Statistical complexity of reasons for encounter in high users of out of hours primary care: analysis of a national service

Sarah Stegink, Alison M. Elliott, Christopher Burton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Background: Managing demand for urgent and unscheduled care is a major problem for health services globally. A particular issue is that some patients appear to make heavy use of services, including primary care out of hours. We hypothesised that greater variation (statistical complexity) in reasons for attending primary care out of hours services may be a useful marker of patients at high risk of ongoing heavy service use. 

Methods: We analysed an anonymised dataset of contacts with the primary care out of hours care for Scotland in 2011. This contained 120,395 contacts from 13,981 high-using patients who made 5 or more contacts during a calendar year. We allocated the stated reason for each encounter into one of 14 categories. For each patient we calculated measures of statistical complexity of reasons for encounter including the count of different categories, Herfindahl index and statistical entropy of either the categories themselves, or the category transitions. We examined the association of these measures of statistical complexity with patient and healthcare use characteristics. 

Results: The high users comprised 2.4% of adults using the service and accounted for 15% of all contacts. Statistical complexity (as entropy of categories) increased with number of contacts but was not substantially influenced by either patient age or sex. This lack of association with age was unexpected as with increasing multi-morbidity one would expect greater variability in reason for encounter. Between 5 and 10 consultations, higher entropy was associated with a reduced likelihood of further consultations. In contrast, the occurrence of one or more contacts for a mental health problem was associated with increased likelihood of further consultations. 

Conclusion: Complexity of reason for encounter can be estimated in an out of hours primary care setting. Similar levels of statistical complexity are seen in younger and older adults (suggesting that it is more to do with consultation behaviour than morbidity) but it is not a predictor of ongoing high use of urgent care.

Original languageEnglish
Article number108
Number of pages10
JournalBMC Health Services Research
Early online date8 Feb 2019
Publication statusPublished - 1 Dec 2019


  • Complexity
  • Entropy
  • Frequent attendance
  • High users
  • Out of hours care
  • Reason for encounter
  • Unscheduled care


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