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Energy and Earth Science 
Vol. 1, No. 1, 2018 

www.scholink.org/ojs/index.php/ees 
ISSN 2578-1359 (Print)   ISSN 2578-1367 (Online) 

42 
 

Original Paper 

A New Tool Preliminary Assessment on Temporal-Comorbidity 

Adjusted Risk of Emergency Readmission (T-CARER) 

Tim Chen1,2,3,4, Asim Muḥammad4, Bertrand Chapron5, C. Y. J. Chen6,7, & Alexander Babanin8 
1 School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham, 

UK 
2 Department of Artificial Intelligence, University of Maryland, Maryland, USA  
3 Faculty of Intelligence Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam 
4 Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia 
5 Laboratoire d'Océanographie Physique et Spatiale, Centre de Brest, IFREMER, Plouzané, France 
6 Industrial Technology Research Institute, Hsinchu, Taiwan 
7 BRAC Univ, Department of Computer Science and Engineering, Dhaka, Bangladesh 
8 Department of Infrastructure Engineering, University of Melbourne, Melbourne, Victoria, Australia 

 

Received: November 6, 2018  Accepted: December 10, 2018  Online Published: December 17, 2018 

doi:10.22158/ees.v1n1p42         URL: http://dx.doi.org/10.22158/ees.v1n1p42 

 

Abstract 

Patients’ comorbidities, operations and complications can be associated with reduced long-term 

survival probability and increased healthcare utilisation. The aim of this research was to produce an 

adjusted case-mix model of comorbidity risk and develop a user-friendly toolkit to encourage public 

adaptation and incremental development. 

It has been shown in healthcare research that demographics, temporal dimensions, length-of-stay and 

time between admissions, can noticeably improve the statistical measures related to comorbidities. The 

proposed model incorporates temporal aspects, medical procedures, demographics, and admission 

details, as well as diagnoses. 

The research resulted in the development of Temporal-Comorbidity Adjusted Risk of Emergency 

Readmission (T-CARER) model using routinely collected hospital data. 

Keywords 

multiple criteria decision making, interval-valued belief distribution, evolutionary algorithm, accuracy, 

efficiency 

 

 



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1. Introduction 

There is increasing evidence that the quantification of high-risk diagnoses, operations and procedures, 

and monitoring changes over time, can greatly improve the quality of readmission models with 

adequate adjustment. There have been two streams of work on risk scoring comorbidities to estimate 

future resource utilisation, emergency admission and mortality. 

Firstly, one stream of research looks at the odds ratio of major diagnoses groups and therefore is highly 

reliant on the whole population statistics. These models stem from crudely summing up the derived 

weights for comorbidities, which are based on the most recent admission of patients with disregard of 

temporal patterns. A popular example is the Charlson Comorbidity Index (CCI) (Charlson, Pompei, 

Ales, & MacKenzie, 1987), which relies on twenty-two comorbidity groups. One of the recent 

translation of the CCI is the National Health Service (NHS) England version of the CCI (NHS-CCI), 

that is continuously being updated (Aylin, Bottle, Jen, Middleton, & Intelligence, 2010; Bottle, Jarman, 

& Aylin, 2011; HSCIC, 2014; 2015; 2016). 

The second stream of models uses a diagnosis classification approach based on simi larities, type, 

likelihood or duration of care. However, they are usually very complex and specialised to highly 

particular settings and populations. Also, these models use a period of care records in past, but temporal 

patterns are greatly ignored. One prominent method is the Elixhauser Comorbidity Index (ECI) 

(Elixhauser, Steiner, Harris, & Coffey, 1998; AHRQ, 2016), which relies on thirty comorbidity groups 

and 1-year lookback period. Unlike the CCI, the ECI is using Diagnosis-Related Groups (DRG), which 

was first developed by Fetter et al. (Fetter, Shin, Freeman, Averill, & Thompson, 1980) and is based on 

ICD (International Statistical Classification of Diseases) diagnoses, procedures, age, sex, discharge 

status, complications and comorbidities. A recent adaptation of the ECI is the AHRQ-ECI, which is 

actively being maintained by the US Public Health Service (AHRQ, 2016). Another well-established 

method is the John Hopkin’s (Weiner & Abrams, 2011) Adjusted Clinical Groups (ACGs), which is a 

commercial tool. The model uses a minimum of 6-month and maximum of 1-year prior care records, 

and it encapsulates 32 diagnoses groups, known as Aggregated Diagnosis Groups (ADGs), and their 

aggregations called Expanded Diagnosis Clusters (EDCs). Moreover, these indices are initially 

developed to adjust for particular risks, like mortality risk and care utilisation, but they are commonly 

used in a variety of risk adjustment problems in critical care health services research. 

In the machine learning pipeline that was developed in the prior stage of our research (Mesgarpour, 

Chaussalet, & Chahed, 2017), comorbidity index was an extremely significant factor and has a high 

potential for further improvement. Presently, comorbidity risk indices have four major weakness areas: 

robustness, temporal adjustment, population stratification, and the inclusion of associated factors to 

comorbidities and complications. 

In this research, we are going to improve on these four major areas. Firstly, to make the risk score 

relevant to different environments, an approach must be used to model complex correlation between 

variables and states. Secondly, to better distinguish the short- and long-term conditions (i.e. prior 



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admission, length-of-stay, and delta-time between admissions), the temporal dimension may be 

included in form of life-table or a polynomial weight function. Thirdly, population stratification is a 

major factor in the prevalence of medical conditions, and therefore must be adjusted. Fourthly, major 

correlated factors to diagnoses may be included directly or indirectly (latent) to improve the risk 

estimates, including secondary diagnoses, operations, procedures and complications. 

The first main outcome of this research was the development of the Temporal Comorbidity Adjusted 

Risk of Emergency Readmission (T-CARER), to address the four mentioned issues. The secondary 

outcome was to release a generic, open source and easy-to-use environment to model the comorbidity 

risk. It consists of a user-friendly IPython Notebook, which calls procedures in MySQL and Python, in 

addition to third-party libraries. The T-CARER Toolkit and documentation are available online (Apache 

2016). Furthermore, comorbidity risk models are constrained by the population and sam ple 

characteristics, data quality (e.g. missing diagnoses or delayed death registration) and modelling 

approach. There is a wide range of literature that focuses on modification and benchmarking 

comorbidity indices, using different datasets, cohorts, complexity, length-of-stay and claims. The 

prediction targets vary, it includes in-hospital and 1-year mortality, and in some cases 7-day and 30-day 

readmission (Austin, Stanbrook, Anderson, Newman, & Gershon, 2012; Holman, Preen, Baynham, 

Finn, & Semmens, 2005; Gagne, Glynn, Avorn, Levin, & Schneeweiss, 2011; Mehta, Dimou, Adhikari, 

Tamirisa, Sieloff, Williams, Kuo, & Riall, 2016; Sharabiani, Aylin, & Bottle, 2012; Januel Luthi, Quan, 

Borst, Taff’e, Ghali & Burnand, 2011). Moreover, there have been many attempts at scoring sur gical 

outcome and complications that are affected by comorbidity (Mehta, Dimou, Adhikari, Tamirisa, 

Sieloff, Williams, Kuo, & Riall, 2016; Armitage & Meulen, 2010; DFI, 2013). However, they are 

mainly based on non-administrative clinical variables or are specialized to very specific outcomes and 

populations. 

 

2. Methodology 

2.1 Data 

In this study, a bespoke extract of the HES inpatient data was used, which contains records from April 

1995 to April 2010. Two main samples were randomly selected from this database, which includes 20% 

of total unique patients from 1999-2004 and 2004-2009 periods. Then, each main sample was divided 

into two equal half, to be used for training and testing.  

Each time-frame was divided into one year of trigger-event, one year of prediction period, and three 

years of prior-history. The population includes all alive patients greater than one-year-old that have an 

admission within the trigger year. The prediction target variables are 30- and 365-day hospital 

emergency admission to the inpatient. 

2.2 Features 

After the data extraction step, several stages of data pre-processing and feature selection were carried 

out using the framework introduced by Mesgarpour et al. (2016). Firstly, a set of data pre-processing 



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steps are applied, then the feature selection steps are carried out. Also, before carrying out the feature 

selection steps, features are aggregated and split into temporal events, to capture the events through 

time. 

2.2.1 Pre-Processing 

The pre-processing stage implements data selection, removals of invalids and imputations of 

observations. Also, the feature re-categorisation was applied in this stage, to reduce sparsity and to 

better capture non-linear relationships. 

In re-categorisation step, a clinical grouper, known as the Clinical Classifications Software (CCS), was 

used to categorise the diagnoses, to better capture comorbidities’ patterns and cross-correlations. The 

CCS categorises the ICD-10 (10th revision of the ICD) diagnoses and operations into a number of 

categories that are clinically meaningful (HSCIC, 2014; Elixhauser & Steiner, 2006; AHRQ, 2016). 

Furthermore, operations and procedures were categorised using the major categories of the OPCS-4, 

but alternative coding categorisation may be used, like ICD-10-PCS. The OPCS-4 is an alphanumeric 

nomenclature (similar to ICD-10-PCS), and is used by the NHS England and has an implicit 

categorisation for operations based on clinical categories rather than cost or risks. 

2.2.2 Life-Table and Aggregation 

Healthcare administrative data are severely unbalanced regarding the amount of longitudinal (panel) 

data per patient and their distributions over the years. Statistical methods are not equipped to handle 

these type of unbalances directly. Therefore, the survival analysis’s life-table approach was used to 

keep track of temporal events (Singer & Willett, 2003). 

Based on previous studies and the initial statistical analyses, four levels of temporal features were 

generated: 0-30, 30-90, 90-365 and 365-730 days. These four levels capture part of the temporal aspect 

of comorbidities, in addition to the delta-time between admissions (gapDays) and the length-of-stay 

(epidur) features that include temporal metadata. Furthermore, in the modelling stage, we applied 

several techniques to capture the complex temporal patterns of patients’ Comorbidities. The temporal 

features were summarized in each temporal level based on several aggregation functions, including 

prevalence, count and average. This stage increased the number of features by more than fifty folds. 

2.2.3 Feature Selection 

After feature generation, a feature pool was produced based on the developed features. Thereafter, the 

feature selection step has been carried out. Firstly, the features were filtered out based on their linear 

cross-correlation, as well as frequency and sparseness (percentage of distinct, and the ratio of the most 

common value to the second most common). 

Thereafter, the continuous features have been transformed using two feature transformations methods: 

scale-to-mean and Yeo-Johnson (Yeo & Johnson, 2000; Breiman, 2001; Hawkins & Blakeslee, 2007). 

Both methods can be used to transform the data, to improve normality. Although, feature 

transformations would not guarantee better convergence or very stable variance for any dataset, they 

have been applied to avoid inputting skewed features into models. Moreover, a downside of 



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transformations is that they make model interpretation harder, and can negatively impact the 

relationship between correlated features in the model. Therefore, the highly correlated features were 

removed after transformations.  

2.3 Modelling Approaches 

The aim of this research is to model emergency readmission using a minimal number of generic 

features that can be used for short and long-term predictions with high correlation to the comorbidity 

risk. In this study, there is no condition on the trigger event admission and a minimal number of 

features are used. This makes it different from general readmission models, like the ERMER 

(Mesgarpour, Chaussalet, & Chahed, 2017), that use a wide range of features and may enforce the 

emergency admission condition for both trigger-event and future-event.  

2.3.1 Logistic Regression  

The first algorithm is a logistic regression with L1 regularisation (1.0), using liblinear optimisation 

algorithm (Fan, Chang, Hsieh, Wang, & Lin, 2008) with the maximum of hundred iterations and a 

warm-up period. The random forest method is an ensemble decision tree, which was first introduced by 

Breiman et al. (2001). It is based on the CART algorithm (Breiman, Friedman, Stone, & Olshen, 1984) 

and the bagging ensemble method (Breiman, 1996). However, the Breiman random forest is sensitive 

to highly correlated features, and the scale or categories of features (Strobl, Boulesteix, Zeileis, & 

Hothorn, 2007; Tolosi & Lengauer, 2011). 

2.3.2 Random Forest  

We used a random forest method using the Breiman algorithm (Breiman, 2001), with gradient boosted 

regression trees, Gini index criterion and 1000 trees in the forest. 

 

3. Deep Neural Network and Results 

We implemented a Deep Neural Network (DNN) based on the Wide and Deep Neural Network 

(WDNN) algorithm, which was introduced by Cheng et al. (2016). DNNs are a class of Artificial 

Neural Networks (ANN) with multiple hidden layers, which allow modelling more complex non-linear 

problems (Bengio et al., 2009; Schmidhuber, 2015). DNN act like ANN, but with better ability to 

model complex non-linear models with a more effective representation of features in each layer. The 

WDNN is a DNN which combines benefits of memorization and generalization. The WDNN consists 

of two parts: the wide model and the deep model. The wide part of the model consists of a wide linear 

model for highly sparse features (random features that are rarely active) and is good at memorizing 

specific cases. The wide part may also include groups of crossed features. Inside of a group of crossed 

features, each level of one feature occurs in combination with each level of other features. The GLM 

(Eq. 1) and the cross-product transformation (Eq. 2) for the wide part are defined as the following: 

 wTy x b                 (1) 



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 
1

ki

d
c

k i
i

x x


  ;  0,1kic              (2) 

, where y is the prediction, x is a vector of features of d features, w is model parameters and b is the 

bias. 

On the other hand, the deep part of the model composed of hidden layers of feed forward neural 

network with an embedding layer and several hidden layers for any other variable. The deep part can be 

particularly good in the generalization of cross-correlations. Each hidden layer performs the following 

operation (Eq. 3). 

 
( 1) ( ) ( ) ( )(w )l l l la f a b                     (3) 

, where W(l), a(l) and b(l) represent weights, actuation’s and bias for layer l, respectively. Finally, the 

WDNN for the logistic regression problem (Y) can be formulated as the following (Eq. 4): 

 
( ), )( 1| ) ( [ ( )] flT T

wide deepp Y w wx x a bx           (4) 

where σ(.) is the sigmoid function, φ(x) is the cross-product transformations of x features and w. are 

the weights. In our study, the WDNN model applies Adadelta optimiser (Duchi, Hazan, & Singer, 2011) 

for the gradients of the deep part, and implements the Rectified Linear Unit (ReLU) activation function 

to each layer of the ANN (LeCun, Bengio, & Hinton, 2015). 

In overall, the WDNN and the random forest models provide a better fit for the 30- and 365-day 

emergency readmission problems. For the 365-day, the WDNN produces a marginally better 

Receiver-Operating Characteristic (ROC) compared to the random forest, and significantly better ROC 

compared to the logistic regression (Figure 1). Also, the WDNN models have very strong precision 

(positive predictive value), accuracy, and micro-average f1-score. On the other hand, the random forest 

models have very high sensitivity (true positive rate) and f1-score. Because the classes are highly 

unbalanced, the precision-recall curve (Figure 2) was used, to compare the area under the curve, 

average precision and average recall. The plot demonstrates that the area under the curves are 

significantly lower for 30-day models compared to 365-day models. Also, sample-2 models have a 

bigger area under the curve across the models. 

 



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Figure 1. The Abstract Graph of the Wide and Deep Neural Network (WDNN) 

 

 

(a) Receiver Operating Characteristic (ROC).                  (b) Precision-recall curve. 

Figure 2. Performance Comparison 

 

4. Discussion and Conclusions 

We compared the performance of the T-CARER against commonly used comorbidity index models 

using different samples and population cohorts across a ten year period. Our analyses of the T-CARER 

and the NHS-CCI for different diagnoses categories demonstrated that our model performed best in the 

majority of comorbidity groups, and in overall T-CARER models show better results against previous 



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surveys of CCIs and ECIs. 

An advanced research will be sought to identify an approach to score commodities by the inclusion of 

diverse categories of diagnoses, operations and complexities. The T-CARER performs consistently 

across tests and validations, and it outperformed against Charl-son and Elixhauser indices which are 

widely used for prediction of comorbidity risks.  

 

Funding Acknowledgement 

This research was in part enlightened by the grant 106EFA0101550 of Ministry of Science and 

Technology, Taiwan. 

 

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