## GH-METHODS

Math-Physical Medicine

### NO. 328

Investigating the relationship between annualized weight and annualized food portion percentage along with a segmentation analysis on lowering weight less than 170 pounds using GH-Method: math-physical medicine

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

Abstract
The author attempts a detailed analysis to identify the relationship between annual body weights and his annual food portion percentages using both Pearson correlation coefficient “R” of statistics to calculate the association between these two variables.  Furthermore, he conducts a segmentation analysis to calculate his annual percentages of daily weights that are less than 170 lbs. with a BMI below 25.  This study utilized his weights and food portion percentage of normal meal size for a period of ~9 years from 1/1/2012 to 9/12/2020.

The author wrote this article as an extension of his previous paper, Investigating the influential factors on body weight and its impact on glucoses using GH-Method: math-physical medicine (No. 327).  As a result, some results and certain parts of the paper are duplicated.

One finding shows his annual weight decreased from 189 lbs. in 2012 to 172 lbs. in 2020, while the food percentage of normal meal size dropped from 101% in 2012 to 68% in 2020.  These two reduction ratios are 9% for weight and 33% for food intake.  These two declined annual datasets for the past ~9 years have a correlation coefficient of 75% that is higher than the same two variables, weight and food, but with daily datasets during ~6 years of 47% correlation.

Another observation for his annualized “lower weight of less than 170 lbs.” portion percentages reflect the entire year’s weight record increasing in a general moving pattern.  However, the results are disconcerting due to the lack of a stabilized pattern for the lower-weight data.  Specifically, they are fluctuating during the sub-period of 2015-2020; therefore, he must work harder to keep his lower-weight portion percentage from continuously increasing year after year.  On the other hand, not only does this phenomenon indicates how difficult it is to control body weight, it also shed some light on how to do it correctly in reducing his weight.

Obesity is the root cause of three chronic diseases such diabetes, hypertension, and hyperlipidemia.  Those three chronic diseases can cause many of other known complications, including, but not limited to, cardiovascular diseases (CVD), strokes, chronic kidney diseases (CKD), foot ulcer, diabetic retinopathy, hypothyroidism, and even cancers and dementia.  Therefore, weight control is the first priority for patients to pay attention in order to be able to control other chronic diseases.

In the United States, approximately 36.5% of adults are obese and another 32.5% are overweight.  In other words, there are only 31% of American adults within the normal range of body weight (BMI < 25).  The author weighed 220 lbs. (110 kg) with a BMI of 32 in 2010.  From 2015 to 2020, his average weight was reduced to 173 lbs. (78.6 kg) with a BMI of 25.54.  Recently, his weight has further decreased to 169 lbs. (76.8 kg) with a BMI of 24.95.  From his 10-year journey, he definitely understands how hard it is to reduce his body weight.  During the past decade, he conducted research on metabolism, endocrinology, and various complications induced by chronic diseases; however, he was not able to identify a clear and significant influential factor for weight control.  Occasionally, he feels that weight seems to have a mind on its own randomly fluctuating according to its will.  Of course, he also realized that weight must have certain controlling factors within itself.

At least, in this study, he is able to prove his intuitive feeling that meal portion” or food quantity is one of the most important contributing factors, even with a moderate R of 47%.  By using the annualized data, he also found a higher R of 75% between his annual weight and annual food portion.  Furthermore, from using segmentation analysis of “lower weight less than 170 lbs.”, he strongly believes that he can achieve his goal of maintaining his BMI less than 25 by controlling his food portion below 70% of his normal meal size.

Introduction
The author attempts a detailed analysis to identify the relationship between annual body weights and his annual food portion percentages using both Pearson correlation coefficient “R” of statistics to calculate the association between these two variables.  Furthermore, he conducts a segmentation analysis to calculate his annual percentages of daily weights that are less than 170 lbs. with a BMI below 25.  This study utilized his weights and food portion percentage of normal meal size for a period of ~9 years from 1/1/2012 to 9/12/2020.

The author wrote this article as an extension of his previous paper, Investigating the influential factors on body weight and its impact on glucoses using GH-Method: math-physical medicine (No. 327).  As a result, some results and certain parts of the paper are duplicated.

Method
1. Background
To learn more about the GH-Method: math-physical medicine (MPM) research methodology, readers can review his specific article, Biomedical research methodology based on GH-Method: math-physical medicine (No. 310), to understand his MPM analysis method.

2. Data Collection
The author started measuring his body weight since 1/1/2012.  He measures weight twice a day, once in the early morning when he wakes up and at night when he is ready to go to sleep.

To understand his overall metabolism situation, using his developed mathematical metabolism index (MI) model from 2014, he needs to collect many lifestyle details.  Although food is the most complicated part of his lifestyle details, in this study, he only focuses on the food intake amount or its quantitative size (i.e. portion size %) while disregarding the food nutritional quality.  It should be pointed out that he used his estimated food intake size based on his available scattered data from 2012 through 2014.

3. Time series analysis
All of the variables including weight and food portion percentage are expressed in the form of “time-series curves”.  These curves have two axes.  The horizontal x-axis is time (date) from 1/1/2012 throughout 9/12/2020, whereas the vertical y-axis is the amount of weight, or food portion percentage, that corresponds to the date on the x-axis.  In order to avoid the “over-presentation” of the results, the author does not include all of his calculated time-series curves in the graphs section in this paper.  As an alternative, he presents a summarized annual data table and the “lower weight” segmented curves.

In terms of segmentation analysis, he chose the weight of 170 lbs., corresponding to a BMI value of 25 in his case, as the dividing line.  His purpose is to identify the size of the lower-weight portion in order to control his weight below 170 lbs. and to maintain his BMI less than 25.

Results
In Figure 1, it shows the summarized background data of this study.  As a result, Figures 2, 3, and 4 are produced based on this background data table.  His average exercise amount is 15,769 walking steps each day and his daily water drinking amount is 2,851 cc.  These two influential factors are generally maintained at constant levels from 2015 to 2020; therefore, the food portion percentage becomes the main influential factor for weight that needs to be studied in this special investigation.

His annualized body weight decreased from 189 lbs. in 2012 to 172 lbs. in 2020 with a total reduction of 9% (Figure 2).  The average weight during these ~9 years is 176 lbs.

Correspondingly, his annualized food portion size percentage has been dropping from 101% in 2012 down to 68% in 2020 with a total reduction of 33% (Figure 3).  The average food intake percentage of his normal meal size during these ~9 years is 88%.  In figure 3, these two declined “annual” curves for the past ~9 years have a correlation coefficient of 75%.  However, this 75% is higher than the same two variables, “daily” weight and daily food portion, which are expressed in the correlation bar for a shorter period of ~6 years with 47% correlation coefficients (Figure 6).  This 47% R value was discussed in the Investigation of influential factors of body weight and its impact on glucoses using GH-Method: math-physical medicine (No. 327).  The difference of 28% in R is due to data difference from the annual vs. daily and timespan difference of 9 years vs. 6 years.

The results are displayed from his weight segmentation analysis in Figures 4 and 5.  The top diagram shows his daily weight curve from 1/1/2012 to 9/12/2020, whereas the bottom diagram shows those daily weight values less than 170 lbs. during the same time period (Figure 4).  It is clear that most of these “lower-weight” data are concentrated in 2018 along with the recent three months in 2020 from 7/2020 – 9/2020.

In Figure 5, it further demonstrated his annualized percentage bars of “lower-weight” portion for each year.  It has proved that 2018 has 30% of his weight less than 170 lbs., while in 2020 thus far, it has 18% of his weight less than 170 lbs.  He still has 3.5+ months to go for the remaining year of 2020; therefore, if he tries hard enough, being persistent on his control of food portion, he would be able to achieve a better performance (i.e., higher percentage number of weight less than 170 lbs.) compared to his previous record in 2018.

###### Figure 6: Correlation between body weight and food quantity (47%) using daily data within ~6 years period (1/1/2015 - 9/11/2020)

Conclusions
Obesity is the root cause of three chronic diseases such diabetes, hypertension, and hyperlipidemia.  Those three chronic diseases can cause many of other known complications, including, but not limited to, cardiovascular diseases (CVD), strokes, chronic kidney diseases (CKD), foot ulcer, diabetic retinopathy, hypothyroidism, and even cancers and dementia.  Therefore, weight control is the first priority for patients to pay attention in order to be able to control other chronic diseases.

In the United States, approximately 36.5% of adults are obese and another 32.5% are overweight.  In other words, there are only 31% of American adults within the normal range of body weight (BMI < 25).  The author weighed 220 lbs. (110 kg) with a BMI of 32 in 2010.  From 2015 to 2020, his average weight was reduced to 173 lbs. (78.6 kg) with a BMI of 25.54.  Recently, his weight has further decreased to 169 lbs. (76.8 kg) with a BMI of 24.95.  From his 10-year journey, he definitely understands how hard it is to reduce his body weight.  During the past decade, he conducted research on metabolism, endocrinology, and various complications induced by chronic diseases; however, he was not able to identify a clear and significant influential factor for weight control.  Occasionally, he feels that weight seems to have a mind on its own randomly fluctuating according to its will.  Of course, he also realized that weight must have certain controlling factors within itself.

At least, in this study, he is able to prove his intuitive feeling that meal portion” or food quantity is one of the most important contributing factors, even with a moderate R of 47%.  By using the annualized data, he also found a higher R of 75% between his annual weight and annual food portion.  Furthermore, from using segmentation analysis of “lower weight less than 170 lbs.”, he strongly believes that he can achieve his goal of maintaining his BMI less than 25 by controlling his food portion below 70% of his normal meal size.

References

1. Hsu, Gerald C., eclaireMD Foundation, USA, No. 310: “Biomedical research methodology based on GH-Method: math-physical medicine”
2. Hsu, Gerald C., eclaireMD Foundation, USA, No. 327: Investigation of influential factors of body weight and its impact on glucoses using GH-Method: math-physical medicine
3. Hsu, Gerald C., eclaireMD Foundation, USA, No. 320: “Accuracy of predicted glucose using both natural intelligence (NI) and artificial intelligence (AI) via GH-Method: math-physical medicine”
4. Hsu, Gerald C., eclaireMD Foundation, USA, No. 307: “Weight control trend analysis and progressive behavior modification of a T2D patient using GH-Method: math-physical medicine”
5. Hsu, Gerald C., eclaireMD Foundation, USA, No. 288: “Diabetes control and metabolism maintenance during COVID-19 period in comparison to three other periods using GH-Method: math-physical medicine”
6. Hsu, Gerald C., eclaireMD Foundation, USA, No. 11: “Relationship Between Weight and Glucose Using Math-Physics Medicine”
7. Hsu, Gerald C., eclaireMD Foundation, USA, No. 321: “Postprandial plasma glucose segmentation analysis of influences from diet and exercise between the pre-COVID-19 and COVID-19 periods”
8. Hsu, Gerald C., eclaireMD Foundation, USA, No. 312: “Segmentation analysis of impact on glucoses via diet, exercise, and weather temperature during COVID-19 quarantine period”
9. Hsu, Gerald C., eclaireMD Foundation, USA, No. 325: “Segmentation and pattern analyses of three meals’ PPG using GH-Method: math-physical medicine”