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Robert F. Waters, Ph.D. (Arizona State University),

A Mathematical Comparison of Multiple Linear Regression Analysis with Inductive Rule Extraction in the Analysis of Data in Alternative Medicine (submitted for publication). Robert F. Waters, Ph.D. (Arizona State University), Michael Goul, Ph.D. (Arizona State University),

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Robert F. Waters, Ph.D. (Arizona State University),

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  1. A Mathematical Comparison of Multiple Linear Regression Analysis with Inductive Rule Extraction in the Analysis of Data in Alternative Medicine (submitted for publication) Robert F. Waters, Ph.D. (Arizona State University), Michael Goul, Ph.D. (Arizona State University), Arben Lasku, M.D., Ph.D., Linda Kim, N.D.

  2. Questions/Comments to be address: • Some have published the suggestion that Naturopathic Medicine is NOT evidence based medicine. • We can show this is not correct…it IS EBM. • Some believe the only way to establish “evidence” is by double blind/placebo controlled experiments. • Maybe there is another way? Was acupuncture proven effective in this way?

  3. A look at the database analyzed • A population (n = 768) of Pima Indian females being differentially diagnosed for Type II Diabetes (dependent variable) with seven independent variables (predictors). • Predictors • Pregnancies, Glucose, Blood Pressure, Skin Folds, Insulin, Age, and Body Mass

  4. Variables • diabetic (0=no or 1=yes) [Dependent Variable] • age (21 to 81) • body mass index (kg/[height in m]2) • 2-hour serum insulin (IU/ml) • triceps skin fold thickness (mm) • diastolic blood pressure (mm Hg) • plasma glucose concentration at 2 hours in an oral glucose tolerance test (mg/dL) • number of times pregnant

  5. First Analysis: MLRA • The generalized equation Y =  + 1*X1 + 2*X2 + ... + n*Xn

  6. The Results using MLRA

  7. The Predictive Equation Y = dependent variable (diabetic) Problem: A “snapshot” predictive equation. Note: Skinfold variable has been removed.

  8. Let us use Inductive Rule Extraction (IRE)…What is IRE? • Inductive Rule Extraction (IRE) is based on “entropy” theory and has been used for over 40 years. • -Entropy = p * log2 (p) + q * log2 (q) • If p = 0.5 and q = 0.5, therefore, -Entropy = 0.5 * log2 (0.5) + 0.5 * log2 (0.5) …. solving we get -E = -0.5 + -0.5 or 1.00 • Very little use in decision making…. • If -E = p * log2 (p) + q * log2 (q), we get –E = 1.0 * log2 (1.0) + 0.0 * log2 (0.0) or Entropy = 0 • Now a definite decision has been made….

  9. IRE is a type of Artificial Intelligence (AI) mathematics. • Therefore, has the ability to “learn” as the population size (n) increases over time.

  10. The Results using IRE • Glucose level has the highest significance in the determination of a patient having diabetes. • When glucose levels are <= 127, a researcher may have a 77% confidence level the patient does not have diabetes. • With glucose levels > 127, the next level appears to be BodyMass. BodyMass <= 29.9 is further split into glucose levels <= 145 giving a 72% confidence level the patient is not a diabetic and glucose levels > 145 produce two terminal nodes, Insulin <=14 producing a 40% confidence level the patient is not diabetic and Insulin > 14 showing a 44% confidence level the patient has diabetes. • When BodyMass is > 29.9, the diagnosis is (with 79% confidence) the patient is a diabetic. • However, when Glucose is <= 157 and BloodPres <=61 a patient is probably a diabetic THIS IS A BIT DIFFICULT TO COMPREHEND…SO LET’S GO TO THE NEXT SLIDE.

  11. Hierarchical Chart

  12. The previous slide is a “predictive algorithm” • We can use “nested if” statements (for example) in computer programming to develop a predictive program that may be useful in diagnostic medicine.

  13. So… We may have a problem here! • Two different mathematical models used on the exact same data… with two somewhat different conclusions. • The physicians in this paper agree with the IRE model computation. • If you use the MLRA model, then a probable treatment would be MORE insulin given to patients to lower glucose. In fact, may be the worst possible treatment. Why? • Insulin stimulates FAS, de novo cholesterol, inhibits lipid mobilization, etc. • These patients usually have hyperinsulinemia, hypertriglyceridemia, hypercholesterolemia, impaired fat mobilization (cannot lose weight), etc. • So…why would you give them more insulin?

  14. In conclusion….the rationale. • MLRA assumptions were not met. • Skewness, kurtosis, etc. • MLRA does not tolerate independent variable interactions. • Confounding of data • MLRA is a probability snapshot in time. • IRE does not have a probability curve, no assumptions…only pattern recognition. • IRE gains “intelligence” over time as (n) increases.

  15. Scientific Evidence vs. Empirical Evidence • Types of evidence • Scientific • Anecdotal • Empirical • Michael Goul, Ph.D. (ASU-mathematician) has also suggested the importance of “social acceptance” in mathematical analysis of data as well. He points out, for example, Galileo Galilei…. correct computation, correct interpretation, but without social acceptance.

  16. Concluding Remark • Nothing wrong with any of the above mentioned types of evidence, but maybe we are using the wrong mathematics, at times, especially when trying to understand the curative aspects of complex holistic medical approaches.

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