# RCT and "Mathematical Embellishment"

A “Mathematical Embellishment” (ME) is the application of complex mathematical formulae to measurement values which are not suitable for the generation of reproducible outputs from the formulae.

The problem is not the formula itself but the mismatch of the formula to the wrong inputs. ME was once a serious problem in clinical critical care and critical care research where measured or calculated values (which might be useful clinically) were mismatched and used as inputs into complex formula cascades. The outputs of these cascades were used for decision making and some formed the basis for now rejected theories of pathophysiologic behavior.

In 1985 we exposed a ME as a potential contributor the Theory of “Flow Dependent Oxygen Consumption” and the responsive 1980s sepsis treatment theory of targeting supernormal values of Cardiac Output and Oxygen Delivery. Effect of measurement error on calculated variables of oxygen transport - PubMed

After that experience, I was no longer impressed by complex formulae without prior due consideration of the measurements clinically available as inputs. “The math was perfect but the patient died”.

A mathematical embellishment may have two common direct adverse components of “error propagation” and “error amplification” but the most important problem is in the embellishment itself. Complex formula cascades look impressive and provide the observer with a basis for trust. Most of the time those making decisions based on ME have no idea that the output is not useful and may be harmful. ME is a common “snake oil” of science fooling both the producer and the consumer. As with any snake oil, reproducibility is something it cannot deliver.

It is obvious that the validity of a complex formula, as it relates to clinical medicine, does not stand on the math alone but rather on the math in relation to the input measurements. However this has been lost to many because the definition of measurement in medicine as the term relates to the input or output of RCT functions, has been poorly understood. “The math was perfect but the RCT was not reproducible”.

Perhaps it would be useful to categorize clinical measurements on a 0-10 scale from highly applicable to statistical formulae to not applicable. We know the many measurements of the Apnea Hypopnea Index (AHI) would be close to 0 but for most measurements it is not at all clear.

Are there any thoughts about how this could be accomplished? I will give a lighthearted gestalt for this. Hopefully there will be other thoughts. Using anything below a 5 in an RCT would probably be folly.

• PCR 10
• Arterial BP 8
• Sedation Scale 7
• Dyspnea Scale 6
• Sepsis Criteria (SOFA) 4
• Apnea Hypopnea Index 0

I’d be looking at the mathematical area known as measurement theory for the tools to answer your question.

Joel Michell is a scholar on the issue of measurement in psychology and psychometrics. He coined the term “pathological science” that seems to describe too much of the “peer reviewed” published literature.

David Hand is a statistician who wrote a relatively recent textbook on modern measurement theory (Measurement Theory and Practice: The World Through Quantification) that might be closer to your immediate needs. His old 1996 paper Statistics an the Theory of Measurement is worth study.

An undervalued application of measurement theory can be found here:

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Absolutely. Wonderful. Robert you are the definitive source. Haven’t made it to the second reference yet.