Using Machine Learning to Improve Care for Homeless Patients

Strategies that work well on data with many normally-distributed features and many linearly related data points, such as principal components analysis (PCA) or k-Means clustering using Euclidean distance measures, did not produce results of interest with this feature set.  

Here, the keys to a successful analysis were a) discovery of a suitable dimension reduction algorithm, b) use of the right projection metric to allow the algorithm to create the dimension-reduced data set, and c) the use of ‘double reduction’ by application of both the right, carefully tuned, dimension reduction algorithm and an additional dimension-reducing clustering algorithm.  

This combination of approaches led to the discovery of a manageable number of clusters that were useful in describing the characteristics of the clinic’s patient sub-populations, allowing for a deeper analysis of each one using both descriptive statistics and classification algorithms.  

The iterative process used to select the algorithms and choose from among several cluster sets was highly collaborative. The Health Care for the Homeless of Manchester clinic team carefully reviewed many sets of clusters to help determine which approaches produced those most descriptive of their clinic patients.

Dimension Reduction

Manifold learning assumes that datasets can be represented as lying on smooth, non-linear manifolds of low dimension by finding a distance mapping function that will preserve the properties of the higher dimensional data in a lower dimension.  Distance-preserving methods may maintain spatial or graph distances and assume linear relationships or not.  

In general, dimension reduction algorithms using eigenvalue decomposition tend to be more effective on normal and linearly related features, while methods that attempt to keep the order or rank of dissimilarity metrics intact do better on non-linear data.  The choice of algorithm depends on an understanding of the dataset’s features and their meanings.  

A relatively new and extremely useful dimension reduction technique, Uniform Manifold Approximation and Projection (UMAP) was developed by Leland McInnes, John Healy, Nathaniel Saul, and Lukas Großberger in 2018.  UMAP’s popularity is justified by its speed and mathematical sophistication, allowing it to produce a low-dimensional graph from complex, high-dimensional data maintaining the proportional distances and relationships between original features. 

UMAP creates a raw distance matrix using similarity scores based on the number of high-dimensional neighbors each data point has.  Fuzzy union operation makes the similarity scores symmetrical.  UMAP then projects the similarity graph into a lower-dimensional space using Spectral embedding, a non-linear calculation process that preserves the local distances between data points – much like Isomap but using a different methodology (Laplacian eigenmaps). This initial projection is then iteratively updated using lower-dimensional similarity calculations. 

UMAP allows for flexibility in distance metrics or dissimilarity calculations.  The user can choose the method the algorithm will use to calculate the similarity scores between high-dimensional neighbors from a series of commonly-used metrics and dissimilarity measures, or even implement their own measures!  Another essential advantage of UMAP is its ability to preserve the global structure of data due to its choice of cost function.  While another popular dimension reduction algorithm, t-distributed Stochastic Neighbor Embedding (t-SNE)’s performance often degrades as perplexity increases, UMAP’s use of nearest neighbor calculation reduces its sensitivity to increases in n-neighbors once the n-neighbor parameter value reaches a threshold. 

Imputation

Before utilizing any dimension reduction technique, it is necessary to have a complete and fully-scaled feature set.  Elimination of NULL values is always a challenge for the researcher, because imputation typically either complicates or over-simplifies feature ranges.  Fortunately, because the patient-level data set’s most key features primarily consist of count data, it was possible to fill most NULL count values with zeros without changing the meaning of these variables.  Interval values were likewise filled with a standard “censorship” value of 730 days.

The remaining missing data were imputed using Sci-kit Learn’s (Pedregosa et al., 2011) experimental implementation of Multivariate Imputation by Chained Equations (MICE) (van Buuren & Groothuis-Oudshoorn, 2011).  This iterative algorithm estimates values for each missing data point using all the other data points in the data set.  As MICE adds data points, it uses these new data points to continue the process of estimating additional missing values.  It continues the process until all of the data points are filled in.  Following imputation, the data set was scaled using Sci-kit Learn’s StandardScaler.

Metric Selection - The Bray-Curtis Dissimilarity

The Bray-Curtis dissimilarity is a non-Euclidean method of obtaining the absolute proportion of dissimilarity between rows of raw count data (Bray & Curtis, 1957).  

The measure is typically used in environmental biology, where counts of species across various sites are commonly compared to one another to pinpoint areas where changes in the ecology may be impacting species counts.  The Bray-Curtis dissimilarity assumes count origins are equal in every way; for example, the measure does not typically scale by computing differences on relative counts.  

The usual objection to the use of the Bray-Curtis dissimilarity is that it is not a “true metric” because it violates the triangle inequality.  This Euclidean axiom demands that, in every case, the distance between two points a and b must be less than the distance from a to b via another point, c.  While many measures violate this property, they are referred to as “dissimilarities” and not “metrics” because this property is part of the mathematical definition of a metric.  

While environmental biologists would need to be concerned with the question of whether or not species counts at sites that vary by size or importance should be considered equal, no such problem exists when using the Bray-Curtis dissimilarity to compare the number of visits or visit reasons by category across individuals in a patient sample.  Considering every patient equal to every other while focusing on the absolute level of difference in each patient’s set of visit counts and visit reasons was precisely the behavior I was hoping the chosen measure would achieve.  Another helpful behavior of the Bray-Curtis dissimilarity in the dataset context is that zero values across pair-wise comparisons result in a NULL value for the dissimilarity score.  Since most algorithms ignore NULL values, this helps increase the salience of information that differentiates patients from one other.

Implementation of the Bray-Curtis dissimilarity in the context of the patient-level data works as follows.  The Bray-Curtis dissimilarity – BCij = 1-(2*Cij)/(Si+Sj) – is computed pair-wise, where Cij is the sum of the lesser values for each of two patients i & j, Si is the sum of counts for the first patient, and Sj is the sum of counts for the second patient.  The result is a decimal between 0 and 1, indicating the % similarity between the patients in terms of diagnosis and visit counts.  Passing this parameter to UMAP  causes the algorithm to utilize this calculation to create a matrix of – in this case – dissimilarity scores, computed pair-wise, for all of the patients in the dataset.  The algorithm then carries out its additional calculations to produce a lower-dimension data projection. 

Spectral Clustering

The name “Spectral” in Spectral clustering comes from the mathematical definition of a matrix’s “spectrum” as its eigenvalues (German: intrinsic values). Eigenvalues determine the magnitude of corresponding vectors (eigenvectors) together summarizing the variance of a multi-dimensional dataset.  

Spectral clustering starts with calculating a graph matrix (G) representing the relationships in the dataset.  To compute the graph matrix, there must be a way of quantifying these relationships.  The proper way of doing so depends upon the data.  Are the data colored pixels?  If so, perhaps the right measurement of difference tells how far away each color is from other colors based on RGB values, for example.  

Many graph representations are computed using k-nearest neighbors, the Gaussian kernel/radial basis function, or Euclidean distance.  Once the graph representation (G) is calculated, three matrixes can be obtained from it:

1.     An incidence matrix (A): An n x m matrix where n is the number of nodes and m is the number of edges or connections.  The incidence matrix summarizes the relationships between the graph’s nodes (points) and edges (links). 

2.     A degree matrix (D): An n x n diagonal matrix summarizing the number of connections between every node and all other nodes.

3.     An adjacency matrix (B): A binary n x n matrix with a diagonal of zeros that establishes whether or not every node is connected to every other node.

The second and third matrixes (the degree and adjacency matrixes) can be used to compute a symmetric, positive, semi-definite matrix called the Laplacian matrix.  It is called “Laplacian” because when Laplace’s finite difference equation is applied to a discrete graph, the resulting matrix represents an undirected graph’s state of equilibrium.  

A typical Laplacian matrix is obtained by subtracting the adjacency matrix from the degree matrix, in this case: L = D - B.  

A normalized version of the Laplacian can also be calculated as D−1(D − B) = I-D−1B, according to the idea that a graph separation can be optimized by computing the probability of a transition from one area of the graph to another via random walk.  

This fits in nicely with the perturbation theory, necessary for computing clusters via eigenvalues of the normalized Laplacian when the separation between areas of the graph is imperfect and varies in density (Stewart & Sun, 1990 in von Luxburg, 2007) – a situation that applies to the separation of this dataset.    

A value for k was tuned (k=40)  to create a graph representation of the features using the k-nearest neighbors’ algorithm before following the remaining steps to compute and analyze the Laplacian eigengaps.  Once the numbers of clusters were tuned, Sci-kit Learn’s implementation of SpectralClustering was used to produce the clusters, and the original feature set was used to predict them using ensemble methods.  Permutation “feature importances” allowed a first insight into the key features used to divide the data into the target clusters.

Clinical Partnership

A crucial step when utilizing unsupervised learning to describe patient sub-populations is the validation and feedback of the clinicians who work with patients daily.  Whether or not the algorithm could divide the clinic’s patients into meaningful groups worthy of further analysis was something only the HCHM team could advise on.  The clustering results were presented for review, along with basic statistics describing demographic and visit data for each cluster set and the ensemble classification results and feature importances.  

The team reviewed and discussed the clustering results independently and eventually agreed that the six “Spectral B” clusters produced using the UMAP feature set should be subject to a deeper analysis.

The “Spectral B” UMAP clusters were imperfect due to the difficulty of dividing the patient data set across many complex features.  However, in large part, the clusters were able to describe recognizable sub-populations of clinic users only hinted at in the descriptive analysis.  

The six “Spectral B” UMAP clusters roughly corresponded to five service groups:

Patients in clusters three and five had the highest acuity levels, the highest numbers of visits, and the highest numbers of diagnosis codes across their visits.  As discussed previously, the utilization patterns and primary condition categories of these two clusters differed dramatically. 

Cluster three, the group with the highest number of emergency department utilizers, had more emergency department codes across all categories than outpatient codes, but their code counts for substance use visits were also elevated in the outpatient setting.  Cluster three’s top emergency department codes (excluding tobacco use-related codes) included alcohol dependence and intoxication, hypertension, depression and suicidal ideation, anxiety, and opioid and other psychoactive substance abuse.  Asthma, COPD exacerbation, urinary tract infections, and other infections - particularly respiratory and skin infections, including abscesses and cellulitis, were also common reasons for emergency department visits within this cluster.

In cluster five, outpatient visits dominated.  While many cluster five patients suffered from mental health and substance use conditions like cluster three patients, they had high numbers of outpatient visits for these conditions and very few emergency visits.  Cluster five patients had more chronic conditions, such as diabetes, hypertension, chronic obstructive pulmonary disease, and cardiovascular conditions.  They also did a better job managing their conditions, with many patients in this cluster coming to the clinic frequently for blood pressure checks, diabetes visits, and mental health treatment.  More patients in cluster five were former smokers and recent quitters, and a smaller proportion of these patients had elevated PHQ-2 and “highest-risk” NIDA scores.  In spite of having many complaints of pain during outpatient, and even some emergency department visits, patients in cluster five seemed to be striving to improve their outcomes and were using the HCHM clinic as a support system for their health maintenance and well-being.

While clusters zero, one, two, and four did not have the elevated levels of acuity found in clusters three and five, there were good reasons to think that low or under-utilizers in some of these clusters – particularly clusters one and two – might become high utilizers in the future, if ways of better engaging them in health maintenance are not discovered.  Each of these clusters had particular conditions that were challenging for them, some uniquely.  For example, contusions, strains, sprains, bites, fractures, and other injuries were an issue for people in these clusters.  Dental problems and mental health issues such as suicidal ideation were high on the list of emergency visit reasons for those in cluster one.  Concussions and other head injuries were also common, as well as alcohol and substance-related diagnoses. 

Several opportunities to improve care for patients in these clinic sub-populations were identified due to this analysis.  

High ED Utilizers

The deep-seated synergistic impact of childhood trauma and its sequelae can lead to profoundly negative alterations in both mental and physical health.  The widespread negative social and economic impacts of this individual tragedy writ large are illustrated by the data presented here; cluster three patients are living out the consequences of both an individual nightmare and a public health emergency.  

Both the Substance Abuse and Mental Health Services Administration (SAMHSA) and the National Health Care for the Homeless Council provide clinicians with excellent guidance that reflects the reality that assisting people recovering from a traumatic past, whether they suffer from overt addiction or mental health conditions or not, is often primarily a matter of encouraging their authenticity and making truthful identification of their desires and emotions less anxiety-provoking.  Learning about and engaging in trauma-informed care and motivational interviewing provides a place to start, and return to, when engaging with people who may be unpredictable or struggle with self-efficacy (Bennett, 2016a). 

The data on cluster three patients affirmed previous findings that people with high-acuity mental health and substance use problems may have difficulty managing their health issues, are at elevated risk for many comorbidities, and can be unpredictable in their resource utilization patterns.  

Actions assistive to the highest emergency utilization group may include:

1. Continuing to focus on therapeutic relationship building, promoting self-acceptance and authenticity in all patient-provider interactions

2. Augmenting the therapeutic relationship and advancing patient-centered care by tailoring care to both the primary care guidelines and patients’ priorities

3. Increasing care and case management services; considering the addition of dedicated care and case management for the highest-risk individuals

4. Advocating for an increase in harm-reduction strategies and the wider availability of both temporary and permanent supportive housing

5. Increasing self-service resource availability, such as recovery meeting lists and recovery literature

6. Increasing access to self-service hygiene care

7. Using standing order protocols to empower RNs to assist clients with common needs such as first-aid and infection prevention, obtaining commonly-needed medications, and obtaining and using blood glucose testing supplies

8. Engaging in frequent community and/or street outreach efforts

9. Establishing a telehealth connection with patients who have access to the internet via a mobile device

10. Increasing the frequency of outpatient communication and follow-up appointments

Low Utilizers / Care Avoiders

Low utilizers (cluster one and two patients) may have many of the same problems as cluster three patients, while their levels of acuity and numbers of comorbidities are lower overall.  Younger cluster one and two patients may be especially difficult to reach because they are still able to function and may find their existing coping strategies workable for now.  Cluster two patients may also be avoiding institutional interactions due to deep discouragement brought on by struggles common to the previously incarcerated.  In addition to health challenges, these patients commonly face widespread employment and housing discrimination, and are ten times more likely to be homeless than the general public according to a recent Prison Policy Initiative report produced using Bureau of Justice Statistics’ survey results (2018).  These rates increase for those who have been incarcerated more than once, and for former inmates of color.  

In a large study of care avoidance in the general population (Taber, Leyva & Persoskie, 2015), researchers found that people typically avoid interactions with the health care system due to combinations of factors including perceived cost, other priorities, lack of insurance, and the assumption that their symptoms will get better over time.  Care avoidance among people experiencing homelessness may be explained by similar rationales but exacerbated by frequent negative encounters with the health care system and institutions in general.   Clinicians caring for homeless people do not expect such people to be well-groomed, however in a qualitative study of street sleepers in London, UK, researchers found that many homeless people reported being ashamed when they were not able to put themselves together, stating they might not go to a clinic even if they needed care because they were tired or unkempt, or because they would have to carry all their belongings with them when they went (Ungpakorn & Rae, 2019). In an effort to alleviate the isolation homeless people may feel and the lack of access to care this may result in, many communities, including Manchester, NH, have put together mobile outreach programs, enabling clinicians to meet the homeless where they are.  

In summary, actions assistive to low-utilization patients might include:

1. Focusing on causal relationship-building more than health care administration

2. Increasing the frequency and regularity of contact both in the clinics and with street outreach

3. Advocating for harm-reduction

4. Increasing opportunities for free dental assessments and care

5. Increasing self-service hygiene and resource availability

6. Increasing access to first-aid and commonly-needed medications

7. Expanding telehealth for patients with access

8. Increasing supportive programs for the previously incarcerated, connecting them with community, housing, and employment resources after release

Moderate and Higher-Acuity Clinic Utilizers

For patients in clusters zero and five, regular clinic visits were already a common occurrence.  Many were engaging in regular appointments to help with the control of chronic conditions and participating in substance recovery and mental and behavioral health treatment programs.  Integrated, trauma-informed care already happens at the clinics; however, variations in provider patterns show that some providers make more frequent follow-up appointments with patients, engaging them more frequently for health maintenance.  These patients tend to participate in more follow-ups overall, and their glucose and blood pressure control is superior to that of other patients. 

Hypertension

An area of concern for the clinic in general, but for higher-acuity patients in particular, is the high number of patients with poor control of their hypertension.  Hypertension is a significant risk factor for heart attack and stroke and is poorly controlled across the U.S. population.  According to the Centers for Disease Control and Prevention (2020), only about 1 in 4 adults (24%) with hypertension have their condition under control.  Blood pressure control among homeless people is likely to be worse.  After a retrospective chart review study of homeless New Yorkers, Asgary et al. (2016) concluded that approximately 40.1% of homeless patients had uncontrolled blood pressure (p = .29) and that 15.8% had stage 2 hypertension (p = .27).  Blood pressure treatment in homeless adults is complicated by more than decreased access or reasons for care avoidance.  Patients experiencing homelessness may be further limited in their ability to monitor treatment through regular self-checking of blood pressures, and in their ability to avail themselves safely of more aggressive medication regimens requiring shorter-acting medications with frequent dosing schedules.  

Asthma & COPD

Other frequent drivers of emergency visits among higher-acuity patients were asthma and chronic obstructive pulmonary disease.  Care for these common chronic respiratory diseases is extraordinarily difficult when patients are experiencing homelessness.  Many environmental triggers may be present for these patients, including animal and insect droppings, pollen, mold,  and smoke.  These patients may also experience frequent exposure to contagious upper respiratory infections such as pneumonia, influenza, and even tuberculosis.  Clinicians recommend frequent outreach to provide regular peak flow testing and immunizations, and to assess patients’ access to and use of prescribed medications or inhalers.  They also recommend frequent reassessment for symptoms of worsening allergies or burgeoning respiratory infections requiring further treatment or intervention (Gracy et al., 2018). 

Medical Respite Care

Another issue common across adult patient cluster groups was the presence of emergency department visits following prior hospitalizations or procedures.  Top emergency department code lists for several of the patient clusters indicated that patients may be having difficulty caring for themselves following medical procedures, leading to readmissions or complications such as infections.  A recent retrospective study of 232,373 general, vascular, and orthopedic surgeries occurring on homeless veterans in the Veterans Health Administration between 2008 to 2014 (Titan et al., 2018) found that hospital readmissions were higher in people experiencing homelessness who were discharged to the community following surgery.  In addition to better care coordination and increased communication between primary care and inpatient clinical teams, the National Health Care for the Homeless Council advocates for the establishment of Medical Respite Care for all homeless people (NHCHC, 2022c).  

Medical respite care provides temporary, longer-term shelter for people recovering from hospitalizations, surgeries and other acute illnesses, preventing discharge back to the street or a homeless shelter following acute care.  Currently, thirty-eight out of fifty states have at least one medical respite care facility available for homeless people (NIMRC, 2021b).  California has forty-one such facilities, while New Hampshire and Maine are among the twelve states with no such facilities.  Neighboring Vermont has one such facility, and Massachusetts has three,  including one of the earliest such facilities. Two recent studies conducted in Denmark demonstrated that Medical respite care for homeless people was cost-effective and prevented increased utilization (Bring et al., 2020), as well as providing homeless individuals with an environment where they could rest, reflect on their lives, and make plans for a better future (Pedersen et al., 2018). 

Translation Services

A little more than half of the patients in cluster five identified a language other than English as their primary mode of communication.  The majority of these patients are refugees from Asia and Africa, including Bhutan and the Democratic Republic of the Congo.  Refugees in the community experience many barriers to health services access, including racism, xenophobia, reduced access to transportation, and a lack of available interpreters.  Many refugees also experienced persecution or torture in their countries of origin, but few had mental health diagnoses or scored high on depression screenings.  It is possible that some of these patients are reluctant to discuss difficulties with their mental health or seek out treatment for post-traumatic stress disorder related to their traumas. With face-to-face communication support and the development of a stable and trusting relationship with the HCHM care team, it is possible these patients may become more willing to receive treatment related to their experiences.

Functional Challenges

While I was not able to discover many patients struggling with disabilities through data mining, the most patients with ‘disability’ mentions in their clinic visit notes were in cluster zero.  People facing functional challenges are a commonly-identified sub-population among homeless people (HUD, 2022) who may benefit from collaborative assessments and referrals that can improve their independence and assist them in accessing transportation, employment, health care, and other necessities.

Assistive actions for moderate and higher-acuity engaged outpatients might include:

1. Increasing pre and post-hospitalization follow-up and care planning

2. Advocacy for medical respite care in the State of New Hampshire

3. Increasing the frequency of follow-up contacts and visits either in the community or at the clinics, using telehealth where available

4. Increasing the availability of paid or volunteer translators for patients for whom English is not a primary language

5. Continuing to assist refugee families with connections to additional refugee services

6. Assessing patients with functional challenges for disability, and assisting them to access services that increase their health, independence, and quality of life

Children of Refugees

Cluster four consisted primarily of children of refugee families living in the Manchester area.  Many of these children face similar difficulties to their parents in integrating into the larger English-speaking society and adapting to a new culture in the United States.  

Primary causes of emergency visits for these patients were similar to those of other children and adolescents around the nation.  Emphasis on prevention and safety, as well as the development of good habits and the avoidance of unhealthy habits (sugary drinks, prolonged or early exposure to screens and social media, early pregnancy, smoking, and drug use), are just as appropriate for the primary care of these children as all others.  

The availability of face-to-face interpreters may be key to establishing pathways of trust and communication between these children, their parents, and the care team.  Better quality communication may enable the care team to better assess patients’ needs and provide them, and their families, with supportive interventions and education. 

Assistive actions for children of refugees might include:

1. Increasing the availability of translators

2. Establishing ongoing relationships and trust with children, parents, and the refugee community

3. Providing education about safety, prevention, and risks associated with adolescence

4. Collaborating with schools and after school programs to help build trauma-informed care teams and community programs promoting literacy and social support for these children

Copyright © 2022, Kyle Partridge Rasku

Citation: Rasku, Kyle Partridge, "Using Machine Learning Techniques on Real-World Data to Understand the Characteristics of the Manchester, NH Health Care for the Homeless Patient Population for Risk Factor Identification and Intervention Improvement" (2022). Master's Theses and Capstones. 1572.

https://scholars.unh.edu/thesis/1572 

Please download the paper for a full list of references.