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A Two-Stage Model to Predict Surgical Patients’ Lengths of Stay from an Electronic Patient Database

Abstract: Soaring healthcare costs and the growing demand for services require us to use healthcare resources more efficiently. Randomness in resource requirements makes the care delivery process less efficient. Our aim is to reduce the uncertainty in patients’ resource requirements, and we achieve that objective by classifying patients into similar resource user groups. In this article, we develop a two-stage classification model to classify patients into lower variability resource user groups by using electronic patient record. There are various statistical tools for classifying patients into lower variability resource user groups. However, classification and regression tree (CART) analysis is a more suitable method for analyzing healthcare data because it has some distinct features. For example, it can handle the interaction between predictor variables naturally, it is nonparametric in nature, and it is relatively insensitive to the curse of dimensionality. We found that the CART analysis is also useful for determining the patient attributes that can explain the variability in resource requirements. Furthermore, we observed that some of the covariates, such as the principal prescribed procedure code, the admission point,

and the operating surgeon, were able to explain up to 53:43% of the variability in patients’ lengths of stay (LoS). Reducing the uncertainty in patients’ LoS predictions helps us manage patient flow efficiently and subsequently obtain a better throughput.

Existing System: The common finding of all these researchers was that the multi-stage models were a better fit to healthcare LoS data and that there exist some natural clusters of patients with similar resource requirements Many researchers have worked on identifying a relationship between healthcare LoS and patient attributes. Tang, Luo, and Gardiner fitted Coxian distributions to acute myocardial infarction patients’ LoS data and computed the partial effect of various covariates on the mean LoS. Furthermore, they fitted a Coxian PH regression model to compute the posterior mean of intercept and coefficients of various covariates. Clark and Ryan ] fitted a piecewise exponential model to predict the probability of hospital mortality and the LoS by using various patient attributes or risk factors on admission. Carter and Potts used a Poisson regression model and a negative binomial model to predict the LoS of knee replacement surgery patients from patient attributes such as age, gender, ethnicity, deprivation, and consultant.

Proposed System: Many researchers have worked on identifying a relationship between healthcare LoS and patient attributes. Tang, Luo, and Gardiner fitted Coxian distributions to acute myocardial infarction patients’ LoS data and computed the partial effect of various covariates on the mean LoS. Furthermore, they fitted a Coxian PH regression model to compute the posterior mean of intercept and coefficients of various covariates. Clark and Ryan fitted a piecewise exponential model to predict the probability of hospital mortality and the LoS by using various patient attributes or risk factors on admission. Carter and Potts used a Poisson regression model and a negative binomial model to predict the LoS of knee replacement surgery patients from patient attributes such as age, gender, ethnicity, deprivation, and consultant. Rouzbahman, Jovicic and Chignell used k-mean clustering as a pre-processing of the data to improve predictions from the regression analysis.

Ridley et. al. Found that classification and regression tree (CART) analysis is

useful for classifying ICU patients into iso-resource user groups. They used the source of admission, age, and specialty as independent variables and the ICU LoS as a dependent variable. Happer developed Apollo , a statistical analysis program, in which he incorporated CART analysis to classify patients into similar resource user groups. He classified patients into groups according to their surgery times and found that the patient’s age and surgery type were the main explanatory variables. Ting et al utilized time series models for predicting the number of discharges.

Advantage: They also stated that it is more advantageous to create these groupings according to patients’ resource requirements. In hospitals, patients are grouped together according to their surgery type because they share the same resources after surgery.

However, when we group patients based entirely on their post-operative wards, the variability in their LoS is large, and the average LoS is a poor predictor of each individual’s LoS. Iskane and Rajagopalan observed that classifying patients according to their surgery type lumped together patients whose resource requirements were completely different.

Litvak found that each patient responded differently to the same treatment In the second method, we split the data according to each possible partition of each independent variable, and then we greedily select the split that minimises the weighted sum of variation in the dependent variable.

This method is more advantageous for our problem as it clusters patients according to their LoS and their clinically crucial attributes. When We clustered patients using the regression tree method, we observed that there was some overlap between different LoSpatient flow in subsection V-E.

Disadvantage: To manage patient flow in a surgical suite efficiently, we need to have effective strategic patient flow management (SFM) and operational patient flow management (OFM) policies. SFM deals with long-term decision making, such as

designing a master surgery schedule (MSS) whereas OFM focuses on efficient management of patient flow every day.

We can improve both SFM and OFM policies, if we can predict patients’ resource requirements or LoSs accurately. This is because we can schedule the elective patients’ arrivals according to the resource availability.

Modeling and analyzing patient flow In the second method, we split the data according to each possible partition of each independent variable, and then we greedily select the split that minimises the weighted sum of variation in the dependent variable.

This method is more advantageous for our problem as it clusters patients according to their LoS and their clinically crucial attributes. When we clustered patients using the regression tree method, we observed that there was some overlap between different LoS. The problem may be modeled as a combinatorial optimization problem to obtain an optimal partitioning. In future, we will investigate some of these modeling techniques to solve this problem.

Modules: Classifying patients: Our work is closely related to the work by Ridley et. Al . and Happer .

However, there are some important distinctions between their work and ours.

Classifying patients into groups according to their surgery type is not enough because the remaining variability in patients’ LoS is still significantly large for efficient planning. We were required to explore other covariates that could be helpful in explaining the remaining variability. Classifying patients according to their surgery type lumped together patients whose resource requirements were completely different. Litvak found that each patient responded differently to the same treatment. He defined this variation as clinical variability and stated that it was unavoidable. We agree with Litvak that there is some clinical variability among patients. Because of the clinical variability, it is very difficult to predict

each patient’s LoS accurately. However, we can eliminate the effect of all other eliminable sources of variability, such as the variability due to inappropriate clustering. By clustering patients into appropriate lower-variability LoS groups, we can improve the accuracy of predictions and subsequently improve .

Length of stay: The random arrival time and the uncertainty in resource requirements of each individual are the sources of variability in demand for services . In hospitals, resources are bundled together, and medical professionals work in teams. A patient’s resource consumption is measured by one’s length of stay (LoS) at various care steps, such as the LoS in the ICU, the LoS in a surgical ward, and one’s surgery duration. Therefore, the variability in resource requirements can be approximated by the variability in LoS. Moreover, in the case of elective operations, patients’ arrival times are scheduled by the hospital administration. The remaining source of variability in the elective patient flow process is the randomness in LoS . We can manage a surgical suite more efficiently if we can predict patients’ LoS accurately.

Regression: There are various statistical techniques to cluster and classify data. Most of the clustering techniques come under unsupervised learning techniques. In unsupervised learning, the model is not trained with known results, and the algorithm clusters data points into groups according to their statistical properties, such as the mean, the median, and the variance. However, under supervised learning techniques, the predictions are based on the training sample containing joint observations of dependent and independent variables. Statistical techniques such as multivariate regression analysis, logistic regression analysis, Fisher’s discriminant analysis, support vector machine, neural networks, and decision tree analysis or classification and regression tree (CART) analysis, are some of the commonly used classification techniques. In order to evaluate the performance of the CART, we compare the CART analysis results with that of the random forest (RF) [19] and the k-nearest neighbor (knn) regression [20]. In regression tree model, we repeatedly make binary splits in the response variable according to the most promising predictor variable at each node until the stopping criteria are met.

In RF, we grow a large number of uncorrelated classification or regression trees, and we compute the response variable by averaging predictions across all the trees.

Managing patient flow: Patient flow failure is the long-stay patients. When many long-stay patients show up together, they use a significant amount of resources for a long time, causing cancellations and misplacements. Our aim is to partition patients into the short-stay, medium-stay, and long stay patient groups in each surgical department.

Furthermore, we also investigate the effect of some specific covariates, such as patient’s risk of ICU admission after surgery on the patient’s LoS. In general, a patient’s ICU admission status become available after operation. However, as we will discuss in section V, we used this knowledge in a novel way to improve our classification model.