Preventable hospital readmissions have been identified as one of the primary targets for reducing costs and improving healthcare delivery. However, most data driven studies for understanding readmissions have produced non-interpretable black boxes, which precludes them from being used effectively within the decision support systems in the hospitals. A novel strategy to improve the interpretability of a linear model by incorporating domain knowledge is proposed here. The central idea is to exploit the hierarchical relationships among the features (medical diagnosis codes, in this case) using a tree-structured sparsity-inducing regularization norm. The proposed method transforms the hierarchical relations among features into a graph and then applies graph-guided regularization during the model learning. Additionally, an evaluation metric is proposed to quantify the interpretability of a linear model with respect to the domain hierarchy. Results on two healthcare claims data sets are shown, where a model is learnt to predict a patient’s risk of readmission, based on the medical history and other relevant features. Results show that the proposed method is able to learn a model which can predict readmission risk with accuracies that are comparable to existing methods, but produces a highly interpretable output, which allows medical experts to draw clinically relevant insights and identify key factors associated with hospital readmissions. Some of these factors conform to existing beliefs, e.g., impact of surgical complications and infections during hospital stay. Other factors, such as the impact of mental disorder and substance abuse on readmission, provide empirical evidence for several pre-existing but unverified hypotheses. The findings of this study will be instrumental in designing the next generation decision support systems for preventing readmissions. Hospital readmissions are prevalent in the healthcare system and contribute significantly to avoidable costs. In United States, recent studies have shown that the 30-day readmission rate among the Medicare beneficiaries1 is over 17%, Copyright held by the author(s). In A. Martin, K. Hinkelmann, A. Gerber, D. Lenat, F. van Harmelen, P. Clark (Eds.), Proceedings of the AAAI 2019 Spring Symposium on Combining Machine Learning with Knowledge Engineering (AAAI-MAKE 2019). Stanford University, Palo Alto, California, USA, March 25-27, 2019.
1A federally funded insurance program representing 47.2 %
($182.7 billion) of total aggregate inpatient hospital costs in the
with close to 75% of these being avoidable
Given that the rate of avoidable readmission has now
become a key measure of the quality of care provided in
a hospital, there have been increasingly large number of
studies that use healthcare data for understanding
readmissions. Most existing studies have focused on building
models for predicting readmissions using a variety of available
data, including patient demographic and social
characteristics, hospital utilization, medications, procedures, existing
conditions, and lab tests
While the predictive models have shown promise, their moderate performance means that they are still not at a stage where hospitals could use them as “black-box” decision support tools. Moreover, such models are not easily interpretable to provide actionable insights to the decision makers. At the same time, beyond the selection of the initial set of features to learn from, these solutions do not explicitly utilize the rich information available in the medical domain.
In this paper, we explore incorporation of one such
domain information, into the model learning process.
Specifically, we utilize the hierarchical relationships among
different medical diagnosis codes, available as a taxonomical tree
(See Section 3 for details). The tree structure is utilized as
a regularization penalty, to enforce the model (logistic
regression) to learn a sparse solution such that the non-zero
weights are localized within a few sub-trees. The key idea
is that such a solution would be easier to interpret compared
to a solution in which the weights are “scattered” across. A
graphical illustration is provided in Figure 1. The proposed
method falls under the general class of structured
sparsity regularization based machine learning models (Mosci
et al. 2010), which consists of numerous schemes to
exploit different types of relationships among features,
including groups
The proposed regularization scheme transforms the tree
structure into a weighted graph that uses the “tree-distance”
as the weight of the edge between the corresponding nodes
in a graph, and then employs a graph based penalty to force
the machine learning algorithms to favor solutions in which
the non-zero weights are strongly linked in the graph. The
regularizer is incorporated into a standard logistic
regression classifier, using truncated gradient descent
By analyzing the model trained on the MDW data, we
infer several important insights to improve the
understanding of readmissions. Some of our findings conform to
existing beliefs, for example, the importance of bacterial
infections during hospital stay. Other findings provide empirical
evidence to support existing hypotheses amongst healthcare
practitioners, for example, the effect of the type of insurance
on readmissions
We believe that such findings can have a significant impact on how healthcare providers develop effective strate(a) No taxonomy-guided regularization
(b) Taxonomy-guided regularization gies to reduce readmissions. At present, the healthcare efforts in this context have been twofold. First is the effort to improve the quality of care within the hospital and the second is to develop effective post-discharge strategies such as telephone outreach, community-based interventions, etc. The results from this study inform the domain experts on both fronts.
The rest of the paper is organized as follows. We review existing literature on readmission prediction in Section 2. We describe the data used for our experiments in Section 3 and formulate the machine learning problem in Section 4. We discuss the classification methodology in Section 5. We present the algorithm for measurement of model’s interpretability in Section 6. The results are presented in Section 7. We discuss the importance of interpretable outcome by including a real world case study in Section 8. Infectious & Parasitic
Intestinal Infections Tuberculosis Zoonotic Bacterial Infections : : : Neoplasms Malignant (Lip, Oral Cavity, : : :) Malignant (Digestive) : : : : : :
Injury & Poisoning
External cause
status
Activity
Railway Accidents
: : :
Coincident with the rising importance of readmissions in
reducing healthcare costs, there have been several papers
that use clinical and insurance claims information to build
predictive models for readmissions
Finally, the hierarchical relationship has never been
exploited for building predictive models for readmission.
Singh, et. al,
3
For the experiments, we explored two different data sets that consist of healthcare insurance claims and electronic health records (EHR).
The fist dataset is obtained from the New York State Medicaid Data Warehouse (MDW). Medicaid is a social health 2http://www.icd9data.com/2015/Volume1/ default.htm care program for families and individuals with low income and limited resources. We analyzed four years (2009–2012) of claims data from the MDW. The claims correspond to multiple types of health utilization including hospitalizations, outpatient visits, etc. While the raw data consisted of 4,073,189 claims for 352,716 patients, we only included the patients in the age range 18–65 with no obstetrics related hospitalizations. The number of patients with at least one hospitalization who satisfied these conditions were 11,774 and had 34,949 claims.
For each patient we have information of patient’s admission medical history extracted from four years of claims data represented as a binary vector that indicates if the patient was diagnosed with a certain disease in the last four years.
The second dataset is Multi-parameter Intelligent
Monitoring in Intensive Care (MIMIC-III) public dataset
While the database includes information such as demographics, vital sign measurements made at the bedside (one data point per hour), laboratory test results, procedures, medications, caregiver notes, imaging reports, and mortality (both in and out of hospital), we focus on admission records to extract the medical codes as part of each patient’s history.
According to the dataset we retrieved from the MIMICIII dataset, there are 46516 patients in total with 3996 of patients flagged as readmissions. The medical history for each patient consists of 6783 diagnosis codes.
Disease information is encoded in insurance claims and medical records using diagnosis codes. The International Classification of Diseases (ICD) is an international standard for classification of disease codes. The data used in this paper followed the ICD-9-CM classification which is a US adaptation of the ICD-9 classification. Conceptually, the ICD-9-CM codes are structured as a tree (See Figure 2 for a sample) with 19 broad disease categories at level 1. The entire tree has 5 levels and has total of 14,567 diagnosis codes. While the primary purpose of ICD taxonomy has been to support the insurance billing process, it contains a wealth of domain knowledge about the different diseases.
For each patient in the above described cohort, we assign a binary flag for readmission risk. The readmission risk flag is set to 1 if the patient had at least one pair of consecutive hospitalizations within 30 days of each other in a single calendar year, otherwise it is set to 0.
4
Given a patient’s disease history, we are interested in
predicting the readmission risk (binary flag) for the patient. The
problem formulation is different from many existing
studies
We denote each patient i as a vector xi consisting of 11,881 elements for the MDW dataset and 6,873 elements for the MIMIC-III admission dataset corresponding to the number of disease codes showed in data respectively. Note that while ICD-9-CM classification contains 14,567 codes, only 11,881 and 6,783 codes are observed in each data set used in this paper. We selected patients that age in between 18 and 65 and excluded pregnancy related diseases. All elements in the vector are binary. The readmission risk flag is denoted using yi 2 f0; 1g where 1 indicates readmission risk.
From machine learning perspective our task is to learn a N classifier from a training data set hxi; yiii=1 which can be used to assign the readmission risk flag to a new patient represented as x . Note that the input vector xi is highly sparse. For example, in the NY Medicaid dataset, on average, there are only 36 non-zeros out of total 11,884 possible codes. 5
We use a logistic regression (LR) model
1 1 + exp( >x) (1) Where is the LR model parameter (regression coefficients). We assume that x includes a constant term corresponding to the intercept.
The model parameter are learnt from a training data set
N (hxi; yiii=1) by optimizing the following objective function:
N ^ = arg min X log(1 + exp( yi >xi)) + ( ) (2) k Gij k1 where G denotes the tree constructed using the hierarchy of the diagnosis codes. Gij denotes the jth node in the tree at the ith level. Thus G01 denotes the root level, and so on. ( ) =
1
The TSGL regularizer, discussed above, treats the tree structure as a special overlapped group, which ignores the hidden relationship between nodes at different levels. To overcome this deficiency, we propose a different way to exploit the tree structure. The new regularization penalty is defined as: m m X X Where the i and i are coefficients of features i and j, respectively and Dij is the tree distance between features i and j and will be introduced in next subsection. The first penalty term ensures that the selected features are closer to each other in the taxonomy tree while the second term, k k1, ensures the overall sparsity of the solution. where the first term refers to the training loss and the second terms is a regularization penalty imposed on the solution; being the regularization parameter.
L1 Regularizer Different forms of regularization
penalties have been used in the past, including the widely used
l1 and l2 norms
However, l1 regularizer does not explicitly promote
structural sparsity. Given that the features used in predicting
readmission risk have a well-defined structure imposed by the
ICD-9 standards, we explore regularizers that leverage this
structure for model learning:
Sparse Group Regularizer This regularizer (also referred
to as Sparse Group LASSO or SGL) assumes that the input
features can be arranged into K groups (non-overlapping or
overlapping)
K ) X k Gk k2 k=1 where Gk are the coefficients corresponding to the group Gk. The above penalty function favors solutions which select only a few groups of features (group sparsity). For the task of readmission prediction, we divide the features corresponding to all numbers of diagnosis codes included into 19 non-overlapping groups, based on the top level groupings in the ICD-9-CM classification (See Table 1).
Tree Structured Group Regularizer This regularizer, also referred to as Tree Structured Group LASSO (TSGL), explicitly uses the hierarchical structure imposed on the features. The TSGL regularizer is given by: Distance Matrix for Tree The distance between any two nodes in the tree, Dij is defined in terms of the length of the path between the two nodes. If the node i is an “ancestor” of node j, or vice-versa, the distance is defined as:
Dij = (li lj )2 where li denotes the level or the number of steps from the root for node i. If the nodes i and j do not share any ancestral relationship, then the distance is defined as:
Dij = ((li lc)2 + (lj lc)2)3 where c is the node that is the nearest common ancestor for nodes i and j. The cubic power is used to sharply increase the weight with the number of levels to go up by to find the common ancestor. Thus, Dij will be largest for two leaf nodes whose common ancestor is the root node.
The data matrix consisting of the distances between all pairs of leaf nodes (features) from the MIMIC-III data set is shown in Figure 3.
Optimization To solve the optimization problem in (2) using the regularization penalty defined in (5), we first convert the first penalty term (tree structure sparsity) into a graph constraint as: where L is a m
m matrix, such that:
m m
X X
Truncated Gradient Descent Note that the objective
function and the tree penalty term have a convex form such
that one can calculate the gradient of the objective function
with respect to the weight vector, , and use that within a
gradient descent algorithm. However, due to the presence
of the l1 term (k k1), a direct gradient descent
formulation is not possible. We employ Truncated Gradient
Descent
The idea behind truncated gradient descent is to ignore the l1 term when calculating the gradient, and round small coefficients (that are not larger than a small threshold) to zero after every k online steps, i.e., at every kth step: (t) = T0( (t 1) rJ ) Where rJ is the gradient without the l1 penalty term and T0 defined by:
T0( j ; ) = 0 if j j j < j otherwise
That is, we first apply the standard gradient descent rule, and then round small coefficients to zero to enforce the l1 sparsity. (11) (12)
In classical sparsity inducing models, sparsity is measured using the number of non-zero coefficients or weights. While this is reasonable for settings with “flat” structure, e.g., LASSO or Group LASSO, this does not reveal the true interpretiveness of a solution, in the context of a tree structure. For instance, Figure 1 illustrates how two solutions with same number of non-zero coefficients can have different interpretability.
We propose a novel measure to assess the interpretiveness of a solution. The proposed measure is calculated in a bottom-up fashion, starting from the leaf nodes. For the ith node in the tree, we define the purification noise, Pi as: Pi = Ei + X
Pj j2Ci where Ci is the set of non-leaf children of node i and Ei is the Shannon Entropy of the current ith node by measuring the information loss of all leaf child nodes, i.e., children that are actual features:
Ei =
pi log2(pi) where pi is the fraction of leaf children of node i with a nonzero coefficient. Starting from the parents of the leaf nodes, the purification noise is recursively computed, and finally the purification noise for the root node, i.e., Proot is treated as the overall purification noise for the entire solution. 7
In this section we present our findings by applying
logistic regression classifier for the task of readmission
prediction on the MDW data and MIMIC-III data described
earlier. We first compare the performance of the different
regularization strategies to the classification task using the area
under the ROC-curve (AUC) for each classifier as our
evaluation metric due to the imbalance of data. We also compare
the different strategies to report the purification noise
(interpretability score) value for each solution. For each strategy,
we run 10 experiments with random 80-20 splits for
training and test data, respectively. The optimal values for the
regularization parameters for each strategy are chosen using
cross-validation. We use the MATLAB package, SLEP
Here we compare the performance of different regularization methods discussed in Section 5. The results are summarized in Table 2 and Figure 4.
For the MIMIC-III data set, the best performance, in terms of AUC is obtained using the classical, l1 and l2 regularizations. However, the interpretability is highest for the proposed tree-structured measure, followed by the earlier published TSGL algorithm. On the other hand, the results for (13) (14) the MDW data set show that the tree based regularizations perform on par with the classical methods. However, the interpretability is significantly higher for the proposed treebased regularization scheme. The l2 regularizer, for obvious reasons, does not produce a sparse solution (194.85 of MDW and 716.48 of MIMIC-III), while the other three regularizers induce significant sparsity. However, the structured regularizers are able to achieve significantly low structured sparsity (30.12 of MDW and 21.69 of MIMIC-III) which is consistent with the ICD-9-CM hierarchy.
regularization parameter, 1, in (10) is to control the penalty on the tree-structure of the solution. Figure 4 shows how the AUC score and the interpretability score vary with 1. By increasing 1, we note significant improvement of performance by leveraging more prior hierarchical information as well as outstanding decrease on purification noise, which indicates highly interpretability. ... ... ... ... (451459) Diseases Of Veins & Lymphatics, & Other Diseases Of
Circulatory System ...
453 Other venous embolism and thrombosi 453.8 Acute venous embolism & thrombosis of other specified veins 458 Hypotension 458.9 Hypotension, unspecified ...
(580629) Diseases Of The Genitourinary
System (580589) Nephritis, Nephrotic
Syndrome, And
Nephrosis ...
584 Acute kidney failure 584.5 Acute kidney failure with lesion of tubular necrosis 584.9 Acute kidney failure, unspecified
585 Chronic kidney disease (ckd) 585.6 End stage renal disease
585.9 Chronic kidney disease, unspecified ...
(760779)
Certain Conditions ... Originating In The ...
Perinatal Period (800999) Injury And Poisoning
(V01v91) Supplementary Class Of Factors Influencing Health Status & Contact With
Health Services ... ...
... ...
Figure 5 provides a graphical illustration of the non-zero
features learnt by the proposed model. The red nodes
denote the actual diagnosis codes that had non-zero weights.
The blue nodes are the ancestors of the selected leaf nodes.
We first note that the model consists of only 87 (out of
11567) features or disease codes. Additionally, the 87 codes
are concentrated within a few higher level disease
categories. Since the sub-trees containing the non-zero
features are relatively dense, it is easy to summarize them
with a higher order disease category. For instance, one can
determine that Disorders of fluid electrolyte
and acidbase balance is an important factor in
determining readmissions, which has been confirmed in actual
clinical studies
On the other hand, a similar visualization for l1 regularization shows a highly non-interpretable result, as seen in tracheal or bronchial tuberculosis ..., which has a non-zero weight. It is unclear why only that diagnosis code is selected whereas the other 35 siblings (other forms of tuberculosis) are ignored.
Section 7 shows that leveraging the hierarchical information in the ICD-9CM classification improves the predictive capability of logistic regression while gaining better interpretability. In this section, we demonstrate the necessity of high level interpretation to a medical record prediction model from the healthcare perspective. The focus is to show that an interpretable decision support tool for readmission risk prediction can be effective, as shown in the following real world case study.
As shown in Figure 5, the model is well-informed by the ICD-9-CM hierarchy. Interpretable learning grants the model the ability to conclude high-level important category that are more understandable to the healthcare providers in the medical facilities. For example, the result of proposed model suggests 428-Heart Failure as a important disease category results in readmission instead of extremely specific ICD-9-CM disease code like 428.33-Acute on Chronic Diastolic Heart Failure. The high level important concept ab...
765 Disorders relating to short gestation and low birthweight 765.18 Other preterm infants, 2,000 2,499 grams
765.19 Other preterm infants, 2,500 grams and over
765.27 3334 completed weeks of gestation 765.28 3536 completed weeks of gestation
770 Other respiratory conditions of fetus and newborn 770.6 Transitory tachypnea of newbor 770.81 Primary apnea of newborn 770.89 Other respiratory problems after birth ...
...
995 Certain adverse effects not elsewhere classified 995.91 Sepsis 995.92 Severe sepsis ...
(996999) Complications Of Surgical And Medical Care, Not Elsewhere Classified
996 Complications peculiar to certain specified procedures 996.62 Infection and inflammatory reaction due to other vascular
device, implant, and graft 997 Complications
affecting specified body system not elsewhere classified 997.1
Cardiac complications, not elsewhere classified 998
Other complications of procedures not elsewhere classified 998.59
Other postoperative infection ...
(V50V59)
Persons Encountering
Health Services For Specific Procedures And Aftercare (V40V49) Persons With A Condition Influencing Their Health
Status V44 Artificial opening status
V44.0 Tracheostomy status
V44.1 Gastrostomy status
V58 Encounter for other and unspecified procedures and aftercare
V58.61 Longterm (current) use
of anticoagulants
V58.67 Longterm (current) use of insulin ...
Other 14 categories not selected (010018) Tuberculosis (710739) Diseases Of The Musculoskeletal
(710719) Arthropathies And Related Disorders 720724 (725729)
Rheumatism, Excluding The Back 730739
719.44 Pain in joint, hand
728 Disorders of muscle ligament and fascia Other 4 categories not selected Other 8 categories not selected 717
Internal derangement of knee 718
719 Other and unspecified disorders of joint Contruap7cpt1ue8rr.e 4a 2orm f j oint, lDateeurrana7nsl1pg m7eec.me4inf0eiien sdct u osf, 718.90 deranUgnesmpeencitf ioefd joint, Others e1l9e cctoedde s not site unspecified
728.83 Rupture of muscle, nontraumatic
Text
(800999)  ;Injury And Poisonin..g.
(805809) Fracture Of Spine And Trunk
805
Fracture of vertebral column without mention of spinal cord injury Other 4 categories not selected
805.14 Open fracture of fourth cervical
vertebra
Other 15 categories not selected (960979) Poisoning By Drugs, Medicinals And
Biological Substances
969 Poisoning by psychotropic
agents Other 19 categories not selected
969.6 Poisoning by psychodysleptics (hallucinogens)
Other 22 categories not selected straction makes it easier to focus on important aspects while removing excessive attention from specific disease codes, that may distract the healthcare staff from the key factors during the post-discharge phase.
Case Study: M.J. was a 55-years-old white male with medical history of Hypertension, Coronary Artery Disease and High Cholesterol, and came to the emergency department with left flank pain on 7/1/2018. He was admitted to the hospital for left kidney stone and treated with intravenous fluid and pain medication. M.J. was also found of left hydro nephrosis due to obstructing kidney stone and M.J. underwent urology surgery to have the stone removed on 7/4/2018. However, his hospital course was complicated with sepsis (urinary tract infection) and electrolyte imbalance (hyperkalemia) due to acute renal injury. M.J. finished the course of antibiotics for urinary tract infection and his renal function was back to the baseline. After a 2-week hospital stay, the patient was debilitated so he was discharged to a skilled nursing facility on 7/14/2018 for rehabilitation.
On 7/21/2018, M.J. was found unresponsive and pulse-less by the staff in the skilled nursing facility. He was resuscitated by emergency medical services and readmitted to the intensive care unit for cardiac arrest due to electrolyte imbalance (hyperkalemia). Staff reported that he was not eating or drinking since being discharged to the skilled nursing facility on 7/14/2018. During the ICU, M.J. developed multi-organ failure and died in the intensive care unit on 7/31/2018. Given the patient’s medical history in the above case study, the proposed model would assign a readmission risk to the patient. But at the same time, the model would provide additional factors that could be true for the patient. For instance, electrolyte imbalance would be a factor for readmission, along with the other chronic diseases. The discharge staff would include that in the notes to ensure that it is monitored in rehabilitation phase and possibly save the patient’s life.
In the last decade, there have been numerous studies that link factors pertaining to a patient’s hospital stay to the risk of readmission. However, most studies have been on a focused cohort, limited to one or few hospitals. We show here that similar results can be achieved using claims data, which has fewer elements but provides a large population coverage; the entire state of New York for this study and the wide population coverage of MIMIC-III. Even with the large volume of data, the predictive algorithms are not accurate enough to be used as decision making tools. However, model interpretation can reveal insights which can inform the strategies for reducing and/or eliminating readmissions.
A patient’s disease history is typically expressed using diagnosis codes, which can take as many as 18000 possible values, with many more possibilities in the next generation ICD-10 disease classification. With so many possible features, ensuring model interpretability is a challenge. However, using structured sparsity inducing models, such as the one proposed here, one can ensure that the truly important factors can be identified within the hierarchy.
10 Acknowledgment This material is based upon work partially supported by a seed grant from the University at Buffalo Germination Space Program. We thank Chiahui Chen, MS, RN, FNP-BC, School of Nursing, UB for developing the case study.