We applied the e-norms method to BMI data derived from 34,384 individuals we collected in our practice between 1994 and 2019 to compare the ranges we derive by this method to those obtained from a large actuarially based study of 3.6 million individuals identifying the incident disease, and the ascertainment of death.
The source data for our study are the records of patients attending the clinical neurophysiology department in Canterbury, UK for investigation of possible carpal tunnel syndrome (CTS). The records include BMI because of a previously well documented relationship between high BMI and an increased incidence of CTS[9]. We have generic ethics permission to use anonymized data from this database for our research. The research ethics approval was obtained from South Central (Hampshire A) National Research Ethics Service committee in the UK.
We extracted records made at the patient’s first presentation to the department for diagnosis, thus excluding follow-up visits and including each subject only once. We excluded subjects under 17 years of age and 65 subjects with missing data for height or weight. The extracted data fields for analysis were BMI, age, sex, and the presence or absence of laboratory confirmed CTS, the last being included only so that we would be able to conduct exploratory analyses of whether the disease specific nature of the population might influence the results. Thirty-four thousand and three hundred and eighty-four (34,384) BMI measures of 22,661 females and 11,723 males aged 17–98 years old were analyzed. We derived e-norms based healthy BMI estimates for the entire cohort; for males and females separately; and for four age groups in each (17–49, 50–69, 70–79 and 80–98 years). We chose these age groups to match those used in the study we were using for comparison[3]. Paired two sample t-tests were used to compare e-norms BMI values between males and females of the same age groups.
The e-norms method
The e-norms method[10] allows the use of data derived from a provider’s own cohort to produce normative values for any parameter in their database. The method has been validated by various authors for neurophysiological and non-neurophysiological studies ranging from electrodiagnostic studies,[11],[12],[13],[14],[15] to acetyl choline receptor antibodies (AchRAb) for diagnosing myasthenia gravis (Guan Y, unpublished data), to intra-epidermal nerve fiber density (Authier FJ, unpublished data), and more recently to Ophthalmology, for deriving biometric normative data used for intraocular lens (IOL) power calculation prior to cataract surgery (Shammas H, Jabre, J - In Press, BMJ Open Ophthalmology September 2020)[16]. To date, normative data derived using the e-norms method in all these studies was found to closely match data obtained from traditional studies, producing much needed normative data in populations and cohorts for which no normative values were available. The method has been proven particularly useful in pediatric cohorts where normal values change rapidly with age and works as follows:
A variable’s data is sorted in ascending order in an Excel spreadsheet and plotted against its rank order producing a cumulative distribution plot that reveals an inverted S curve consisting of a steep lower left; a flat or “plateau” middle; and a steep upper right.
First-order derivatives are then calculated for each successive data point by subtracting the second value from the first, the third from the second, and so on until all the differences between successive values have been calculated. The first-order derivatives are then plotted on the same graph as the sorted variables to help in identifying the plateau part of the curve, the one corresponding to the lowest first order differences, consistent with the e-norms clustering behavior.
The e-norms clustering behavior is data neutral and can be illustrated using blood glucose levels as follows:
Fasting blood glucose levels have a minimum to maximum range between 70–99 mg/dl, with a min to max difference a mere 29 mg/dl.
In diabetic patients, such differences are hundreds of times that range. The Guinness World Records lists “Michael Patrick Buonocore (as having) survived a blood sugar level of 2,656 mg/dl when admitted to the Pocono Emergency Room in East Stroudsburg, Pennsylvania on 23 March 2008”[17]. Since an abnormal fasting Blood Glucose can be as low 100 mg/dl, the min to max difference in patients with known diabetes can in theory be an astounding 2556 mg/dl, a much greater difference than in individuals with normal Blood Glucose. E-norms clustering is representative of this behavior and can be used in identifying datasets derived from normal subjects from those derived from subjects with pathology, using the low derivative values to help identify the plateau part of the curve.
To illustrate this concept, we will use a simulation study that displays 1,000 simulated values that have a mean of 20 and a SD of 1.5, with a mean ± 4 SD value of 14 and 26, respectively. We will determine if we can extract the mean ± 2 SD values of 17 and 23 from this graph from the data that lies within the plateau part of the curve. The plot of this simulated data can be seen in Fig. 1.
Data points at the left and right extremes of the curve, display higher first order differences between them than those between points A and B that mark the curve’s points of inflection. Descriptive statistics of the data lying between points A and B within the plateau part of the curve between points A and B reveals values that lie between 17 and 23 identical to the normal limits of the data as predicted by the mean ± 2 SD we set out to represent.
In a recently completed study, plateau identification and determination of the left and right inflection points of the e-norms plot has been proven reliable. Twenty different observers recruited from a diverse pool of hospital workers were asked to visually identify the e-norms plateau in 393 upper and 284 lower limb nerve conduction studies while blinded to the variable they were analyzing. An inter-rater ANOVA without replication testing showed no significant difference between their findings.[18]
A significant advantage of the e-norms method is that it can be performed in minutes using a Microsoft Excel spreadsheet that is uploaded anonymously and securely to an encrypted e-norms web application for this purpose.[19]