Individualized resuscitation strategy for septic shock formalized by finite mixture modeling and dynamic treatment regimen

The study was conducted in 25 tertiary care teaching hospitals in China from January 2016 to December 2017. Participants were retrospectively enrolled by reviewing the electronic medical records, and the patients were followed up during the hospital stay. A site investigator was responsible for this study in each ICU. Additionally, a clinical research coordinator (CRC) was assigned to each hospital to ensure the quality of data collection. The study was approved by the ethics committee of the 8th Medical Center of General Hospital of Chinese People’s Liberation Army (approval no. 309201906171117). The written informed consent was waived by the ethics committee because the study did not involve any interventions. Data were deidentified and stored in an encrypted computer. This study was registered on the Chinese Clinical Trial Registry (Registration No. ChiCTR1900024418).

Sepsis was defined as suspected or documented infection plus an increase in the Sequential [Sepsis-related] Organ Failure Assessment (SOFA) score of 2 points or more. Baseline SOFA score was extracted from past medical history. SOFA score was assumed to be 0 if a subject had no known comorbidities or baseline laboratory measurements. Patients with septic shock were then identified by a vasopressor requirement to maintain a mean arterial pressure of 65 mmHg or greater and serum lactate level greater than 2 mmol/L (> 18 mg/dL) in the absence of hypovolemia (e.g., as determined by the CRCs from participating center based on clinical findings such as increased HR, low CVP, decreased blood pressure and pale, cool and clammy skin) [25]. Patients were enrolled if they had septic shock on ICU admission. Exclusion criteria included pregnancy, age younger than 18 years old, terminal illness or malignancy with do-not-resuscitate order, concomitant acute myocardial infarction or pulmonary embolism with hemodynamic compromise, conditions of immunodeficiency (i.e., hematological malignancy, neutropenia, organ transplantation) and surgical source of infection not controlled.

Clinical and laboratory variables were collected on days 0, 1, 2, 3 and 7 after ICU admission. For numeric variables, the minimum and maximum values during each of these days were collected. Demographic and baseline clinical data included age, gender, type of patient (elective surgery, emergency surgery, non-surgical), weight on admission, comorbidity and site of infection (abdominal, thorax, brain, blood stream, soft tissue and urinary tract infection). Vital signs of body temperature, arterial blood pressure, heart rate and respiratory rate were recorded. Acute physiology and chronic health evaluation (APACHE) II score was calculated within 24 h after ICU admission. Laboratory variables included pH, HCO₃, serum lactate, hemoglobin (HB), hematocrit (HCT), PaCO₂, P/F ratio, base excess (BE), platelet count, red blood cell distribution width (RDWCV), serum creatinine and total bilirubin. Fluid intake volume was calculated by summing up all crystalloids, colloids, blood products, nasogastric (NG) water, NG feed, parenteral nutrition and fluid intake associated with IV drugs administration. Fluid intake and output were measured on the daily basis. Vasopressors including norepinephrine, epinephrine, dopamine and dobutamine were recorded. Vasopressors were converted to equivalent dose of norepinephrine by the equation (all in mcg/kg/min, except vasopressin in units/min) [26]:Patients with 20% or more of missing values were excluded from analysis. For other patients with missing values, the longitudinal data were imputed by firstly applying last observation carried forward (LOCF) and then next observation carried backward (NOCB) methods [27].

The classes of septic shock were explored by using finite mixture modeling (FMM) by assuming Gaussian distributions of feature variables, and variances were constrained to be equal across classes, and covariances were fixed to 0 (Fig. 1). Correlation between feature variables was examined using Pearson’s correlation analysis. We removed highly correlated variables by domain knowledge. Candidate variables representing several key pathophysiological domains were included for FMM, such as baseline demographics (age, weight), disease severity (APACHE II), vital signs (SBP, DBP, HR, temperature, RR), tissue perfusion (lactate), internal environment (BE, pH, HCO₃), respiration (PaCO₂, PaO₂, PF), inflammatory responses (CRP, RDWCV), hematology (platelet) and renal function (urine output, creatinine). PaO₂, CRP and DBP were removed due to their correlation with other variables with correlation coefficient > 0.7. The FMM was fit to the combined dataset of feature vectors from all patients across days 0, 1, 2, 3 and 7, while allowing class transition across ICU days. The best number of classes was determined by both statistics and clinical importance. Lower values of AIC and SABIC and higher values of entropy were considered as better model fit. Bootstrap likelihood ratio test was performed to compare whether k-class model was better than (k − 1)-class model [28]. The minimum number of patients should be over 4% of the entire study population. The minimum probability of assigning to one class should be over 0.8; otherwise, the class membership is considered as unstable. The best number of classes was also confirmed by the k-means clustering analysis. Statistics such as cubic clustering criterion (CCC), Calinski and Harabasz (CH) index, Davies and Bouldin (DB) index, Hartigan, Krzanowski and Lai (KL) index, Marriot, Rubin and TraceW were reported because they were easily implemented in the package NbClust (V3.0) [29]. PCA was also used to visualize the identified classes to show that the classes of septic shock can be visualized in lower-dimensional space.

Characteristics of each class were compared using Kruskal–Wallis rank sum test or analysis of variance (ANOVA) for numeric data, and Chi-square test or Fisher’s exact test for categorical data [30]. Interactions between class membership and fluid volume (\(\mathrm{Class}\times \mathrm{Fluid}\,\mathrm{Volume}\)) or norepinephrine use (\(\mathrm{Class}\times \mathrm{Norepinephrine}\, \mathrm{Dose}\)) were explored in two multivariable Cox regression models with time-varying covariates. Other covariates including comorbidity, APACHE II, urine output, creatinine and age were adjusted for. A statistically significant interaction might indicate potential differing effect size of the intervention (either fluid volume or norepinephrine equivalence dose) on survival outcome in different classes.

Optimal dynamic treatment regimes can be inferred from observational medical data using reinforcement learning algorithm [31, 32]. Alternatively, DTR can also be used to estimate optimal treatment strategy across multiple treatment stages, so that the final clinical outcome can be optimized [33, 34]. In this study, the treatments are continuous variables including fluid volume intake and norepinephrine dosing. The regression-based method was used for estimating the optimal dosing strategy across days 0, 1, 2, 3 and 7 after ICU admission. More specifically, the mortality outcome \(E\left(Y|x,a\right)\) was modeled in terms of treatment-free model \(f\left({x}^{\beta }; \beta \right)\) and a blip function \(\gamma \left({x}^{\psi }, a; \psi \right)\): \(E\left(Y|x,a\right)=f\left({x}^{\beta }; \beta \right)+\gamma \left({x}^{\psi }, a; \psi \right)\), where \(x\) is a vector of covariates and \(a\) is the treatment strategy. \({x}^{\beta }\) and \({x}^{\psi }\) are subsets of observed covariates vector \(\mathbf{x}\). The blip function is parameterized in terms of \(\psi\) and characterizes the treatment effect. DTR model also requires specification of a treatment model, which is a propensity score for receiving treatment: \(\pi \left(a|x\right)={f}_{A|x}\left(a|x\right)\). The goal of parameter estimation is to optimize the final outcome \(Y\) in a sequential manner. The estimation was performed by dynamic weighted ordinary least squares [33, 34]. The results of the DTR model would return individualized optimal dosing strategy for both fluid volume and norepinephrine dosing across days 0, 1, 2, 3 and 7. Then, the actual treatment strategy was compared to the optimal treatment strategy. Fluid overloading was defined as those receiving > 1000 mL/day than the optimal volume, and norepinephrine overdosing was those receiving > 0.1 mcg/kg/min than the optimal dose. Risk factors for fluid and norepinephrine overdosing were explored by using stepwise backward elimination and forward selection logistic regression models with AICs. (More details are given in Additional file 1.) All analyses were performed using R (version 4.0.1), and codes are available in Additional file 2.

The eICU Collaborative Research Database (eICU-CRD), which was a multi-center intensive care unit (ICU) database with high-granularity data for over 200,000 admissions to ICUs monitored by eICU Programs across the USA, was utilized for model validation [35]. Septic shock patients were defined as those with the admission diagnosis of sepsis plus the use of vasopressor including norepinephrine, dopamine and epinephrine. The same feature variables were used for FMM and DTR modeling. The classification of septic shock was validated in the eICU-CRD database. The cluster membership for new samples in eICU-CRD was determined by the highest posterior probability of the class membership. The FMM can also be helpful for the application our model to external dataset. Downstream DTR validation was performed by predicting the optimal treatment strategy for patients in the eICU-CRD. Then, the optimal strategy was validated by the fact that it was associated with the lowest mortality.

A total of 4024 patients with septic shock were screened during the study period. After application of exclusion criteria, 1459 patients were enrolled for the study. However, 22 patients were further excluded because of predefined proportion of missing values. As a result, we included 1437 patients for subsequent analysis (Fig. 1). The median age of the study population was 67 years (IQR 54 to 78 years). There were more male (912/1437, 63%) than female patients. The median APACHE II was 22 (IQR 16–27). The primary site of infection included thorax (48%), abdomen (38%), UTI (7%) and soft tissue (3%). Medical patients accounted for 56% of all patients, followed by emergency surgery (32%) and elective surgery patients (12%).

A total of 17 features (age, weight, HR, APACHE II, SBP, temperature, pH, HCO₃, LAC, BE, PF, PaCO2, HCT, platelet, RDWCV, creatinine, urine) were included for FMM. The values of AIC and SABIC declined form 2-class to 8-class models, but the smallest class contained less than 3% patients from 6-class to 8-class models (Fig. 2B). Thus, the 5-class model was considered as the best model. Furthermore, the 5-class model showed an entropy of 0.849, which was among the largest values. The 5-class model was confirmed by k-means clustering analysis (Fig. 2A). The class membership transition is shown in Fig. 2C, showing that patients can move from class to class over ICU days. Patients transitioned to class 1 were more likely to survive on hospital discharge. The five classes could be well separated in the first three principal components (explaining 15.6%, 10.3% and 8.7% of the total variance, Fig. 2D). Characteristics of the five classes are visualized in Fig. 2E, and statistical comparisons are shown in Table 1. Class 1 is the largest class over all study days (it is not the largest class on day 0 as shown in Table 1) with all clinical features around the population mean (the baseline class). Class 2 is characterized by poor tissue perfusion (high serum lactate level: 11.10; IQR 9.05–14.25 mmol/L) and the highest mortality rate (41%) and can be called the critical class. Class 3 is characterized by highest serum creatinine and metabolic acidosis and can be called renal dysfunction class (Fig. 2E). Class 4 is characterized by the highest PaCO₂ (60; IQR 50–77 mmHg) and low PF ratio (169; IQR 118–232 mmHg) and can be designated as respiratory failure class. Class 5 is characterized by young age (42; IQR 30–51 years) and low mortality (21%) and can be considered as the mild class.

In multivariable Cox regression models with time-varying covariates, we included interaction terms between class membership and fluid intake or norepinephrine dosing. The results showed that the main effect of fluid intake volume was positively associated with increased risk of death (HR 1.15; 95% CI 1.04–1.29; p = 0.009). There were significant interactions between class membership and fluid volume intake. While more fluid intake was associated with increased risk of death in class 4, more fluid intake was associated with reduced risk of death in class 2 (HR 0.81; 95% CI 0.69–0.95; p = 0.009). The effect of fluid volume on survival outcome is less prominent in other classes (Fig. 3A, C). Larger doses of norepinephrine were consistently associated with increased risk of mortality (HR 3.17; 95% CI 2.06–4.89; p < 0.001), and there was significant interaction between class 3 and norepinephrine dose (HR 0.28; 95% CI 0.14–0.58; p < 0.001; Fig. 3B, D).

The optimal fluid volume and norepinephrine dosing were estimated using the DTR model. The predicted cluster labels by FMM were included in the DTR’s blip function. The actual and optimal treatment strategies were compared (Fig. 4A). The coefficients for the cluster labels 2, 3, 4 and 5 (one-hot encoding) in the blip function were 0.0575 (95% CI 0.0234–0.0876), 0.0453 (95% CI 0.0241–0.0761), − 0.0115 (95% CI: − 0.0761 to − 0.0034) and − 0.0126 (95% CI − 0.0616 to − 0.0021), respectively. Interestingly, the optimal fluid volume estimated by the DTR model showed a pattern with initially large volume over the first 2 days, followed by reduced volume requirement. This pattern is consistent with the concept of resuscitation and de-resuscitation in the management of septic shock. However, there is large difference among these classes. Class 2 showed longer period of resuscitation that significantly larger volume is required over the first 7 days than other classes. Norepinephrine was more likely to be overdosed on day 0 for class 2, while classes 1 and 3 were more likely to be underdosed (Fig. 4E). Analysis in the original dataset showed that smaller difference between actual and optimal dose resulted in a lower mortality risk (Fig. 4B, D, F, H).

To investigate risk factors for fluid overloading or norepinephrine overdosing, logistic regression models were built. The results showed that greater values of heart rate (OR for each 10 beats/min increase: 4.38; 95% CI 2.85–6.73; p < 0.001), class 3 (OR: 1.93; 95% CI 1.49–2.50; p < 0.001) and class 5 (OR 1.71; 95% CI 1.27–2.31; p < 0.001) were associated with increased risk of fluid overloading (Fig. 4C). Class 3 (OR 0.27; 95% CI 0.21–0.34; p < 0.001), body weight (OR for every 10-kg increase: 0.62; 95% CI 0.44–0.87; p = 0.007) and urine output (OR for every 100-mL increase: 0.82; 95% CI 0.72–0.93; p = 0.001) were associated with decreased risk of norepinephrine overdosing (Fig. 4G).

The logistic regression models require the assumption of a monotonic relationship between the dependent variable and the outcome, and this assumption is often violated in practice. Thus, we further used XGboost to identify risk factors for fluid overloading or norepinephrine overdosing [36]. The variable contribution to the model was explored by the SHapley Additive exPlanations (SHAP), in which the Shapley values calculate the importance of a feature by comparing what a model predicts with and without the feature [37]. ICU day was the most important variable predicting fluid overload. Patients in class 3 were more likely to receive fluid overload (the purple color indicates class 3 patients, and they contribute to increased risk of fluid overload as represented by the positive value on x-axis; Fig. 5A). SHAP values of individual features in predicting the risk of norepinephrine overdosing (top 20 features are shown in the figure). Higher heart rate (purple color) was found to be associated with increased risk (positive SHAP value on x-axis) of norepinephrine overdosing (Fig. 5B).

A total of 5856 patients with septic shock on ICU admission were identified from the eICU-CRD database. The mortality rate was 26.7% (1582/5865). The FMM model identified five classes of septic shock. The class membership in the eICU-CRD dataset was also predicted using the FMM method, which showed similar class distribution in the eICU-CRD (Fig. 6A, B). Furthermore, the DTR model was used to predict optimal dosing of fluid and norepinephrine on the eICU database. The differences between actual versus optimal dosing were calculated. The result showed that larger absolute value of the difference between actual and optimal doses was associated with increased hospital mortality (Fig. 6C–F).