Osteoporosis International

, Volume 28, Issue 3, pp 819–832 | Cite as

Clinical fracture risk evaluated by hierarchical agglomerative clustering

  • C. Kruse
  • P. Eiken
  • P. Vestergaard
Original Article



Clustering analysis can identify subgroups of patients based on similarities of traits. From data on 10,775 subjects, we document nine patient clusters of different fracture risks. Differences emerged after age 60 and treatment compliance differed by hip and lumbar spine bone mineral density profiles.


The purposes of this study were to establish and quantify patient clusters of high, average and low fracture risk using an unsupervised machine learning algorithm.


Regional and national Danish patient data on dual-energy X-ray absorptiometry (DXA) scans, medication reimbursement, primary healthcare sector use and comorbidity of female subjects were combined. Standardized variable means, Euclidean distances and Ward’s D2 method of hierarchical agglomerative clustering (HAC), were used to form the clustering object. K number of clusters was selected with the lowest cluster containing less than 250 subjects. Clusters were identified as high, average or low fracture risk based on bone mineral density (BMD) characteristics. Cluster-based descriptive statistics and relative Z-scores for variable means were computed.


Ten thousand seven hundred seventy-five women were included in this study. Nine (k = 9) clusters were identified. Four clusters (n = 2886) were identified based on low to very low BMD with differences in comorbidity, anthropometrics and future bisphosphonate compliance. Two clusters of younger subjects (n = 1058, mean ages 30 and 51 years) were identified as low fracture risk with high to very high BMD. A mean age of 60 years was the earliest that allowed for separation of high-risk clusters. DXA scan results could identify high-risk subjects with different antiresorptive treatment compliance levels based on similarities and differences in lumbar spine and hip region BMD.


Unsupervised HAC presents a novel technology to improve patient characteristics in bone disease beyond traditional T-score-based diagnosis. Technological and validation limitations need to be overcome to improve its use in internal medicine. Current DXA scan indication guidelines could be further improved by clustering algorithms.


Clustering Densitometry Machine learning Osteoporosis Risk factors 



The Obel Family Foundation and the Department of Clinical Medicine at Aalborg University are acknowledged for providing grants that enable the PhD fellowship of Dr. Christian Kruse. Statistics Denmark is acknowledged for providing data. The community around the R statistical software is acknowledged for the programming packages and guidance that enable studies such as this.

Compliance with ethical standards

Conflicts of Interest

CK has received travel grants from Eli Lilly, Otsuka Pharmaceutical, and is a speaker for Novartis and Otsuka Pharmaceutical. PE is an advisory board member with Amgen, MSD and Eli Lilly and at the speakers bureau with Amgen and Eli Lilly, stocks from Novo Nordisk A/S. PV has received unrestricted grants from MSD and Servier, and travel grants from Amgen, Eli Lilly, Novartis, Sanofi-Aventis, and Servier.

Supplementary material

198_2016_3828_MOESM1_ESM.pdf (156 kb)
ESM 1 (PDF 156 kb)


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Copyright information

© International Osteoporosis Foundation and National Osteoporosis Foundation 2016

Authors and Affiliations

  1. 1.Department of EndocrinologyAalborg University HospitalAalborgDenmark
  2. 2.Department of Clinical MedicineAalborg University HospitalAalborgDenmark
  3. 3.Department of Cardiology, Nephrology and EndocrinologyNordsjaellands HospitalHilleroedDenmark
  4. 4.Faculty of Health and Medical SciencesUniversity of CopenhagenCopenhagenDenmark

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