GH-METHODS

Math-Physical Medicine

NO. 381

Examination of the correlation coefficients between urinary albumin-to-creatinine ratio and other 12 biomarkers using GH-Method: Math-physical method

Corresponding Author: Gerald C. Hsu, eclaireMD Foundation, USA.

Abstract
Diabetes mellitus is a lifelong, incapacitating disease affecting multiple organs. Worldwide figures estimate that there are 422 million diabetic patients in 2014.  National Diabetes Statistics Report 2020 of CDC in USA also estimates that there are 34.2 million Americans, just over 1 in 10, have diabetes in 2020.

The American Diabetes Association (ADA) released research on March 22, 2018 estimating the total costs of diagnosed diabetes have risen to $327 billion in 2017 from $245 billion in 2012.  This figure represents a 26% increase over a five-year period.  The total estimated 2017 cost of diagnosed diabetes of $327 billion includes $237 billion in direct medical costs and $90 billion in reduced productivity.

The largest components of medical expenditures are:

  • Hospital inpatient care (30% of the total medical cost)
  • Prescription medications to treat complicationsof diabetes (30%)
  • Anti-diabetic agents and diabetes supplies (15%)
  • Physician office visits (13%)

People with diagnosed diabetes incur average medical expenditures of $16,752 per year, of which about $9,601 is attributed to diabetes (57% of total expenditures).  On average, they have medical expenditures approximately 2.3 times higher than what expenditures would be in the absence of diabetes.

Diabetes is associated with devastating chronic complications including coronary heart disease and stroke (macro-vascular disease) as well as microvascular disorders leading to damage of the small blood vessels of the kidney (nephropathy), eye (retinopathy) and peripheral nerves (neuropathy).  These complications impose an immense burden on the quality of life of the diabetes patients.

Urinary albumin-to-creatinine ratio (ACR) is a biomarker of diabetic nephropathy (kidney complications) and microvascular damage.  Metabolic-related traits are observationally associated with ACR, including glycemic, lipid, and adiposity traits.  Specifically, they are glycemic (FPG), adiposity (BMI or weight), dyslipidemia (Triglyceride or TG), and insulin resistance (two TyG biomarkers including logarithm of both TG and FPG) which are associated with elevated ACR levels and microvascular damage.

Instead of applying the method of “Mendelian Randomization” (MR) Study, which focuses on causal effect and confounding factors, the author decided to apply the traditional statistical method of “Correlation Coefficients” (R) to calculate the strength of connectivity between two biomarkers.  Using this correlation approach, he concentrated on the mutual influence and connectivity only, not the cause versus the effect, between two biomarkers.

In this study, he focuses on investigating the ACR and its degree of inter-connections with the following 12 biomarkers in 5 categories:

  1. Lipid: TG, HDL-C, LDL-C, and TC (total cholesterol)
  2. Glucose: FPG and HbA1C (FPG & PPG)
  3. Blood pressure: SBP and DBP
  4. BMI: Weight
  5. Others: TyG-A and TyG-B (logarithm of both TG and FPG), along with TSH.

The following table summarizes the results of this study regarding the 12 sets of correlation coefficients:

  • ACR vs. DBP: 85% (strong)
  • ACR vs. SBP: 80% (strong)
  • ACR vs. TSH: 58% (strong)
  • ACR vs. TyG-A: 46% (less strong)
  • ACR vs. TyG-B: 44% (less strong)
  • ACR vs. TG: 41% (less strong)
  • ACR vs. Weight: 38% (moderate)
  • ACR vs. FPG: 35% (moderate)
  • ACR vs. A1C: 22% (weak)
  • ACR vs. HDL: -19% (weak)
  • ACR vs. TC: -14% (weak)
  • ACR vs. LDL: -3% (weak)

From above table, it has been proven that ACR has connectivity, at different strength level, with 8 out of 12 selected metabolic-related traits, including adiposity (Weight), dyslipidemia (TG), blood pressure (SBP, DBP), and insulin resistance (two TyG biomarkers including both TG and FPG).  In addition, ACR also has a strong connection with the biomarker of thyroid, TSH.  Overall, above conclusion from this report is highly similar to Terrell report cited in Reference 2.

Professor Jessica Terrell and her team in the United Kingdom (UK) have discovered that using the MR study, there are 7 out of their selected 11 metabolic risk factors or metabolic traits having causal effects on ACR.  In this particular study, the author has discovered that, using the correlation study, there are 8 out of his selected 12 biomarkers that have either moderate or strong correlations with ACR.  Most of the findings from these two different studies have similar conclusions but with two major differences.  First, the author’s study includes TSH, a thyroid biomarker, which has a strong correlation of 58% with ACR.  Second, his correlation between ACR and LDL-C is almost non-existent (-3%), which contradicts with Terrell’s MR study of a higher LDL cholesterol causing a higher ACR.  The author needs additional research to find appropriate biomedical interpretations.

Also, there are three key differences between the two studies:

  1. Terrell’s study used the MR method to identify causal effect relationship, while the author’s study uses the R method to identify connectivity strength.
  2. Terrell’s study utilized 440,000 UK big biobank data.  Although the data size is impressive, this big dataset may contain some interfering data or non-consistent information which could bring a confounding effect.  On the other end of spectrum, the author’s study focuses on his own historical data which covers a period of 7+ years or 87 months. During this period, he utilized 13 consistent biomarker datasets with an average of 6.7 months between two adjacent medical  All of these 13 biomarkers should be somewhat stabilized during these averaged periods of ~6.7 months.
  3. Although these two studies have similar objectives with somewhat different emphases, there is still a strong relationship between the “causal-effect investigation” and “correlation investigation”. Therefore, the research findings from these two studies could assist and reinforce each other. Other than the LDL-C, all of the conclusions related to the other biomarkers, including adiposity (BMI or weight), dyslipidemia (Triglyceride or TG), and insulin resistance (TyG including both TG and FPG), are the same.

The author hopes his study can add some value on further understanding ACR which could provide some help on controlling micro-vascular disorders.

Introduction
Diabetes mellitus is a lifelong, incapacitating disease affecting multiple organs. Worldwide figures estimate that there are 422 million diabetic patients in 2014.  National Diabetes Statistics Report 2020 of CDC in USA also estimates that there are 34.2 million Americans, just over 1 in 10, have diabetes in 2020.

The American Diabetes Association (ADA) released research on March 22, 2018 estimating the total costs of diagnosed diabetes have risen to $327 billion in 2017 from $245 billion in 2012.  This figure represents a 26% increase over a five-year period.  The total estimated 2017 cost of diagnosed diabetes of $327 billion includes $237 billion in direct medical costs and $90 billion in reduced productivity.

The largest components of medical expenditures are:

  • Hospital inpatient care (30% of the total medical cost)
  • Prescription medications to treat complicationsof diabetes (30%)
  • Anti-diabetic agents and diabetes supplies (15%)
  • Physician office visits (13%)

People with diagnosed diabetes incur average medical expenditures of $16,752 per year, of which about $9,601 is attributed to diabetes (57% of total expenditures).  On average, they have medical expenditures approximately 2.3 times higher than what expenditures would be in the absence of diabetes.

Diabetes is associated with devastating chronic complications including coronary heart disease and stroke (macro-vascular disease) as well as microvascular disorders leading to damage of the small blood vessels of the kidney (nephropathy), eye (retinopathy) and peripheral nerves (neuropathy).  These complications impose an immense burden on the quality of life of the diabetes patients.

Urinary albumin-to-creatinine ratio (ACR) is a biomarker of diabetic nephropathy (kidney complications) and microvascular damage.  Metabolic-related traits are observationally associated with ACR, including glycemic, lipid, and adiposity traits.  Specifically, they are glycemic (FPG), adiposity (BMI or weight), dyslipidemia (Triglyceride or TG), and insulin resistance (two TyG biomarkers including logarithm of both TG and FPG) which are associated with elevated ACR levels and microvascular damage.

Instead of applying the method of “Mendelian Randomization” (MR) Study, which focuses on causal effect and confounding factors, the author decided to apply the traditional statistical method of “Correlation Coefficients” (R) to calculate the strength of connectivity between two biomarkers.  Using this correlation approach, he concentrated on the mutual influence and connectivity only, not the cause versus the effect, between two biomarkers.

In this study, he focuses on investigating the ACR and its degree of inter-connections with the following 12 biomarkers in 5 categories:

  1. Lipid: TG, HDL-C, LDL-C, and TC (total cholesterol)
  2. Glucose: FPG and HbA1C (FPG & PPG)
  3. Blood pressure: SBP and DBP
  4. BMI: Weight
  5. Others: TyG-A and TyG-B (logarithm of both TG and FPG), along with TSH.

Methods
1. Background
To learn more about the author’s GH-Method: math-physical medicine (MPM) methodology, readers can refer to his article to understand his developed MPM analysis method in Reference 1.

2. ACR study using Mendelian Randomization (MR) method
Professor Jessica Terrell has conducted a study regarding the ACR and published a paper: “A Mendelian Randomization Study Provides Evidence That Adiposity and Dyslipidemia Lead to Lower Urinary Albumin-to-Creatinine Ratio, a Marker of Microvascular Function” (Reference 2).

Here is an excerpt from their paper:

Here, we confirmed ACR as a marker of microvascular damage and tested whether metabolic-related traits have causal relationships with ACR. The association between ACR and microvascular function was tested in the SUMMIT study. Two-sample Mendelian randomization (MR) was used to infer the causal effects of 11 metabolic risk factors, including glycemic, lipid, and adiposity traits, on ACR.  MR was performed in up to 440,000 UK Biobank and 54,451 CKDGen participants.  ACR was robustly associated with microvascular function measures in SUMMIT.  Using MR, we inferred that higher triglyceride (TG) and LDL cholesterol (LDL-C) levels caused elevated ACR.  A 1 SD higher TG and LDL-C level caused a 0.062 (95% CI 0.040, 0.083) and a 0.026 (95% CI 0.008, 0.044) SD higher ACR, respectively.  There was evidence that higher body fat and visceral body fat distribution caused elevated ACR, while a metabolically favorable adiposity” phenotype lowered ACR. ACR is a valid marker for microvascular function.  MR suggested that seven traits have causal effects on ACR, highlighting the role of adiposity-related traits in causing lower microvascular function.

The urinary albumin-to-creatinine ratio (ACR), a marker of diabetic nephropathy, is used as a proxy for damage to the systemic microcirculation (1) and predicts first myocardial infarction and mortality in those with diabetes, poststroke, and in the general population (2–4). There is evidence linking metabolic-related traits, including adiposity, dyslipidemia, and insulin resistance with elevated ACR levels and microvascular damage (5,6). It is well accepted that tight glucose control in patients with type 2 diabetes (T2D) reduces the risk of microvascular retinal complications (7,8), and there is evidence that adiposity per se is associated with increased ACR. For example, population studies suggest that microalbuminuria is associated with central adiposity (9), and results from the Framingham Heart Study show that visceral but not subcutaneous fat is associated with increased albuminuria (10).  Not all evidence linking metabolic-related traits comes from randomized control trials, and in absence of these, the next best evidence of causality comes from genetic studies using a technique known as Mendelian randomization (MR).

3. Mendelian randomization study
The following is a simple explanation of the Mendelian randomization (MR) study from Wikipedia:

Mendelian randomization (MR) is a method that allows one to test for, or in certain cases to estimate, a causal effect from observational data in the presence of confounding factors.  From a statistical perspective, Mendelian randomization (MR) is an application of the technique of instrumental variables” with genotype acting as an instrument for the exposure of interest.  The method has also been used in economic research studying the effects of obesity on earnings, and other labor market outcomes.  Accuracy of MR depends on a number of assumptions: That there is no direct relationship between the instrumental variable and the dependent variables, and that there are no direct relations between the instrumental variable and any possible confounding variables.  

4. Input data of biomarkers
The author was diagnosed with severe metabolic disorder for over 25 years, including T2D, hyperlipidemia (TG at 1161 in 2010), hypertension (SBP 150, DBP 92), five cardiac episodes, kidney complications (ACR at 160 in 2010), foot ulcer (infected toe for over 3 months), diabetic retinopathy (micro-vascular complications), and hypothyroidism (TSH 6.32).  As a result, he has suffered all of the known diabetic complications except for having a stroke.

During the past 10 years, he has maintained a routine of having his medical examination conducted at the same medical laboratory or hospital on a quarterly basis.  However, his main focus has been on controlling his diabetes conditions; therefore, he has paid more attention directly to the diabetes related biomarker, such as HbA1C.  For the past 8 years from 2013 to 2020, he has had 36 medical examinations which include 19 examinations containing TG data and 13 examinations containing ACR data.  That is why he can only apply these 13 cases with his collected ACR data for this study.  As a long-term veteran of chronic diseases and a dedicated endocrinology research scientist, he concentrated on his own conditions first in order to save his life.  As a result, he is most familiar with his own body situations and health conditions through his 11 years of self-study on medicine based on his 2 million collected data and his persistent medical research efforts.  This study period covers 7+ years, actually 87 months, where he utilized 13 consistent biomarker datasets with an average of 6.7 months between two adjacent medical examinations for each sub-period.  From a macro-viewpoint, all of these 13 biomarkers should be more or less stabilized during the sub-periods of 6.7 months.

5. Pearsons correlation coefficient
The calculated results of correlation coefficient (R) between ACR versus the other 12 biomarkers were using the formula in the following table from Wikipedia:

6.TyG (triglycerides and glucose index)
Here are the two equations for TyG-A and TyG-B, as well as the equation of Delta i.e., the difference between these two TyG values (Reference 10):

  • TyG-A = (ln(TG) + ln(FPG)) / 2
  • TyG-B = ln(TG+FPG) – ln (2)
  • Delta = (TyG-B) – (TyG-A) or
  • Delta =(ln(((TG+FPG)/2)²/(TG*FPG)) / 2

Results
There are only two figures resulted from this particular study, with one extra figure to demonstrate an application of using the correlation coefficient method to predict his FPG value.

Figure 1 shows the raw input data of these 13 biomarkers, including ACR itself and the other 12 biomarkers during the period of 7+ years from 8/9/2013 through 10/21/2020.  At the bottom row of the data table, it also lists the 12 calculated correlation coefficients of ACR vs. the12 other biomarkers.

Figure 1: Raw input data of 13 biomarkers on 13 medical examination dates and 12 calculated correlation coefficients of ACR versus other 12 biomarkers

Figure 2 displays a bar chart diagram of the resulting correlation coefficients of ACR vs. the 12 other biomarkers.  In this study, he has focused on investigating the ACR and its degree of inter-connectivity with the other 12 biomarkers within five categories of metabolic traits:

  • (9) Lipid: TG, HDL-C, LDL-C, and TC (total cholesterol)
  • (6) Glucose: FPG and HbA1C (FPG & PPG)
  • (7) Blood pressure: SBP and DBP
  • (8) BMI: Weight
  • (9) Others: TyG-A and TyG-B (logarithm of TG & FPG), along with TSH

The following table summarizes the results of correlation coefficients in percentages from Figure 2:

  • ACR vs. DBP: 85% (strong)
  • ACR vs. SBP: 80% (strong)
  • ACR vs. TSH: 58% (strong)
  • ACR vs. TyG-A: 46% (less strong)
  • ACR vs. TyG-B: 44% (less strong)
  • ACR vs. TG: 41% (less strong)
  • ACR vs. Weight: 38% (moderate)
  • ACR vs. FPG: 35% (moderate)
  • ACR vs. A1C: 22% (weak)
  • ACR vs. HDL: -19% (weak)
  • ACR vs. TC: -14% (weak)
  • ACR vs. LDL: -3% (weak)

In this particular study, the author discovered that there are 8 biomarkers out of the 12 biomarkers with moderate and strong correlations with ACR.

In Figure 2, the author identified two phenomena.  However, he is unable to provide an immediate and reasonable biomedical interpretations because he is not a medical doctor and lacks the background and formal academic training in biology and chemistry.  For over the past 11 years, he relied solely on his strong background in mathematics, physics, engineering, and computer science to conduct his needed medical research work.

In the first puzzle, his study includes TSH, a thyroid biomarker, which has a strong correlation coefficient of 58% with ACR.  Why does TSH relate to ACR so close?  

For the second puzzle, why do the correlation coefficients between ACR versus other 3 lipid biomarkers (LDL-C, HDL-C and TC) have extremely low negative values (-3%, -19%, and -14%)?  His co-existing high R percentage of ACR vs. TG at 41% and moderate R percentage of ACR vs. FPG at 35% could provide an explanation for the high R of ACR vs. two TyG values at 44% and 46% for TyG-A and TyG-B, respectively, since TyG (a biomarker for insulin resistance of diabetes, fatty liver, and cardiovascular risk) is related to the natural logarithm of both TG and FPG.

Figure 2: Bar chart diagram of calculated correlation coefficients of ACR versus other 12 biomarkers

Figure 3 provides an example of glucose and weight application using the correlation coefficient method.  In 2016, he discovered the high correlation (68%) existing between his weight and FPG.  Therefore, he applied this finding to develop his predicted FPG model.  By using his 5+ years data, from 4/11/2015 to 12/20/2020, the correlation coefficient between his predicted FPG versus his actual FPG is 86% with an extremely high prediction accuracy of 99.2% over averaged FPG.  

Figure 3: Example of 68% correlation coefficient between weight and FPG which resulted into an extremely high 99.2% prediction accuracy of FPG based on weight input

Conclusions
The following table summarizes the results of this study regarding the 12 sets of correlation coefficients:

  • ACR vs. DBP: 85% (strong)
  • ACR vs. SBP: 80% (strong)
  • ACR vs. TSH: 58% (strong)
  • ACR vs. TyG-A: 46% (less strong)
  • ACR vs. TyG-B: 44% (less strong)
  • ACR vs. TG: 41% (less strong)
  • ACR vs. Weight: 38% (moderate)
  • ACR vs. FPG: 35% (moderate)
  • ACR vs. A1C: 22% (weak)
  • ACR vs. HDL: -19% (weak)
  • ACR vs. TC: -14% (weak)
  • ACR vs. LDL: -3% (weak)

From above table, it has been proven that ACR has connectivity, at different strength level, with 8 out of 12 selected metabolic-related traits, including adiposity (Weight), dyslipidemia (TG), blood pressure (SBP, DBP), and insulin resistance (two TyG biomarkers including both TG and FPG).  In addition, ACR also has a strong connection with the biomarker of thyroid, TSH.  Overall, above conclusion from this report is highly similar to Terrell report cited in Reference 2.

Professor Jessica Terrell and her team in the United Kingdom (UK) have discovered that using the MR study, there are 7 out of their selected 11 metabolic risk factors or metabolic traits having causal effects on ACR.  In this particular study, the author has discovered that, using the correlation study, there are 8 out of his selected 12 biomarkers that have either moderate or strong correlations with ACR.  Most of the findings from these two different studies have similar conclusions but with two major differences.  First, the author’s study includes TSH, a thyroid biomarker, which has a strong correlation of 58% with ACR.  Second, his correlation between ACR and LDL-C is almost non-existent (-3%), which contradicts with Terrell’s MR study of a higher LDL cholesterol causing a higher ACR.  The author needs additional research to find appropriate biomedical interpretations.

Also, there are three key differences between the two studies:

  1. Terrell’s study used the MR method to identify causal effect relationship, while the author’s study uses the R method to identify connectivity strength.
  2. Terrell’s study utilized 440,000 UK big biobank data.  Although the data size is impressive, this big dataset may contain some interfering data or non-consistent information which could bring a confounding effect.  On the other end of spectrum, the author’s study focuses on his own historical data which covers a period of 7+ years or 87 months. During this period, he utilized 13 consistent biomarker datasets with an average of 6.7 months between two adjacent medical  All of these 13 biomarkers should be somewhat stabilized during these averaged periods of ~6.7 months.
  3. Although these two studies have similar objectives with somewhat different emphases, there is still a strong relationship between the “causal-effect investigation” and “correlation investigation”. Therefore, the research findings from these two studies could assist and reinforce each other. Other than the LDL-C, all of the conclusions related to the other biomarkers, including adiposity (BMI or weight), dyslipidemia (Triglyceride or TG), and insulin resistance (TyG including both TG and FPG), are the same.

The author hopes his study can add some value on further understanding ACR which could provide some help on controlling micro-vascular disorders.

References

  1. Hsu, Gerald C., eclaireMD Foundation, USA, No. 310: “Biomedical research methodology based on GH-Method: math-physical medicine”
  2. Terrell, Jessica, Corresponding author: (tyrrell@exeter.ac.uk) Diabetes 2020 May; 69(5): “A Mendelian Randomization Study Provides Evidence That Adiposity and Dyslipidemia Lead to Lower Urinary Albumin-to-Creatinine Ratio, a Marker of Microvascular Function”, Francesco Casanova1, Andrew R. Wood, Hanieh Yaghootkar, Robert N. Beaumont, Samuel E. Jones, Kim M. Gooding, Kunihiko Aizawa1, W. David Strain, Andrew T. Hattersley, Faisel Khan, Angela C. Shore1, Timothy M. Frayling and Jessica Tyrrell, 1072-1082. https://doi.org/10.2337/db19-0862
  3. ADA-American Diabetes Association, “The cost of diabetes”
  4. “Microalbuminuria as an Early Marker for Cardiovascular Disease”, Dick de Zeeuw, Hans-Henrik Parving and Robert H. Henning, JASN August 2006, 17 (8) 2100-2105; DOI: https://doi.org/10.1681/ASN.2006050517
  5. “Urinary albumin to creatinine ratio as potential biomarker for cerebral microvascular disease”, Amanda L StricklandHeidi C Rossetti, Roland M Peshock, Myron F WeinerPaul A NakoneznyRoderick W McCollKeith M HulseySandeep R DasKevin S King, Affiliations expand: PMID: 24875487 PMCID: PMC4795813 DOI: 2174/1567202611666140530130327, Published: 13 July 2016, https://www.ncbi.nlm.nih.gov/
  6. “Microvascular endothelial dysfunction is associated with albuminuria and CKD in older adults”, Stephen L. Seliger, Shabnam Salimi, Valerie Pierre, Jamie Giffuni, Leslie Katzel & Afshin Parsa
  7. “Microalbuminuria as an Early Marker for Cardiovascular Disease”, Dick de Zeeuw, Hans-Henrik Parving and Robert H. Henning, JASN August 2006, 17 (8) 2100-2105; DOI: https://doi.org/10.1681/ASN.2006050517
  8. “Comparative effects of microvascular and macrovascular disease on the risk of major outcomes in patients with type 2 diabetes”, Kamel Mohammedi, Mark Woodward, […], and John Chalmers, https://www.google.com/url?sa=t&source=web&cd=&ved=2ahUKEwjL_cPvmd_tAhXSu54KHRPCDWAQFjABegQIDhAL&url=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5530952%2F&usg=AOvVaw0FGrMAPPMR0FVFM4l3T0U7
  9. Hsu, Gerald C., eclaireMD Foundation, USA, No. 034:  “Risk Probability of Kidney Complications Resulting from Chronic Diseases (Math-Physical Medicine)”
  10. Hsu, Gerald C., eclaireMD Foundation, USA, No. 380:      “A summary report of two biomarkers for triglyceride and glucose index (TyG) and accuracy sensitivity analysis in estimating the insulin resistance status based on GH-Method: math-physical medicine”