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I am not a health professional and am a little bit puzzled by this. There appear to be two ranges of obesity prevalence estimates (I am particularly interested in the rate in adults in England):

  1. Quality and Outcomes Framework (QOF) survey (link), which reports the prevalence of obesity among adults in England at 9.8%. This underpins the reports published by NHS Digital and Public Health England.

  2. There is another set of figures which are in a different league.

    • This government website reports the prevalence of obesity at 26.9% in men and 26.8% in women in 2015 in England.
    • This is more in line with this 2014 estimate of 19.2% (although this is for the whole of UK, not just England).
    • This 2014 WHO report (p. 109) reports 26.9% and 29.2% in men and women, respectively.
    • This newspaper article ranks the UK the third most obese country in Europe with the rate of obesity at 27.8%, citing another WHO report.
    • The Eurostat reports the 2014 data showing obesity rates in UK adults between 29.0% and 64.0%, depending on age-group; while this Eurostat tool shows the 2014 average for UK adults at 20.1%, which agrees with this table showing a close 2017 estimate of 21.0%.

If the estimates are so variable, are any of them reliable? Which would be the ultimate, most official and most reliable estimate? Particularly, the QOF estimates reported by NHS & PHE (1) appear to be less than half those reported elsewhere (2). Why would that be the case?

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You should not use QOF data for epidemiological measures.

Differences may occur because QOF registers do not necessarily equate to prevalence as may be defined by epidemiologists. For example, recorded prevalence figures based on QOF registers may differ from prevalence figures from other sources because of coding or definitional issues

via QOF Data quality statement and frequently asked questions

I'm not super familiar with the QOF, but in reading through these FAQs I believe the issue is that they define obesity as:

patients need to be aged 18 or over, and have a body mass index greater than or equal to 30 recorded in the previous 12 months

so there may be patients in the 'denominator' who have not had a BMI recorded in the previous 12 months, therefore they are not classified as obese in the QOF even if their latest BMI was recorded >=30 if that record was not in the previous 12 months. Those denominators come from the

latest Exeter National Health Application and Infrastructure Services (NHAIS) extract

Given that the total is ~44.7 million adults in England, this seems to be the entire (adult) population of England, and likely not all of them visited a physician during a 12 month period.

As you point out, the other measures vary but not by all that much, and there are likely smaller demographic sampling biases or definitions, different attitudes towards adjustment based on demographics, etc that explain those smaller differences.

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