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K-Means Cluster Analysis of Rehabilitation Service Users in the Home Health Care System of Ontario: Examining the Heterogeneity of a Complex Geriatric Population

      Abstract

      Armstrong JJ, Zhu M, Hirdes JP, Stolee P. K-means cluster analysis of rehabilitation service users in the home health care system of Ontario: examining the heterogeneity of a complex geriatric population.

      Objective

      To examine the heterogeneity of home care clients who use rehabilitation services by using the K-means algorithm to identify previously unknown patterns of clinical characteristics.

      Design

      Observational study of secondary data.

      Setting

      Home care system.

      Participants

      Assessment information was collected on 150,253 home care clients using the provincially mandated Resident Assessment Instrument–Home Care (RAI-HC) data system.

      Interventions

      Not applicable.

      Main Outcome Measures

      Assessment information from every long-stay (>60d) home care client that entered the home care system between 2005 and 2008 and used rehabilitation services within 3 months of their initial assessment was analyzed. The K-means clustering algorithm was applied using 37 variables from the RAI-HC assessment.

      Results

      The K-means cluster analysis resulted in the identification of 7 relatively homogeneous subgroups that differed on characteristics such as age, sex, cognition, and functional impairment. Client profiles were created to illustrate the diversity of this geriatric population.

      Conclusions

      The K-means algorithm provided a useful way to segment a heterogeneous rehabilitation client population into more homogeneous subgroups. This analysis provides an enhanced understanding of client characteristics and needs, and could enable more appropriate targeting of rehabilitation services for home care clients.

      Key Words

      List of Abbreviations:

      ADLs (activities of daily living), CHESS (Changes in Health, End-Stage Disease, and Signs and Symptoms Scale), IADLs (instrumental activities of daily living), OT (occupational therapy), PT (physical therapy), RAI-HC (Resident Assessment Instrument–Home Care)
      WITH THE AGING of the population and pressures to limit the use of inpatient/hospital services, home-based services are an increasingly important component of the health care system. In the Canadian province of Ontario, as well as many other jurisdictions, many older adults rely on services from the home care sector to continue living in their own homes. Included in the array of services offered by home care in Ontario are rehabilitation therapies (physical therapy [PT] and occupational therapy [OT]), which have been demonstrated to be effective for supporting the independence of older persons in home-based settings.
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      Methods

      In this article, we aimed to explore the heterogeneity of home care clients who use rehabilitation services, discover previously unidentified patterns of clinical characteristics, and create client profiles to illustrate the different subgroups found within this complex client population. This study used data collected based on the Resident Assessment Instrument–Home Care (RAI-HC).
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      • Landi F.
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      The RAI-HC assessment system has been mandated for use for all clients expected to use home care services for more than 60 days, which provides Ontario census-level data on long-stay home care clients. For this exploratory cluster analysis, we used the RAI-HC data of 150,253 clients who received rehabilitation services (OT or PT) within the first 3 months of their initial home care assessment. Data were collected between April 2005 and August 2008. Ethics approval was granted by the University of Waterloo's Office of Research.
      The RAI-HC is one of a suite of standardized assessment tools developed by the international interRAI consortium.
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      The instrument contains a wide variety of assessment items including demographic information, cognition, physical functioning, disease diagnoses, nutrition/hydration status, environmental assessment, and service use. Collected by frontline workers using data entry software, the assessment system has checks during data input that constrain item entries as nonmissing, within correct ranges, and with logical checks.
      Because of the large number of variables available within this assessment data (≥300), variables to be used in the K-means cluster analysis were selected through quantitative variable selection techniques (Proc Varclus in SAS 9.1)a and consultation with fellow researchers from the infoRehab team (http://www.inforehab.uwaterloo.ca), who have knowledge of rehabilitation services for home care clients. In total, 37 variables were used for the K-means cluster analysis; these included activities of daily living (ADLs), instrumental activities of daily living (IADLs), disease diagnoses, sex, Changes in Health, End-Stage Disease, Symptoms and Signs (CHESS), a health instability outcome measure,
      • Hirdes J.
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      The MDS-CHESS scale: a new measure to predict mortality in institutionalized older people.
      and age. A complete list of all the measures used and their brief descriptions can be found in table 1. This table also includes the proportion of the entire rehabilitation service user population.
      Table 1Variables Included in K-Means Cluster Analysis
      Margin of error for these percentages is ≤1%.
      MeasureDefinition% of Overall Client Population
      IADLs performance: ordinary houseworkNeeds assistance94.8
      IADLs performance: shoppingNeeds assistance91.7
      IADLs performance: meal preparationNeeds assistance82.4
      ADLs performance: bathingNeeds assistance81.2
      IADLs performance: transportationNeeds assistance75.3
      Unsteady gaitClient displays gait that is considered unsteady67.6
      SexFemale66.7
      IADLs performance: managing medicationsNeeds assistance65.0
      Daily painClient complains or shows evidence of pain daily60.8
      ArthritisArthritis present55.4
      ADLs performance: dressing lower bodyNeeds assistance45.4
      ADLs performance: dressing upper bodyNeeds assistance38.5
      Living aloneLiving alone (no partner or caregiver in home)35.1
      Cognition: decision-makingThe ability for the client to make decisions is impaired32.5
      Heart diseaseCoronary artery disease diagnosed26.3
      ADLs performance: transferNeeds assistance23.7
      OsteoporosisDiagnosed with osteoporosis23.6
      ADLs performance: eatingNeeds assistance23.2
      ADLs performance: locomotion in homeNeeds assistance22.7
      ADLs performance: toilet useNeeds assistance22.4
      History of strokeStroke has been diagnosed in past19.1
      COPD/emphysema/asthmaPresence of COPD/emphysema/asthma18.3
      Frequent fallingClient has fallen ≥2 in the last 90d17.0
      CancerCancer present13.7
      Psychiatric diagnosisAny psychiatric diagnosis13.3
      Congestive heart failureCongestive heart failure present12.9
      DementiaClient has received a diagnosis of dementia (Alzheimer's or non-Alzheimer's type)12.6
      FrailtyCHESS score ≥212.2
      History of fractureFractures have previously occurred11.5
      ADLs performance: mobility in bedNeeds assistance10.9
      Pressure ulcerCurrent pressure ulcer on the client's body7.0
      Neurologic disorderPresence of Parkinson's or multiple sclerosis6.8
      Hip fractureHip fracture in client's history5.6
      DepressedDepression Rating Scale score ≥53.3
      Head traumaHead trauma present1.4
      End stage diseasePrognosis <6mo to live0.9
      NOTE. Age was included in the K-means cluster analysis (standardized using Euclidean distance). Average age was 76.8 years; sample size (N) was 150,253.
      Abbreviation: COPD, chronic obstructive pulmonary disease.
      low asterisk Margin of error for these percentages is ≤1%.
      Thirteen ADLs and IADLs items were included, which covered a variety of physical functioning domains. These items were reduced to a dichotomous form (independent vs dependent). Fourteen disease diagnosis categories were also included, and these were also coded dichotomously as present/not present. Additional variables included in the cluster analysis were sex, age (standardized using Euclidean distance), presence of daily pain, multiple recent falls (≥2 vs <2), unsteady gait, problems with decision-making, presence of pressure ulcers, CHESS score (≥2 vs <2), and home living status (alone vs living with caretakers).

      K-Means Cluster Analysis

      In this study, we sought to discover patterns of clinical features by using the K-means algorithm,
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      a popular data partition method widely used in many fields including data mining, pattern recognition, decision support, machine learning, and image segmentation. This algorithm is considered by the data mining and machine learning community to be an unsupervised learning technique, because it searches for patterns among input variables without using an outcome variable to dictate how the pattern is formed. In other words, K-means clustering is a way to use data to uncover natural groupings within a heterogeneous population. To uncover patterns, the algorithm starts by first assigning data points into random groups. The group centers are then calculated and the group memberships are reassigned based on the distances between each data point and the group centers. This process is repeated until there are no changes in the group memberships from the previous iteration. With the exception of age, all variables used in the K-means cluster analysis were dichotomized. This allows for easy interpretation as a mean score of a dichotomous variable directly relates to the proportion of clients with a score of 1.
      To perform this analysis, we used the procedure FASTCLUS in SAS.a We chose the K-means algorithm and the SAS implementation in particular because of its suitability for analyzing relatively large data sets, as well as its use of a spacing heuristic for initial group assignments in order to avoid suboptimal solutions.
      • MacQueen J.B.
      Some methods for classification and analysis of multivariate observations.
      All analyses were performed in SAS version 9.1.a
      Because of the fact that K (the number of clusters) needs to be specified prior to analysis, we used an iterative process to explore a range (2–20) of possible cluster solutions. For each possible cluster solution, we examined 3 statistical criteria: (1) the cubic clustering criterion,
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      (2) the pseudo F,
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      and (3) the squared multiple correlation. To compare these 3 criteria over the range of solutions, each of 3 statistics were graphed by the number of potential clusters.

      1-Year Service Outcomes

      In addition to the clinical variables collected with the RAI-HC, service outcome data were available for each of these clients for the time period of 1 year after the clients' initial home care assessment. These service outcomes indicate if the clients left the home care system and include: successful completion of care plan (released to live at home), hospitalization, long-term care placement, and mortality. After the cluster analysis, service outcomes were used to examine outcome differences between the clusters.

      Results

      The first column in table 1 presents the variables used in the cluster analyses, as well as the full sample baseline demographic, functional, and health characteristics. For the entire sample, the average age ± SD was 76.8±13.2 years, 12.6% were diagnosed with dementia (Alzheimer's and non-Alzheimer's dementias), 5.6% had a previous hip fracture, 19.1% had stroke, and two thirds of these clients were women (66.7%). The majority of clients had daily pain (60.8%), arthritis (55.4%), and unsteady gait (67.6%). Because of the extremely large sample size, the margin of error for these percentages is ≤1%.
      We used the K-means algorithm to find a cluster solution that generated a small number of relatively homogenous subgroups in this client population. From this process, outlined in the Methods section, we determined that a 7 cluster solution was most appropriate for this data. The approximate overall R2 of the K-means (K=7) cluster analysis was .130, which represents the estimated overall variance accounted for by the clusters.

      Client Clusters

      Figure 1 contains 36 bar graphs showing the proportions in each of the 7 clusters for the dichotomous measures used in the cluster analysis. This series of graphs illustrates the variability and heterogeneity between the subgroups on a measure by measure basis. To further explicate the heterogeneity found within this population, a heat map technique was used to create figure 2. This heat map is a graphical illustration of the relationship between the 7 clusters and the distributions of each of the 37 variables used in the cluster-means cluster analysis.
      Figure thumbnail gr1
      Fig 1Cluster proportions for dichotomous variables used in K-means cluster analysis. The variables are ordered by between-cluster variations (from high to low variation). Abbreviation: COPD, chronic obstructive pulmonary disease.
      Figure thumbnail gr2
      Fig 2The colors in this heat map represent quantiles. Black boxes indicate the cluster is on the low end of the distribution for the particular variable. White boxes indicate that the cluster is on the high end of the distribution for the particular variable. Clusters are ordered in similarity to each other. Variables are ordered in similarity to each other, in terms of their distribution over the 7 clusters. Abbreviation: COPD, chronic obstructive pulmonary disease.
      In order to describe the patterns found within this client population, cluster averages were used to create profiles for each cluster highlighting the major and differential characteristics of the 7 subgroups. Clusters were ordered from most dependent to most independent, based on the measures used in the analysis.

      Cluster Profiles

      Cluster 1 (9%): dependent and immobile clients with cognitive problems

      This cluster had an average age of 76.3 years and was 60% women. High rates of dementia (15%), stroke (27%), neurologic disorders (multiple sclerosis and Parkinson's disease; 13%), heart disease (25%), and incontinence (58%) were found in this cluster with 20% of this cluster having a high score on the CHESS scale. This cluster was highly dependent across all ADLs and IADLs domains, including a relatively high rate of dependency on bed mobility (47%), transferring between surfaces (96%), and locomotion in home (89%).

      Cluster 2 (23%): dependent but mobile clients with cognitive problems

      The largest of the 7 subgroups, cluster 2 had an average age of 78.9 years and was 46% women. Similar to cluster 1, cluster 2 was characterized by clients having a high rate of dementia (48%) and problems with daily decision-making (86%). However, this cluster differs from cluster 1 in that these clients were relatively mobile (bed mobility: 3% required assistance; transferring between surfaces: 10%; locomotion in home: 7%), yet they were still highly dependent in performing all other ADLs and IADLs.

      Cluster 3 (14%): primarily women clients requiring assistance with IADLs and some ADLs

      This client cluster had an average age of 76.5 years and was primarily women (77%). The majority of this cluster reported daily pain (84%). Out of all 7 clusters, this cluster is most likely to self-report poor health (28%), and 75% of these clients are in danger of falling because of unsteady gait. On average, they required assistance with ADLs and IADLs domains including meal preparation (95%), housework (100%), managing their medications (67%), shopping (99%), transportation (87%), dressing their upper body (70%), dressing their lower body (99%), and bathing (97%).

      Cluster 4 (15%): primarily women clients requiring assistance with IADLs

      Primarily women (89%) with an average age of 79.3 years, this cluster is characterized by their need for help with IADLs: housework (99%), medication management (67%), and shopping (98%). Of the 7 subgroups, this group of clients had one of the highest proportions of clients with arthritis (84%) and reporting daily pain (90%). Approximately half of all cluster 4 members lived alone (49%). Thirty-seven percent had a recorded diagnosis of osteoporosis. Compared with clusters 1 to 3, this cluster of clients was relatively independent, because they did not require assistance with dressing their upper body (2%) or dressing their lower body (0.1%).

      Cluster 5 (19%): clients requiring assistance with IADLs and bathing

      Cluster 5 had an average age of 78.2 years and was 58% women. This group had the smallest proportion of clients reporting daily pain (20%), yet they had high prevalence of dementia (26%) and problems with daily decision-making (61%). Clients within cluster 5 were much more independent in ADLs compared with clusters 1 to 4, with the exception of bathing (78% required assistance). What makes this cluster distinct is that a large majority of these home care clients required assistance in all 4 IADLs domains (managing medications 93%; housework 98%; shopping 98%; transportation 84%), most likely because of their impaired cognition.

      Cluster 6 (10%): ADLs independent cognitively intact younger clients

      The youngest of all of the clusters with an average age of 70.6 years of age, this subgroup is characterized by being primarily men (69%). These clients had low rates of stroke (11%), osteoporosis (6%), multiple falls (10%). and cognitive impairment (5.8% had troubles with daily decision-making, 1.8% with a dementia diagnosis). These home care clients mainly required assistance with housework (90%) and shopping (76%) and were relatively independent in bathing (35%), transportation (30%), and medication management (22%). Surprisingly, this cluster had a rate of cancer (29%) that was approximately 3 times the rate of the other clusters.

      Cluster 7 (10%): clients who live alone and require some assistance with housework and bathing

      Subjects in this subgroup were primarily women (86%), with an average age of 76.4 years. A large proportion of these clients reported having arthritis (70%) and osteoporosis (29%) and the majority lived alone (83%). Cluster 7 had low rates of both dementia and problems with daily decision-making—2% and 8%, respectively. The majority of this cluster also reported daily pain (69%) and arthritis (70%). In terms of ADLs and IADLs impairments, this cluster needed assistance mainly with housework (75% required assistance) and bathing (61%). This cluster can be considered the most independent of the 7 subgroups.

      1-Year Service Outcomes

      For the outcome of successfully completing their care plan, the percentage of clients with this outcome ranged widely across the clusters. The most successful clusters were clusters 6 (36%) and 7 (29%), while the least successful clusters were 2 (13%) and 1 (14%). Clusters 1 and 2 also had the highest proportion of clients who suffered mortality within 1 year of assessment (11% and 8%, respectively). Additionally, clusters 1 and 2 also had the highest proportion of clients placed into long-term care (8% and 11%, respectively). The hospitalization rates ranged between 11% and 17%, with the highest rates falling within clusters 1, 2, 3, and 4. See table 2 for details.
      Table 21-Year Outcome (% of clients in each cluster)
      Margin of error for these percentages is ≤1%.
      ClusterSuccessfully Complete Care PlanHospitalizedLong-Term Care PlacementMortality
      114.416.97.911.2
      320.416.54.36.7
      422.215.14.54.8
      213.214.411.07.9
      522.013.36.46.1
      636.811.22.07.0
      728.510.92.23.3
      low asterisk Margin of error for these percentages is ≤1%.

      Discussion

      The findings of this cluster analysis demonstrate that rehabilitation service users in the home care system are a heterogeneous group that can be grouped into smaller, more homogeneous clusters based on available health information. By applying the K-means clustering algorithm, we were able to identify 7 relatively homogeneous subgroups from within the entire population of rehabilitation services users in the Ontario home care system.
      This article illustrates the use of an alternative approach to dealing with individual differences in complex health service data. The need to better understand naturally occurring groupings within client populations in home health care systems will grow in the upcoming years, because the aging population and the multiplicity of health care needs will lead to home health care populations that are increasingly complex and challenging to manage.
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      Clinical quality needs complex adaptive systems and machine learning.
      can enhance our ability to understand geriatric patient populations and inform us how we can best target our limited health care resources, which would benefit both patients and the health system.
      The resulting 7 clusters clearly illustrate that functional abilities, as measured by the ADLs and IADLs measures, can cluster together to form patterns across the population of home care clients that are provided with rehabilitation services. Clusters 1 and 2 were very dependent for many tasks of daily living including bathing, dressing lower body, and transportation. In contrast, clusters 6 and 7 were relatively independent, yet were still provided with some rehabilitation services. These differences demonstrate that there are subgroups within the overall rehabilitation client population. Home health care is currently restrained by having limited resources; the development of this type of information can be used to better target individuals who are at greatest need and/or to those who would benefit most. Because of the heterogeneity found within this client population, we can assume that services required, the impact of services, and the predictors for various outcomes vary significantly across the entire population of rehabilitation service users. More research is needed to determine what types of clients benefit most from rehabilitation services and what types of clients require more or less services. The consideration of heterogeneity in care populations is also important for future work on how electronic health information can be used to better target services, and how data can be used to inform service planning including prioritizing clients for rehabilitation services and effective allocation of services.
      In this study we were able to look at the 1-year outcomes of the home care clients and significant variation was found across the identified clusters. These differences provide some validation of the results of the cluster analyses; however, this study should be considered exploratory and further analyses should be completed to further validate and simplify the results. Although there is never one perfect solution when it comes to population segmentation in complex care populations, multiple iterations of cluster analyses will reveal patterns that can be used to enhance our understanding of the rehabilitation service users. Future research should further examine the impact of client clusters in rehabilitation services in the Ontario home care system and explore how health informatics can assist in health care decision-making processes and in the creation of decision support systems.

      Study Limitations

      This study is not without limitations. The cluster analysis focused on long-stay rehabilitation clients who received rehabilitation services and did not include individuals who could benefit from rehabilitation therapy but did not receive it. Furthermore, the RAI-HC data system only captures long-stay clients and therefore these findings cannot be generalized to all home care clients. The K-means algorithm also has limitations. As previously mentioned, the number of clusters has to be specified prior to running analyses. This is the major disadvantage of this algorithm, because the ideal number of clusters is most often unknown in exploratory analyses. Additionally, the K-means algorithm can be sensitive to outliers when setting initial seeds.

      Conclusions

      This investigation identified 7 subgroups of rehabilitation service users within the long-stay home care client population in Ontario. This work supports the idea that older home care clients form a diverse, heterogeneous population and clustering methodologies can be used to further our understanding of the patterns or groups that naturally form within the rehabilitation client population. Researchers can use cluster analyses within large administrative databases to focus on pattern discovery in both a general fashion (as done in this study) or in a more targeted fashion focusing on specific domains of interest (ie, physical functioning, cognition, chronic disease diagnoses).
      • a
        SAS Institute Inc, 100 SAS Campus Dr, Cary, NC 27513.

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