis group. In terms of biochemical parameters, the serum calcium level in the sepsis group was significantly lower than that in the non-sepsis group (8.29 ± 0.72 vs. 8.78 ± 0.60, P < 0.001). Additionally, the anion gap (14.10 ± 3.19 vs. 13.43 ± 2.98, P = 0.003), blood glucose levels (131.49 ± 43.1 vs. 119.67 ± 39.74, P < 0.001), and renal function indicators (creatinine: 1.13 ± 0.58 vs. 0.99 ± 0.47; blood urea nitrogen: 21.61 ± 11.89 vs. 17.88 ± 10.64, both P < 0.001) were significantly elevated ( Table 1 ).

In the training set, we conducted LASSO regression analysis based on the differential indicators identified in Table 1 . Using a lambda value of 1se = 0.035, we selected the following feature variables: platelet count, white blood cell count (WBC), calcium, blood urea nitrogen, anion gap, and glucocorticoid use ( Figure 2A ). Logical regression models were constructed using these selected characteristic variables. After the collinearity test, the variance inflation factors were all less than 10. A nomogram model was developed based on the logical regression model ( Figure 2B ).

In the training set, the model achieved a C-index of 0.813, and the goodness-of-fit test (Hosmer-Lemeshow test) yielded a chi-squared value of 13.251 with a P-value of 0.104. The area under the curve (AUC) was 0.813, with a 95% confidence interval (CI) of 0.769-0.857 ( Figure 3A ). The calibration curve indicates a high degree of agreement between the predicted probability and the actual probability ( Figure 3B ). Moreover, the Decision Curve Analysis (DCA) also demonstrates good clinical benefit - gaining ability ( Figure 3C ). In the validation set, the C-index was 0.763, with a goodness-of-fit test yielding a chi-squared value of 8.483 and a P-value of 0.388. The AUC was 0.763, with a 95% CI of 0.703-0.823 ( Figure 3D ). Calibration curves ( Figure 3E ) and DCA curves ( Figure 3F ) also indicated that the model possesses good predictive capability in the validation sets.

Based on the data of the training set, the SHAP values of the feature variables were calculated using the machine - learning random forest algorithm, and their importance was sorted and presented using a bee swarm plot. The results indicated that serum calcium had the greatest contribution among the selected feature variables in predicting the occurrence of sepsis ( Figure 4A ). Furthermore, the RCS curve analysis in the training set suggested a nonlinear relationship between serum calcium levels and the occurrence of sepsis ( Figure 4B ).

The logistic regression model demonstrated the best performance across various evaluation metrics, achieving an accuracy of 84.8%, an AUC of 0.742, a precision of 0.682, and a specificity of 0.984. In comparison, the random forest model exhibited an accuracy of 83.7%, an F1 score of 0.190, a Matthews correlation coefficient (MCC) of 0.197, and an AUC of 0.766, indicating satisfactory overall performance ( Figure 5 ).

The logistic regression model emerged as the most effective tool for predicting hospitalization outcomes in patients with psoriasis, exhibiting high accuracy and excellent specificity, thus making it suitable for clinical prediction ( Supplementary Table S3 ).

We analyzed the relationship between serum calcium levels and the occurrence of sepsis during hospitalization in patients with psoriasis. The results indicated a significant negative correlation between serum calcium levels and the incidence of sepsis. In Model 1, the odds ratio (OR) for serum calcium levels was 0.290 (95% CI: 0.225–0.371, P < 0.001). In the adjusted models, the OR for serum calcium levels showed slight variation but remained significantly negatively correlated across all levels (all P < 0.05). Furthermore, after adjusting for covariates such as age, sex, platelet count, white blood cell count, blood urea nitrogen, anion gap, and glucocorticoids, the association between serum calcium levels and the occurrence of sepsis remained significant. The trend tests across all models reached statistical significance (P < 0.001) ( Table 2 ).

Subgroup analyses revealed that this reverse association was consistently observed across different clinical characteristics. Notably, in the subgroup analysis for AKI, a significant negative correlation between serum calcium and sepsis risk was observed in non-AKI patients (OR = 0.303, 95% CI: 0.192–0.496, P < 0.001), while this association was attenuated in AKI patients (OR = 0.595, 95% CI: 0.378–0.937, P = 0.025). Additionally, a significant interaction between the subgroups was noted (P for interaction = 0.023) ( Supplementary Table S4 ).

Serum total calcium exhibited a significant negative correlation with both 90-day and 365-day all-cause mortality rates. In Model 1, which did not adjust for any covariates, the hazard ratio (HR) for total calcium associated with 90-day mortality was 0.574 (95% CI: 0.419–0.785, P < 0.001), while the HR for 365-day mortality was 0.662 (95% CI: 0.528–0.831, P < 0.001). In Model 3, which adjusted for various covariates, the HR for 90-day mortality was 0.594 (95% CI: 0.422–0.835, P = 0.003), and the HR for 365-day mortality was 0.642 (95% CI: 0.502–0.821, P < 0.001). Furthermore, analysis grouped by quartiles of total calcium revealed a significant downward trend in both 90-day and 365-day mortality rates with increasing calcium levels (P for trend = 0.012 and 0.004, respectively) ( Table 3 ).

Subgroup analysis indicated that the serum calcium was negatively correlated with the 90 - day all - cause mortality (HR = 0.662, 95% CI: 0.476–0.920, P = 0.014). Gender-based subgroup analysis revealed that the negative correlation between serum calcium and mortality was more pronounced in male patients (HR = 0.472, 95% CI: 0.306–0.729, P < 0.001), while no significant association was observed in female patients (P = 0.870). Additionally, no significant association was found in patients with concurrent COPD (P = 0.219) ( Supplementary Table S5 ). Similar effects were observed in the subgroup analysis related to 365-day all-cause mortality ( Supplementary Table S6 ).

Platelet count serves as a significant mediator in the relationship between serum calcium and 90-day all-cause mortality. The proportion of the mediation effect was found to be 0.246 (95% CI: 0.066 - 0.590, P = 0.020). In the analysis of 365-day all-cause mortality, the proportion of the mediation effect for this analysis was 0.220 (95% CI: 0.076–0.450, P < 0.001) ( Table 4 ) ( Figure 6 ).

A total of 151 patients had complete serum calcium data measured repeatedly on the 1st, 3rd, and 5th days after admission, and were finally included in the GBTM analysis. With reference to the AIC criterion, BIC criterion and taking into account the simplicity of the model, the three - trajectory model was finally determined for selection.

Using a three-trajectory model, three distinct trajectory patterns were identified. Trajectory 1 exhibited a slow increase in calcium levels, ranging from 8.5 to 9. Trajectory 2 demonstrated an initial decline followed by an increase, starting below 8. Trajectory 3 began with higher calcium levels above 9 but showed a downward trend ( Figure 7 ).

Comparing the differences in adverse prognostic outcomes among the three estimated populations revealed significant differences in the incidence of sepsis (P = 0.021). Specifically, Trajectory 3 had the lowest sepsis incidence at 28.57%, while Trajectory 2 exhibited the highest incidence at 55.88%. These findings may reflect variations in infection risk across the different trajectory groups ( Table 5 ).

In Model 1, the risk of sepsis for patients in Trajectory 2 was significantly increased compared to the baseline group (Trajectory 1), with an OR of 2.303 (95% CI: 1.144-4.723, P = 0.021). This indicates that patients in Trajectory 2 have a higher risk of developing sepsis. After adjusting for age and sex in Model 2, this association remained significant, with an OR of 2.400 (95% CI: 1.163-5.068, P = 0.019). This further supports the conclusion that patients in Trajectory 2 are at a higher risk for sepsis ( Table 6 ).

In the sensitivity analysis of the retained sample, comparisons between the sepsis group and the non-sepsis group indicated consistent inter-group difference metrics with those observed post-imputation ( Supplementary Table S7 ). Serum calcium levels consistently showed a significant inverse correlation with the occurrence of sepsis ( Supplementary Table S8 ). Regarding the impact on all-cause mortality at 90 and 365 days, significant inverse association was observed across all three models ( Supplementary Table S9 ). The RCS curve analysis also revealed a non-linear relationship between calcium levels and the incidence of sepsis, as well as all-cause mortality at 365 days ( Supplementary Figure S1 ). Additionally, the mediation analysis further supports the mediating effect of platelets ( Supplementary Table S10 ). After further excluding patients with comorbid CKD and those using immunosuppressants, the impact of serum calcium on the incidence of sepsis ( Supplementary Table S11 ), the impact of serum calcium on all - cause mortality ( Supplementary Table S12 ), and the results of the mediation analysis ( Supplementary Table S13 ) were consistent with the previous findings.