Peritonitis, an acute disease, is caused by the inflammation of the peritoneum [1] and often develops from bacterial or fungal infections [16]. Upon diagnosis with peritonitis, patients need immediate treatment (typically within 3 days), because it can progress rapidly and develop into life-threatening sepsis or septic shock [1]. Patients with peritonitis have higher mortality rates than those without peritonitis [17]. Several factors, such as age, sex, clinical conditions, and the living environment are associated with peritonitis-related mortality [17].

As two crucial phenotypic expressions of hepatic complications after peritonitis surgery, AHE and HRS can cause severe patient outcomes [7,18]. For patients with peritonitis who also have liver cirrhosis, intestinal bacterial overgrowth inside the body is responsible for hyperammonemia, which leads to AHE [19]. Similarly, HRS is a crucial complication phenotype of peritonitis with advanced cirrhosis too, that is characterized by renal failure and major disturbances in the circulatory function [8]. The underlying mechanisms of HRS may result from complex changes in splanchnic and general circulation, as well as systemic and renal vasoconstrictors and vasodilators [20]. Both phenotypes are clinically important; however, AHE is more severe than HRS because it can deteriorate in a matter of hours.

In general, AHE is diagnosed by liver specialists, whereas HRS is diagnosed by liver specialists and nephrologists. Clinically, the determination of each phenotype depends on laboratory results and the patient’s condition. Patients with AHE typically have hyperammonemia, hyperbilirubinemia, and central nervous system symptoms. Patients with HRS often display splanchnic arterial vasodilation and inflammation, which cause ascites and renal function impairment. Patients with AHE should receive lactulose and neomycin enema, which are infrequently used for other conditions according to the national health reimbursement policies in Taiwan. Thus, the occurrence of AHE can be assessed by the patient’s condition. Patients with HRS are usually prescribed albumin and terlipressin, which can then be used to determine the occurrence of HRS. Each phenotype has a particular ICD-9 code: 572.2 for AHE and 572.4 for HRS.

The heterogeneity and variability in manifestations of hepatic encephalopathy among patients make it difficult to assess or predict patient conditions [21,22]. Previous studies have shown that AHE may be present in 50%-70% of patients with peritonitis who have cirrhosis, including those with abnormalities detectable only with psychometric testing [23]. The clinical manifestations of AHE include brain dysfunction and deep coma [7]. This phenotype represents a vital disease entity because the risk of dying within a year exceeds 60% after its development [24]. Furthermore, patients with spontaneous bacterial peritonitis have an estimated 30% chance of developing HRS [20]. Clinically, the only curative treatment for AHE and HRS is liver transplantation, but systemic infection is a contraindication to liver transplantation. Without timely detection and proper interventions, AHE and HRS can develop rapidly, create patient impairments, lead to life-threatening conditions, and have alarming mortality rates [7,9]. These phenotypes have unique clinical characteristics and features that can be analyzed with data-driven analytics for prediction. Overall, existing data-driven techniques for phenotype predictions can be classified as rule-based, machine learning–based, or deep learning–based. We review the representative studies of each in the upcoming sections.

Rule-based techniques [25-29] use clinically important features to depict the underlying phenotypes. A typical rule-based technique iteratively updates heuristic rules until its sensitivity and specificity satisfy the prespecified thresholds. Developing heuristic rules is labor intensive and time consuming because it requires iterative rule generation and substantial involvement from human experts. The prediction of disease phenotypes entails the extraction of clinically important features; essential features and their combinations in turn indicate the underlying disease phenotype. Guided by domain knowledge, previous research has developed heuristic rules to extract essential features (eg, medications, laboratory results, diagnoses) from EHRs for phenotype predictions, and then updated the extracted rules iteratively until sensitivity and specificity reached the prespecified levels. For example, the rule-based eMERGE technique uses EHRs, in combination with DNA biorepositories, to identify diabetic phenotypes and medication-induced liver lesions [29].

Machine learning techniques coupled with EHRs can support and enhance the care and management of patients with peritonitis. For example, by integrating cellular and soluble biomarkers, support vector machines and tree-based algorithms can help physicians in predicting pathogen-specific immune responses of patients with peritonitis and guide them to formulate optimal antibiotic and operative therapies [30]. Previous research has also applied machine learning algorithms to predict phenotypes [5,28].

Existing machine learning–based techniques can be categorized as clustering analysis, graph-based learning, and probabilistic modeling. Techniques that rely on clustering analysis create phenotype clusters, such that patients in the same phenotypic cluster are more similar to one another than to patients in a different cluster. In essence, clustering analysis–based techniques [5,31] generate patient clusters so that patients with similar phenotypic expressions are in the same cluster. They usually use cross-sectional patient data to produce distinct clusters at a given time or analyze longitudinal clinical data to infer phenotypes that remain consistent over time [5]. However, existing clustering algorithms cannot deal robustly with high-dimensional patient data, and their applications are restricted to smaller, more homogenous data sets [5]. Most clustering-based techniques are applied to patient data at a single time point. Thus, clustering analyses of temporal data would require multiple applications of the chosen technique at different time points [31], further creating instability in the resulting phenotype clusters.

Graph-based techniques [32-34] can cope with temporal heterogeneities in longitudinal patient data (eg, pattern, time interval, frequency). They often assume sequential linkages of distinct clinical events and represent those events as temporally connected nodes in a graph [32]. However, this assumption does not always hold clinically. For example, patients frequently and concurrently receive multiple laboratory tests, treatments, or therapeutic procedures. Moreover, the graph construction process does not include laboratory results (values) that can be essential for inferring clinical outcomes [32]. In addition, probabilistic modeling can uncover the underlying phenotypes. For example, Pivovarov et al [35] propose UPhenome—an unsupervised, generative probabilistic model that can learn phenotypes from heterogeneous patient data. To identify chronic obstructive pulmonary disease subtypes that are similar in progression characteristics, Ross et al [36] develop a novel Bayesian nonparametric model that uses disease trajectory to represent the underlying biological or genetic similarity within the subtype.

The crucial peritonitis complication phenotypes that we study—AHE and HRS—can occur rapidly without any predictive signs, thereby hindering the use of conventional machine learning techniques for predictions. Recent advancements in deep learning promise better predictions of patient outcomes [37,38] because they can learn from clinical sequences to account for complex patterns and relationships in sequential inputs. To illustrate, representation learning can extract complex relationships and nonlinearities among temporal events. Moreover, deep learning architectures, such as recurrent and convolutional neural networks, can be applied to better predict patient outcomes [39-41]. In the following sections, we review representative deep learning–based techniques that can deal with high-dimensional and temporally heterogeneous patient data.

The use of predictive analytics for clinical decision support and patient management often involves large amounts of heterogeneous patient clinical data and needs to consider temporal relationships [42]. Fueled by fast-growing computational power and proliferating EHRs, deep learning has been applied in a broad array of diagnostic tasks, including those related to phenotypes [43,44]. For example, reconstructed RNNs with rectified linear units can impute missing values in genotype data to predict phenotype sequences [45]. Deep autoencoder techniques for unsupervised feature learning help clinicians in identifying acute leukemia phenotypes [46]. By combining latent representation learning of deep neural networks and causal inferences, Kale et al [40] discovered latent phenotypes that are causally predictive of clinical outcomes in patients in the intensive care unit. Moreover, deep RNNs can model multivariate clinical time series in a large data set and then transfer the knowledge to the limited labeled instances to classify the phenotypes of patients in the intensive care unit [47]. Existing literature suggests the value and feasibility of using deep learning in different diagnostic tasks and clinical contexts.

Particularly, EHRs contain rich, longitudinal patient clinical data that can be modeled as RNNs that can represent patients’ records in an accurate and robust way [48]. These networks are effective for modeling patient (clinical) records as temporal logs of diagnostic results. For a particular patient, the state of disease or illness at time t is a summary of the diagnostic records before t. With each record represented as a feature vector, the vectors at different time points can provide sequential inputs to an RNN. The outputs at time t+1 can be used to produce a vector that represents the patient’s state at t+1. Such patient-level vector representations can be further input into other (hidden) layers of the neural network to predict clinical outcomes (eg, readmission, mortality, complications). For predictive analytics in clinical scenarios, RNN-based deep learning architectures may be advantageous over traditional machine learning techniques. For example, an RNN can reduce or prevent adverse drug events by integrating heterogeneous, multidimensional drug data from different sources [49]. In addition, by coping with various clinical and temporal data, an uncertainty-aware convolutional RNN can predict patient mortality, with uncertainty denoting the irregular time intervals in patients [50].

Many clinical diagnoses feature relatively few crucial cases among patients, which need to be properly addressed by data-driven techniques for prediction. If a sample has a substantially fewer number of minority class cases, standard classifiers generally cannot perform well because their predictions tend to steer toward the majority class. Cost-sensitive learning can address the imbalanced distributions of patient outcomes in a sample. It considers the misclassification cost (and possibly other costs) by assigning a high penalty (cost) to the misclassifications of a minority-class instance, without modifying the original data distribution in the sample [51]. Such learning essentially shifts the bias of a classification model in the favor of the minority class. By adjusting the costs associated with different misclassified labels [52], and with the goal of minimizing the total cost, cost-sensitive learning can produce greater predictive utilities. In many clinical scenarios, the minority class is relatively more important and has a higher misclassification cost. However, the overall performance of a classification model, whether machine learning– or deep learning–based, can be dominated by the majority-class instances. This issue may be addressed by combining evaluation results (eg, F-measure, AUC) and the costs associated with different outcome classes (eg, complication phenotypes) to optimize the cost parameter for effective classifications [51].

This review of extant literature reveals several gaps. First, existing prediction techniques may be inadequate or ineffective for acute disease scenarios because previous phenotype research focuses largely on patients with chronic diseases [53,54], whose clinical conditions change less drastically than those of patients with acute diseases. In addition, patients with chronic diseases usually have fewer complications that develop rapidly and have more clinical data available for predictions compared with patients with acute diseases. Second, most previous research works [5,40,46,55] tend to overlook the data insufficiency constraint, which limits the use of early disease stage patient data to build effective computational models for predicting complication phenotypes. Several studies have identified disease phenotypes by assuming full patient data availability [40,46]; however, clinical data captured in the early stages of an acute disease may lack essential information for predicting complication phenotypes. Some important clinical characteristics and factors of complication phenotypes may be available in the early stages but are not sufficiently informative for predicting phenotypic outcomes. Third, complication phenotypes associated with an acute disease often have an imbalanced distribution of different outcomes. Fourth, the clinical efficacy of data-driven techniques for complication phenotype predictions still requires adequate empirical evaluations, especially in acute disease situations that feature data insufficiencies and imbalanced distributions of patient outcomes.

Effective complication phenotype predictions need to address these challenges and consider patients’ heterogeneities and disease progression variations over time while coping with the data sufficiency constraint. We propose a deep learning–based method that leverages temporal feature space representation to address temporal heterogeneities in patient data. Although previous research works have acknowledged the importance of unobserved latent factors for influencing phenotypes [40,56], few studies have explicitly considered such factors for phenotype predictions. As a remedy, we incorporate a latent parameter matrix to account for unobserved (subsequent) patient condition and disease progression variations. In addition, our method addresses missing values in patient data and includes cost-sensitive learning, which can address imbalanced outcome distributions by combining evaluation results (F-measure and AUC) and the cost associated with each complication phenotype to optimize cost parameters for an improved predictive performance.

We obtained a clinical data set from the Department of Laboratory Medicine at the Chang Gung Memorial Hospital, which is accredited by the Taiwan Accreditation Foundation and approved by the American College of Pathologists [62,63]. This data set consists of 10,354 records pertaining to 6545 patients who underwent peritonitis surgery between 2003 and 2015. Designated professionals at the hospital integrated patient records in EHRs, according to the common format of the Chang Gung Research Database (CGRD) that provides standardization and facilitates data extraction, transformation, and loading for analyses [64].

The CGRD links directly to the National Health Insurance Research Database (NHIRD), which informs reimbursement decisions [62,63]. To prevent fraud and contain costs, the National Health Insurance Administration of the Ministry of Health and Welfare performs frequent, random audits. Thus, the data in the NHIRD and CGRD are reliable and accurate. Information systems professionals at the hospital also assessed the data conversion process and integrity to ensure that all patient records (including diagnoses and laboratory results) are correctly transferred to the CGRD without errors or losses [64]. Experienced personnel from the Research Institute of Chang Gung Memorial Hospital assisted us in compiling the data set. In particular, they performed data preprocessing and consolidation to ensure that each patient’s records were collected within the same time interval.

In the data set, each laboratory test has a time stamp that indicates when the results are available (reported). We used the date of peritonitis surgery as the starting point and collected patient data over the next 3 days. This procedure ensured that all patient records were collected within the same time interval after surgery. Each patient had at least one clinical record within the three-day window. Specifically, 3665 patients had 1 clinical record, 1951 patients had 2, and 929 patients had 3 clinical records. Each record contains the patient’s demographic and clinical data (eg, age, sex, comorbidity) and potentially multiple laboratory results, which we used to predict the complication phenotypes (AHE, HRS, or neither).

Table 1 summarizes the patient demographic and clinical variables in the data set. We adopted the International Classification of Diseases, Ninth Revision, Clinical Modification comorbidity coding algorithm [65] to define the Charlson comorbidities in administrative and clinical data. Accordingly, the comorbidity types in our study span 17 categories, from mild liver disease to moderate or severe liver disease to myocardial infarction. Among the 6545 peritonitis patients in the data set, 41 developed AHE, and 174 developed HRS, that is, the distribution of different outcome classes (AHE, HRS, or neither) is highly imbalanced. Furthermore, AHE and HRS have profound implications for patient outcomes and mortality. For example, 9 of the 41 patients with AHE in the sample died, with a mortality rate of 22%; patients with AHE or HRS had an average length of stay of 25 days (hospitalization), whereas patients without these phenotypes had an average of 17 days.

For the 41 patients with AHE in the sample, the complication phenotype occurred between 6 and 17 days after peritonitis surgery, with a mean of 13 days. For the 147 patients with HRS, the complication phenotype developed between 4 and 47 days after the surgery, with a mean of 14 days. In their clinical trial, Huang et al [66] reported a survival curve that indicated that most patients discontinued antibiotic treatment within 3 days after peritonitis surgery, suggesting that AHE and HRS seldom occur within those 3 days. In general, complication phenotypes, including AHE and HRS, arise approximately 2 or 3 weeks after peritonitis surgery [66,67]. For example, HRS is characterized by a rapid, progressive impairment of renal function. Furthermore, it develops, on average, about 2-3 weeks after peritonitis surgery [68,69]. Similarly, patients develop AHE approximately 2 weeks after peritonitis surgery [70,71]. The combined evidence from the relevant literature and clinical findings indicates the appropriateness of using the data available 3 days after surgery to predict subsequent AHE and HRS occurrences.

In total, three prevalent techniques were included in the evaluation as benchmarks: temporal MMCBR [10], time fusion CNN [12], and T-LSTM [11]. First, temporal MMCBR performs clustering analyses to identify similar (patient) temporal sequences in a sample [10]; therefore, it can handle temporal patient data that vary in their time intervals and granularity. Second, time fusion CNN, a deep learning–based technique, learns patient representations and measures pairwise similarity in temporal patient data to capture important characteristics specific to individual patients [12]. Third, patient subtyping through T-LSTM, another deep learning–based technique, can cope with patient data that feature temporal heterogeneities by employing autoencoders to learn patient representations, which helps cluster patients into subtypes [11]. Our benchmarks do not include graph-based techniques because concurrent laboratory tests in the data set make them inadequate for representing patient conditions and disease progression in a 2D graph. We also exclude probabilistic modeling that offers limited predictive utilities in situations involving imbalanced samples. In the evaluation, the proposed method and all benchmark techniques employed the same cost-sensitive matrix.

All the evaluations were performed on a computer with a dual-core processor of 2.7 GHz and 8 GB of memory, running macOS Catalina. We used the SMOTEENN algorithm from the Python imbalanced-learn library and applied the Python Shapley Addictive Explanations (SHAP) package to obtain SHAP values for the feature importance analysis. The proposed method and benchmark techniques were implemented using PyTorch. Our method constructs an 8-layer RNN to map the disease progression space with a latent regulator and adopts a multilayer perceptron neural network with three dense layers to predict complication phenotypes. Specifically, the RNN embedding produces a 2D vector, 8×8 in size, which depicts the temporal disease progression space. We randomly split the data set into 80% for training and 20% for testing. The testing set had 12 AHE cases, 35 HRS cases, and 1262 neither cases. For misclassified labels, we set the initial cost parameter for each phenotype (AHE or HRS) to 200, in line with a related research [72]. We performed a series of parameter tuning analyses, and then used the results to determine essential hyperparameter values (Table 2), including an optimal number of layers for each neural network.

A clinical record contains the results of the laboratory tests prescribed by the physician, that is, a record has one timestamp. As noted, patients in the data set have different numbers of records within the 3-day window after peritonitis surgery, which are used for model construction. Because the proposed RNN-LR method requires the same number of clinical records for each patient, we employed zero padding to ensure that each patient had three sequential records. As a result, the data set contains a total of 19,635 clinical records: 6545 patients × 3 (sequential) records. We illustrate the zero-padding process in Figure 4. If a patient has only one clinical record within the 3-day window, we place that record at the end of the sequence and fill the first 2 records with zeroes, according to the length of the longest sequence (three). Hence, our method uses input sequences of the same length for model training.

We used the ReLU for activation and the cross-entropy function for optimization. Finally, the Adam optimizer was applied to update the model parameters. Figure 5 presents the learning curves of the proposed method versus benchmark techniques [73]. As shown, the hyperparameters appear to converge toward optimality after 100 epochs. Notably, our method consistently achieves a greater AUC than the benchmark techniques after 60 epochs.

We evaluated predictive performance in terms of recall, precision, F-measure, and AUC. In line with previous research works [74,75], we adopted the one-against-all strategy to examine the respective techniques across different performance measures and outcome classes. To illustrate, we combine HRS and neither as a single class to calculate the precision, recall, and F-measure while evaluating AHE predictions. This approach reduces 3 outcome classes to 2 (AHE and no AHE), with AHE as the positive class and no AHE as the negative class. Similarly, we consider HRS as the positive class and no HRS as the negative class while assessing HRS predictions. Recall, or sensitivity, indicates the fraction of correctly predicted positive observations among all actual positive-class observations, calculated as: