Innumeracy in the NHS
Innumeracy (mathematical illiteracy) unfortunately is very common in clinical medicine. In the UK, the NHS England Clinical Commissioning Policy on lung volume reduction surgery (https://www.england.nhs.uk/wp-content/uploads/2020/11/1622-Policy.pdf) carries an innocuous statement where patients need to have a degree of hyperinflation for referral:
"Residual Volume (RV): Total Lung Capacity (TLC) > 55%"
Whilst the meaning may be intuitive, can anyone spot any errors in the above statement?
The use of the colon ":" in mathematics implies a ratio, and ratios do not have units (because the units cancel each other out on the division). The above statement implies: 1/2=50%, which is not quite correct, it should be 1/2 x 100% = 50%
Ok, lets let it go, simple error, let's look further down in the document where it stipulates the criteria for surgery:
"RV:TLC >60"
What's wrong here? They now correctly remove the percentage, recognizing ratios don't have units and stipulate a figure of "60"? This now implies: 1/2 = 50, which is now completely wrong because 1/2=0.5. The error is now off by a magnitude of 100 fold! I'm not sure if it is humanly possible to fulfil that ratio!
Are we being overtly critical? I don't believe so, because we need clarity in our recommendations. Apart from stipulating the mathematics correctly, we need to specify the units. Here's a real life example if we use the RV/TLC ratio by volume (L) or percentage predicted (%):
When calculated by actual volume in this case it is: 4.09 L / 9.13 L = 0.45
When calculated by percentage predicted in this case it is: 156% / 121% = 1.29
The difference is almost 3 fold!
More to the point, the NETT trial for which is the principal evidence to which surgical LVRS is recommended did not stipulate any such ratio for trial entry, so where does this recommendation come from?
We are of course very grateful to the NHS for considering commissioning lung volume reduction surgery, but it is equally important that we as a surgical community keep a keen eye on the sensibility of evaluation and recommendations.
For information on statistics for medicine: www.statisticscourse.com
Consultant Respiratory Physician, Royal Free Hospital, London
4yThe differences between relative and absolute changes in a metric are poorly or not understood surprisingly often. Incredibly important when weighing up risk/benefit ratios to make decisions.
not exclusive to clinicians Eric - asked similar questions/challenges as a non exec director at a Clinical commissioning group about numbers and words used incorrectly with scant regard for accuracy in published documents to websites and similar external forums that project a less than competent perspective to others. so important when outcomes/external perceptions and treatments are at stake....