I was able to create a file to export. Many thanks. David Cundiff ... View more

That worked! Thanks.    Now the next part is also a problem. I want to export data that I create in libname Projects, specifically a file called Projects.source. I get error messages: Code:  libname Projects "/home/u43393119/Projects"; proc sort data=Projects.source; by weighted_no; run; quit; libname Projects xlsx 'C:\Users\user\Documents\MDM\Health outcomes formulas manuscripts \CVD Statistical tables and SAS codes\CVD output.xlsx'; %put My version of SAS is &sysvlong; options validvarname=v7; data Projects.source; set Projects.source; run;   Log shows errors:      Errors, Warnings, Notes    Errors (2)  Warnings (1)  Notes (6)       1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK; 72 73 74 libname Projects "/home/u43393119/Projects"; NOTE: Libref PROJECTS was successfully assigned as follows: Engine: V9 Physical Name: /home/u43393119/Projects 75 76 proc sort data=Projects.source; 77 by weighted_no; 78 run;   NOTE: Input data set is already sorted, no sorting done. NOTE: PROCEDURE SORT used (Total process time): real time 0.00 seconds user cpu time 0.00 seconds system cpu time 0.00 seconds memory 2456.46k OS Memory 42128.00k Timestamp 03/04/2021 11:58:32 PM Step Count 272 Switch Count 0 Page Faults 0 Page Reclaims 634 Page Swaps 0 Voluntary Context Switches 4 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 0     78 ! quit; 80 81 libname Projects xlsx 82 'C:\Users\user\Documents\MDM\Health outcomes formulas manuscripts 83 \CVD Statistical tables and SAS codes\CVD output.xlsx'; NOTE: Libref PROJECTS was successfully assigned as follows: Engine: XLSX Physical Name: C:\Users\user\Documents\MDM\Health outcomes formulas manuscripts\CVD Statistical tables and SAS codes\CVD output.xlsx 84 %put My version of SAS is &sysvlong; My version of SAS is 9.04.01M6P110718 85 options validvarname=v7; 86 87 run; 88 89 data Projects.source; 90 set Projects.source; ERROR: File PROJECTS.source.DATA does not exist. 91 92 run;   There are no variables for the output file ERROR: File PROJECTS.source.DATA does not exist. NOTE: The SAS System stopped processing this step because of errors. WARNING: The data set PROJECTS.source was only partially opened and will not be saved. NOTE: DATA statement used (Total process time): real time 0.00 seconds user cpu time 0.00 seconds system cpu time 0.00 seconds memory 2202.87k OS Memory 42892.00k Timestamp 03/04/2021 11:58:32 PM Step Count 273 Switch Count 0 Page Faults 0 Page Reclaims 859 Page Swaps 0 Voluntary Context Switches 0 Involuntary Context Switches 0 Block Input Operations 0 Block Output Operations 0     93 94 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;   How do I reference my file of interest: Project.source; ? Thanks.  ... View more

Thanks, Dr. Miller, for these comments.    “PLS does not throw out variables. Five factors indicates that five new factors/dimensions (these are different words for the same thing) are computed and used in the modeling. All variables contribute to the fitted model, some more than others, according to what the data is saying, but nothing is thrown out. The final regression equation from PROC PLS will use all 25 variables.”.   What is critical to our methodology and why it makes sense out of multicollinearity chaos is that, in the 20 food composite variable, each individual food is multiplied by the kilocalories/day on average consumed worldwide and also by the R 2 of the correlation with BMI. PROC PLS did fine with the three independent variable multiple regression of the (1) composite dietary variable, (2) physical activity, and (3) sex (variance accounted for by the BMI formula=68.55%, same as with PROC REG. But without that initial food variable formatting, PROC PLS was not helpful with the 20 individual foods. In addition, PROC REG allows us to take the SAS results to do the necessary calculations in Excel to create the final BMI formula with the coefficients of each dietary and other variable expressed in percent weights (sometime termed “population attributable fractions”), totaling the BMI formula percent weight. Creating the final 25 risk factor BMI formula this way and harmonizing it with worldwide BMI by equating their SDs and mean values allows much more. We can test the functionality of the formula with the nine Bradford Hill causality criteria (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898525/) and test different risk factor scenarios based on BMI formula estimates as shown in Table 2.   “PLS does not throw out variables. Five factors indicates that five new factors/dimensions (these are different words for the same thing) are computed and used in the modeling. All variables contribute to the fitted model, some more than others, according to what the data is saying, but nothing is thrown out. The final regression equation from PROC PLS will use all 25 variables.”. What is critical to our methodology and why it makes sense out of multicollinearity chaos is that, in the 20 food composite variable, each individual food is multiplied by the kilocalories/day on average consumed worldwide and also by the R 2 of the correlation with BMI. PROC PLS did fine with the three independent variable multiple regression of the (1) composite dietary variable, (2) physical activity, and (3) sex (variance accounted for by the BMI formula=68.55%, same as with PROC REG. But without that initial food variable formatting, PROC PLS was not helpful with the 20 individual foods. In addition, PROC REG allows us to take the SAS results to do the necessary calculations in Excel to create the final BMI formula with the coefficients of each dietary and other variable expressed in percent weights (sometime termed “population attributable fractions”), totaling the BMI formula percent weight. Creating the final 25 risk factor BMI formula this way and harmonizing it with worldwide BMI by equating their SDs and mean values allows much more. We can test the functionality of the formula with the nine Bradford Hill causality criteria (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898525/) and test different risk factor scenarios based on BMI formula estimates as shown in Table 2.   Table 2. Testing common dietary and other risk factor scenarios with BMI formula estimates Dietary and other risk factor scenarios BMI kg/M 2 BMI formula estimate World (n=7886 cohorts mean 1990-2017) 21.79 21.79 World with breast feeding discontinued < 6 month in ALL   22.00 World with breast feeding discontinued < 6 month in NONE   21.76 World with ALL children with severe underweight   20.68 World with NO children with severe underweight   22.04 United Kingdom (n=66 cohorts) UK best fit BMI formula 24.99 25.45 USA (n=376 cohorts, 2004—the mean of 1990 and 2017) 26.66 27.27 Following USA Dietary Guidelines 2015-2020 standard recommendations   23.43 Following USA Dietary Guidelines 2015-2020 Mediterranean diet recommendations   22.57 Following USA Dietary Guidelines 2015-2020 vegetarian diet recommendations   21.52 USA with 25% reduction of BMI increasing food intake†   23.31 USA with 50% reduction of BMI increasing food intake†   19.35 USA mean physical activity plus 1 hours/day running at 6 mph   26.31 USA mean physical activity plus 1 hour/day running at 6 mph and 25% reduction of BMI increasing food intake†   22.35 USA with no red or processed meat†   24.44 USA with no sugary beverage intake†   26.44 USA vegetarian (no meat, poultry, fish)†   21.42 USA vegan (no meat, poultry, fish, dairy or eggs)†   19.56 EAT-Lancet diet†   22.88 Low Carbohydrate Mediterranean Diet†   32.53 β BMI formula estimates based on 28 years of following dietary and risk factor patterns † Kcal/day 13 BMI increasing foods isocalorically shifted to the 7 BMI decreasing foods in the BMI formula, distributed equally.     “PROC REG can be considered "more suitable" if you are willing to accept the affects of collinearity on your regression coefficients.”   I am more than willing to accept the affects of collinearity on my regression coefficients because modeling dietary risk factors isn’t like modeling some engineering or chemometric application where the coefficients have to be exactly right. As shown in Table 1 (several posts ago) with the 20 cross validation trials, each coefficient has a fairly wide range of experimentally valid values.   "But it is an empirical approach, it uses the data you provide to determine what the best fitting regression equation is, without regard for the known and previously determined (by others) BMI model."   There is no known and previously determined by other BMI model. The recently published Institute of Health Metrics and Evaluation (IHME) Global Burden of disease risk factor paper said, “At the global level, we find that high BMI is rising considerably faster than low physical activity and poor diet quality. ... Some studies suggest that certain diet components are more likely to contribute to increased BMI than others; the mechanism of these effects can be complex and include effects on appetite, absorption, and displacement of other foods.35 It is currently hard to understand the role of physical inactivity, excess caloric intake, and diet quality in driving the increase in BMI.” (https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30752-2/fulltext). IHME, the place that sent me, as a registered volunteer collaborator, 1.4 gigabytes of raw data on BMI and over 30 risk factors, does not use their own data to model BMI or other health outcomes. Instead, they do systematic literature reviews to draw conclusions about causality of health outcomes.   "And so because either your data is different, or the collinearity causes sufficient problems, that you can get (and apparently do get, based on your earlier statements) coefficients with the wrong sign and coefficients that are so variable due to collinearity that they may be far away from the theoretical value. Maybe you want a mixed "empirical-hard model" model, but I have no idea how to get that, and I'm not even sure such a thing exists. (So I don't agree PROC REG is appropriate, it has the problems mentioned in this paragraph)”   For the sake of argument, consider that we may have developed as least a prototype of an “empirical-hard model” model. But how would you be able to tell a good empirical-hard model model from a poor one? Consider vetting the model with the classical Bradford Hill causality criteria used in epidemiology: (1) strength, (2) experiment (e.g., cross validation), (3) consistency, (4) biologic gradient (i.e., dose response), (5) temporality, (6) analogy, (7) plausibility, (8) specificity, and (9) coherence. Our empirical methodology aced all of these nine criteria. You can read a previous draft of our BMI formula paper to find our errors: https://www.medrxiv.org/content/10.1101/2020.07.27.20162487v1.  As soon as my statistician co-author agrees to include all 25 risk factors and completes the cross validation step, we will update the preprint, which will be at the same link, hopefully, within a week or two. Preprints are not peer reviewed. It would be help us greatly to get the paper into external peer review at the Lancet if you and/or other SAS experts or aspiring experts would peer review the paper and post them as a comments.   Which brings us back to the very first question that I should have asked: what is the goal of this modeling? Is it to fit the data? Is it to confirm the BMI model holds on this data? Is it something else?   The goal of the modeling is to win the Nobel Prize in medicine. Kidding. All of the above—we need to fit the data, confirm the BMI model holds on this data, show that this new empirical methodology works for BMI and potentially for hundreds of other noncommunicable disease health outcomes, and get the paper published in a consequential journal like the Lancet. This modeling also has a potential practical public health application of creating an app based on the BMI formula to provide feedback to individuals wanting to control their weight by diet and exercise. My website has a proof of concept prototype of such an app called, “Future body mass index (BMI) estimator based on diet and exercise.” This app is primitive compared to using IHME GBD data. I created BMI formulas from each of two databases (Diabetes Control and Complications Trial and World Health Organization/Food and Agriculture data) and merged the results of BMI modeling with these two databases into the framework for the app. You input your dietary pattern, exercise level, age, sex, height, and weight and it reports your estimated BMI in 1, 5, 10, and 20 years. You can then change components of your diet and/or exercise data to see what options would lead you to reach your weight control goal.   When someone asks about VIFs and regression modeling, I assume they are talking about empirical modeling and the goal of the modeling is to find a predictive model that fits the data, but now it sounds like that is not the goal.   Our goal only starts with finding a predictive model that fits the data. We have done that. And then it extends up to and including SAS students in college and elsewhere collaborating with us to model many more health outcomes with this methodology. These GBD data cover the years 1990-2017 and will become outdated when the 1990-2019 data (with everything updated) become available to GBD researchers. Eventually, more preprints of GBD data modeling health outcomes will lead to IHME realizing that using their data for statistically modeling health outcomes should complement their razor focus on systematic literature reviews to draw conclusions leading to public health policy strategies.   Spread the word! Many thanks, Dr. Miller.   ... View more

I used NFAC=5, which throws out 19/25 variables, and got the following result:   The PLS Procedure Data Set WORK.SOURCE Factor Extraction Method Partial Least Squares PLS Algorithm NIPALS Number of Response Variables 1 Number of Predictor Parameters 22 Missing Value Handling Exclude Number of Factors 5 Number of Observations Read 7886 Number of Observations Used 7886 ________________________________________ The PLS Procedure Percent Variation Accounted for by Partial Least Squares Factors Number of Extracted Factors Model Effects Dependent Variables Current Total Current Total 1 32.7157 32.7157 77.2347 77.2347 2 7.4541 40.1698 9.1991 86.4338 3 6.6411 46.8109 1.6277 88.0615 4 5.3212 52.1322 0.9785 89.0400 5 5.4688 57.6010 0.4847 89.5247 I read the Tobias paper and understood the gist but not all the details. I’m not a statistician. I am a retired internal medicine physician who got my undergraduate degree in mathematics long before SAS was a company and when we all carried slide rules. The Tobias abstract began saying, “Partial least squares is a popular method for soft modelling in industrial applications.” The referenced uses of PLS included econometrics, neural networks, chemometrics, and social science. A 2013 paper titled, “Evaluation of methodologies for assessing the overall diet: dietary quality scores and dietary pattern analysis” discussed three main approaches to study the overall diet—(1) dietary guidelines based, (2) principle component analysis or cluster analysis, (3) reduced rank regression. (https://pubmed.ncbi.nlm.nih.gov/23360896/). PLS was not mentioned. However, a 2017 paper titled, “An application of for identifying dietary patterns in bone health” did use PLS. They introduced PLS saying, “Partial least-squares (PLS) is a data-reduction technique for identifying dietary patterns that maximizes correlation between foods and nutrients hypothesized to be on the path to disease, is more hypothesis-driven than previous methods, and has not been applied to the study of dietary patterns in relation to bone health.” (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5506508/#:~:text=Partial%20least%2Dsquares%20(PLS),patterns%20in%20relation%20to%20bone). We are not researching dietary patterns that maximize correlations between foods and nutrients. We are modeling the dietary and other risk factors for BMI worldwide.  The Tobias paper introduction included, “In such so-called soft science applications, the researcher is faced with many variables and ill-understood relationships, and the object is merely to construct a good predictive model.” Tobias goes on to say that a good predictive model is usually defined by cross-validation. The BMI formula that we modeled with 24 total risk factors, including 20 dietary risk factors used as a composite variable, was tested by cross-validation with 20 random trials of 100 cohorts (out of a database with 7886 cohorts) and, in each of these cross-validation trials, no signs were flipped and the cross validating BMI formulas were all very close to the initial BMI formula (See Table 1). Table 1. Cross-validation analysis: BMI formulas with 20 groups each with 100 random cohorts BMI Risk factors included in the BMI formula (n=7886 cohorts, representing about 7.8 billion people) BMI formula worldwide BMI formulas of 20 groups of 100 cohorts each Mean percent weight Mean percent weight SD Minimum Maximum + Processed meat kcal/day 0.266 0.246 0.093 0.050 0.472 + Red meat kcal/day 2.951 2.542 0.947 0.734 4.762 + Fish kcal/day 0.014 0.064 0.152 0.004 0.610 + Milk kcal/day 1.578 1.362 0.456 0.404 2.327 + Poultry kcal/day 3.958 3.364 1.023 1.181 5.691 + Eggs kcal/day 1.224 1.084 0.353 0.486 1.912 + Alcohol kcal/day 0.301 0.279 0.307 0.001 0.969 + Sugary beverages kcal/day 0.562 0.901 0.886 0.000 3.247 + Corn kcal/day 0.024 0.072 0.067 0.000 0.227 + Potatoes kcal/day 0.495 0.396 0.366 0.001 1.366 + Saturated fatty acids kcal/day 6.107 5.203 1.892 1.986 8.805 + Polyunsaturated fatty acids 2.831 2.423 0.832 0.916 4.503 + Trans fatty acids kcal/day 0.202 0.204 0.082 0.063 0.354 - Fruits kcal/day 2.078 1.899 0.456 1.248 2.925 - Vegetables kcal/day 2.875 2.596 0.596 1.222 3.530 - Nuts and seeds kcal/day 0.268 0.234 0.093 0.035 0.434 - Whole grains kcal/day 0.297 0.263 0.206 0.000 0.679 - Legumes kcal/day 1.014 0.880 0.366 0.325 1.718 - Rice kcal/day 5.900 5.091 2.056 1.769 9.041 - Sweet potatoes kcal/day 0.069 0.074 0.050 0.006 0.179 - Physical activity 11.797 12.503 2.671 7.660 17.190 - Child severe underweight 19.850 20.781 3.580 15.267 28.867 + Discontinued breast feeding 13.090 13.679 2.084 9.525 16.933 + Sex (1=male, 2=female) 4.479 5.143 2.148 1.053 8.642 Total percent weights 82.230 81.280 3.550 75.240 86.930 The Tobias paper discussion began, “As discussed in the introductory section, soft science applications involve so many variables that it is not practical to seek a ‘‘hard’’ model explicitly relating them all.” Well, we claim that our 24 variable and soon to be 25 variable hard science formula modeling BMI gives excellent predictability. The resultant BMI formula performs equally well with the other eight Bradford Hill causality criteria—the “gold standard” criteria for providing proof in epidemiology.   Dr. Miller, can you please agree that the hard science Proc reg is more suitable than the soft science Proc PLS for this worldwide BMI modeling application and tell my statistician co-author that we shouldn’t have to throw out any variables?   Using this population weighted and formatted database of Global Burden of Disease data from the Institute of Health Metrics and Evaluation, my co-author and I serve as volunteer collaborators modeling risk factors related to health outcomes. We would be happy to help SAS students to model any of over 50 other health outcomes for which we have the formatted data (e.g., systolic blood pressure, cardiovascular diseases, cancers, etc.). I am old. Fifty more papers like this would be too much for me to accomplish in this lifetime. The only requirement would be to register as a volunteer collaborator with the Institute of Health Metrics and Evaluation. By the way this Bill and Melinda Gates funded institute hires many statisticians (http://www.healthdata.org/).   Many thanks, Dr. Miller, for your help. David Cundiff ... View more

Sorry, I put my text rather than the code in the code box:  libname IHME2017 "/folders/myfolders/IHME2017"; data source; set IHME2017.source; Where weighted_no le 7886; label BMI17f1=20 foods combined risk factor; BMI17f1= + pmeat17KCsW * 5.49 * 0.3649 + rmeat17KCsW * 50.70 * 0.4380 + fish17KCsW * 10.01 * 0.0105 + milk17KCsW * 25.37 * 0.4682 + poultry16KCsW * 45.06 * 0.6611 + eggs16KCsW * 19.47 * 0.4731 + Alcohol17KCsW * 81.71 * 0.0277 + Sugarb17KCsW * 297.65 * 0.0142 + corn16KCsW * 34.67 * 0.0053 + potatoes16KCsW * 84.16 * 0.0443 + SFA16KCsW * 191.27 * 0.5038 * 0.477 + PUFA17KCsW * 82.24 * 0.5431 * 0.477 + TFA17KCsW * 13.40 * 0.2379 * 0.477 - fruits17KCsW * 40.39 * 0.3873 - Vegetables17KCsW * 80.14 * 0.270 - nutsseeds17KCsW * 8.51 * 0.2367 - wgrains17KCsW * 55.65 * 0.0402 - legumes17KCsW * 51.66 * 0.1477 - rice16KCsW * 141.23 * 0.3144 - swtpot16KCsW * 22.67 * 0.0230 ; run; quit; Proc reg data=source; model BMI17msW=BMI17f1 PAMets17msW sex_IDsW / selection=STEPWISE slentry=.25 slstay=.25; run;quit; * Results BMI17f1 0.00545 0.00004933 3843.16145 12213.9 <.0001 PAMets17msW -0.13763 0.00710 118.27826 375.90 <.0001 sex_IDsW 0.12293 0.00662 108.47074 344.73 <.0001 1 BMI17f1 foods combined risk factor 1 0.6446 0.6446 1023.48 14300.9 <.0001 2 PAMets17msW Physical activity METs 2 0.0271 0.6717 346.730 650.39 <.0001 3 sex_IDsW sex male 1 female 2 3 0.0138 0.6855 4.0000 344.73 <.0001 * ; *Partial least squares with a composite dietary variable method by contrast; PROC PLS data=source METHOD=PLS; MODEL BMI17msW = BMI17f1 PAMets17msW sex_IDsW ; *OUTPUT OUT=PLSmethod; run; quit; *Result The PLS Procedure Data Set WORK.SOURCE Factor Extraction Method Partial Least Squares PLS Algorithm NIPALS Number of Response Variables 1 Number of Predictor Parameters 3 Missing Value Handling Exclude Number of Factors 3 Number of Observations Read 7886 Number of Observations Used 7886 The PLS Procedure Percent Variation Accounted for by Partial Least Squares Factors Number of Extracted Factors Model Effects Dependent Variables Current Total Current Total 1 45.4455 45.4455 64.7483 64.7483 2 27.6348 73.0804 3.4163 68.1646 3 26.9196 100.0000 0.3819 68.5465 ; *Partial least squares with 20 individual diet variables; PROC PLS data=source METHOD=PLS; MODEL BMI17msW = pmeat17KCsW rmeat17KCsW fish17KCsW milk17KCsW poultry16KCsW eggs16KCsW Alcohol17KCsW Sugarb17KCsW corn16KCsW potatoes16KCsW SFA16KCsW PUFA17KCsW TFA17KCsW fruits17KCsW Vegetables17KCsW nutsseeds17KCsW wgrains17KCsW legumes17KCsW rice16KCsW swtpot16KCsW PAMets17msW sex_IDsW ; *OUTPUT OUT=PLSmethod; run; quit; *The PLS Procedure Percent Variation Accounted for by Partial Least Squares Factors Number of Extracted Factors Model Effects Dependent Variables Current Total Current Total 1 32.7157 32.7157 77.2347 77.2347 2 7.4541 40.1698 9.1991 86.4338 3 6.6411 46.8109 1.6277 88.0615 4 5.3212 52.1322 0.9785 89.0400 5 5.4688 57.6010 0.4847 89.5247 6 6.6591 64.2601 0.1593 89.6840 7 2.9929 67.2530 0.1715 89.8554 8 4.0856 71.3386 0.0753 89.9307 9 4.9696 76.3082 0.0284 89.9591 10 1.9025 78.2107 0.0252 89.9844 11 4.2921 82.5028 0.0042 89.9886 12 2.5422 85.0450 0.0047 89.9932 13 2.5712 87.6162 0.0019 89.9951 14 2.9205 90.5367 0.0007 89.9958 15 2.6019 93.1386 0.0001 89.9959 ; ... View more

Below is a comparison of (1) standard multiple regression analysis with the formatted composite 20 variable diet risk factor, physical activity, and sex; (2) Partial least squares analysis with the formatted composite 20 variable diet risk factor, physical activity, and sex; and (3) PLS analysis with the individual 20 variable diet risk factors, physical activity, and sex.   libname IHME2017 "/folders/myfolders/IHME2017"; data source; set IHME2017.source; Where weighted_no le 7886; label BMI17f1=20 foods combined risk factor; BMI17f1= + pmeat17KCsW * 5.49 * 0.3649 + rmeat17KCsW * 50.70 * 0.4380 + fish17KCsW * 10.01 * 0.0105 + milk17KCsW * 25.37 * 0.4682 + poultry16KCsW * 45.06 * 0.6611 + eggs16KCsW * 19.47 * 0.4731 + Alcohol17KCsW * 81.71 * 0.0277 + Sugarb17KCsW * 297.65 * 0.0142 + corn16KCsW * 34.67 * 0.0053 + potatoes16KCsW * 84.16 * 0.0443 + SFA16KCsW * 191.27 * 0.5038 * 0.477 + PUFA17KCsW * 82.24 * 0.5431 * 0.477 + TFA17KCsW * 13.40 * 0.2379 * 0.477 - fruits17KCsW * 40.39 * 0.3873 - Vegetables17KCsW * 80.14 * 0.270 - nutsseeds17KCsW * 8.51 * 0.2367 - wgrains17KCsW * 55.65 * 0.0402 - legumes17KCsW * 51.66 * 0.1477 - rice16KCsW * 141.23 * 0.3144 - swtpot16KCsW * 22.67 * 0.0230 ; run; quit; *Standard multiple regression analysis with a composite dietary variable, physical activity, and sex modeling body mass index worldwide; Proc reg data=source; model BMI17msW=BMI17f1 PAMets17msW sex_IDsW / selection=STEPWISE slentry=.25 slstay=.25; run; quit; * Results BMI17f1 0.00545 0.00004933 3843.16145 12213.9 <.0001 PAMets17msW -0.13763 0.00710 118.27826 375.90 <.0001 sex_IDsW 0.12293 0.00662 108.47074 344.73 <.0001 1 BMI17f1 foods combined risk factor 1 0.6446 0.6446 1023.48 14300.9 <.0001 2 PAMets17msW Physical activity METs 2 0.0271 0.6717 346.730 650.39 <.0001 3 sex_IDsW sex male 1 female 2 3 0.0138 0.6855 4.0000 344.73 <.0001 Accounts for 68.55% of the variance * ; *Partial least squares with a composite dietary variable method by contrast; PROC PLS data=source METHOD=PLS; MODEL BMI17msW = BMI17f1 PAMets17msW sex_IDsW ; *OUTPUT OUT=PLSmethod; run; quit; *Result The PLS Procedure Data Set WORK.SOURCE Factor Extraction Method Partial Least Squares PLS Algorithm NIPALS Number of Response Variables 1 Number of Predictor Parameters 3 Missing Value Handling Exclude Number of Factors 3 Number of Observations Read 7886 Number of Observations Used 7886 The PLS Procedure Percent Variation Accounted for by Partial Least Squares Factors Number of Extracted Factors Model Effects Dependent Variables Current Total Current Total 1 45.4455 45.4455 64.7483 64.7483 2 27.6348 73.0804 3.4163 68.1646 3 26.9196 100.0000 0.3819 68.5465 Accounts for 68.55% of the variance ; *Partial least squares with 20 individual diet variables; PROC PLS data=source METHOD=PLS; MODEL BMI17msW = pmeat17KCsW rmeat17KCsW fish17KCsW milk17KCsW poultry16KCsW eggs16KCsW Alcohol17KCsW Sugarb17KCsW corn16KCsW potatoes16KCsW SFA16KCsW PUFA17KCsW TFA17KCsW fruits17KCsW Vegetables17KCsW nutsseeds17KCsW wgrains17KCsW legumes17KCsW rice16KCsW swtpot16KCsW PAMets17msW sex_IDsW ; run; quit; *The PLS Procedure with 20 individual dietary factors, physical activity and sex; Percent Variation Accounted for by Partial Least Squares Factors Number of Extracted Factors Model Effects Dependent Variables Current Total Current Total 1 32.7157 32.7157 77.2347 77.2347 2 7.4541 40.1698 9.1991 86.4338 3 6.6411 46.8109 1.6277 88.0615 4 5.3212 52.1322 0.9785 89.0400 5 5.4688 57.6010 0.4847 89.5247 6 6.6591 64.2601 0.1593 89.6840 7 2.9929 67.2530 0.1715 89.8554 8 4.0856 71.3386 0.0753 89.9307 9 4.9696 76.3082 0.0284 89.9591 10 1.9025 78.2107 0.0252 89.9844 11 4.2921 82.5028 0.0042 89.9886 12 2.5422 85.0450 0.0047 89.9932 13 2.5712 87.6162 0.0019 89.9951 14 2.9205 90.5367 0.0007 89.9958 15 2.6019 93.1386 0.0001 89.9959 The top 15/22 variables account for 90% of the variance, but flipping signs of the dietary variables make this nonsense. Since PLS analysis gives us the same result (R2) as proc reg with our formatted 20 diet risk  factor variable, is it reasonable for us to use proc reg this way and not worry about the VIF test used with the 20 individual dietary risk factors? Hopefully, you will save me from having to throw  out variables, which I do not want to do.  I would be honored to list you as a contributor on our paper when we submit it to the Lancet.  Many thanks.  David Cundiff     ... View more

I'll try it. Thanks. ... View more

To finish the Bradford Hill criteria results of this new nutritional epidemiology methodology: (1) strength BMI formula versus BMI: r= 0.907 (95% CI: 0.903 to 0.911) p<0.0001), (2) experiment: 20/20 bootstrap BMI formulas (each n=100 cohorts) have the 25 risk factors with the same risk factor signs as the worldwide BMI formula, (3) consistency: absolute difference between 37 mean BMI and BMI formula outputs < 0.300 BMI units. (4) Dose-response: the absolute differences between 4 mean BMI and BMI formula dose-response outputs < 0.300. (5) temporality: BMI trend formula r≥0.500, p<0.0001. (6) analogy: low density lipoprotein cholesterol (LDL-C) correlates very strongly with the BMI formula (r=0.808, 95% CI 0.800 to 0.816, p<0.0001) and with BMI (r=0.759 95% CI 0.747 to 0.766, p<0.0001). (7) plausibility all 25 BMI formula risk factors are plausible according to literature reviews. (8) specificity: BMI formula is unique and fits no other health outcome. (9) coherence: all evidence supports that the BMI formula accurately models BMI worldwide.   ... View more

Thanks again for working on this with me.    Don't you want to know which of these variables are good predictors? Would it not "make sense" because of multicollinearity? If that's what you are saying ... then I disagree ... you still want to know which of these variables are good predictors. I don't think you want to choose an algorithm and let this drive your choices and force you to throw away information (variables), you want an algorithm that allows you to obtain results that meet the needs.   I agree. We tested this algorithm with the nine Bradford Hill causality criteria and all nine criteria strongly supported the algorithm. https://www.medrxiv.org/content/10.1101/2020.07.27.20162487v1 Since that preprint was published in July, we satisfied the ninth Bradford Hill criterion, specificity. We are introducing a new methodology to nutritional epidemiology, a science that has been criticized as yielding predominantly implausible results (https://www.bmj.com/content/bmj/347/bmj.f6698.full.pdf). When we do a multiple regression of BMI (dependent variable) versus the 20 dietary variables, we get a BMI formula that accounts for 89% of the variance. However, it is nonsense because 8/20 variables flipped signs (+ or -) between univariate correlation and the BMI formula.   Our methodology uses worldwide Global Burden of Disease population weighted data with ecological cohorts representative of about 7.8 billion people in 2020. We consider that all of the 20 dietary variables are good predictors. However, these dietary variables need to be formatted optimally to satisfy the Bradford Hill criteria. Each of the dietary variables is adjusted according to its kilocalories/day consumed percapita and the R 2 of its correlation with BMI. When this is done, the correlation of the composite dietary variable with BMI accounts for about 68% of the variance.     With ordinary least squares regression, people spend a lot of time and get a lot of grey hairs trying to work around multicollinearity. There are many methods proposed that are time consuming and most require throwing away information (variables) and the problem remains that some multicollinearity exists in the x-variables, and all have certain drawbacks, especially stepwise regression, which I avoid like the plague.   So, I suggest you use a fitting algorithm that is extremely robust to multicollinearity. So robust, in fact, that most published papers don't even go through a step of eliminating variables, and they still get models that predict well and are useful. What is that method? It is PARTIAL LEAST SQUARES regression. Then you don't have to throw away variables, and you don't have to spend huge amounts of time figuring out what to do about multicollinearity.   I see how what you are saying would apply well to a field other than nutritional epidemiology. For instance, processed meat (5 kilocalories/day percapita) and red meat (50 kcal/day percapita) are both strongly correlated with BMI (say r=0.70 and r=0.60, respectively). In the BMI formula comprised of these 20 dietary risk factors, processed meat has a “+” sign and red meat has a “–“ sign. So red meat would have to be removed from the algorithm.   How would partial least squares regression solve this problem?   Published papers sometimes have 1000 input variables, highly correlated with each other, and PLS fits the model well, and no effort is spent on eliminating the effects of multicollinearity. I already gave you a link to a paper that took 1000 input variables, highly correlated, and came up with a usable and well-fitting model, said paper written at SAS Institute (have you heard of them?). In this method, the effects of multicollinearity are low, the likelihood that terms in the model will flip signs is very low, and the predicted values have much lower mean squared error than via other methods   We used a composite dietary risk factor methodology which includes all dietary risk factors. Is there any way that switching from our methodology to the partial least squared methodology with 20 individual dietary risk factors or the 12 ones remaining that didn’t switch signs with multiple regression would improve our results of satisfying all nine Bradford Hill causality criteria ((1) strength r= 0.907 (95% CI: 0.903 to 0.911) p<0.0001), (2) experiment: 20/20 bootstrap BMI formulas (n=100 cohorts) have the 25 risk factors with the same risk factor signs as the worldwide BMI formula, (3) consistency absolute difference between mean BMI and BMI formula output < 0.300 BMI units and less than one-third of subgroups are out of range of the 20 bootstrap validating randomly generated BMI formulas. ... View more

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  Thanks for looking at this, Dr. Miller, This is a worldwide population weighted database with cohorts from 195 countries.   libname IHME2017 "/folders/myfolders/IHME2017"; *Dietary variables are highly collinear. There is no way it would make sense to put 20 dietary variables individually into a multiple regression. I did it and 8/20 of the variables switched signs (+ or -) from the univariate correlation to the multiple regression formula sign. Our composite dietary variable was constructed with each variable multiplied times its kilocalories/day consumed and then times the R2 of the univariate correlation with BMI. We arrived at this formatting empirically. No one else has ever done this kind of statistical analysis of worldwide population weighted data from the Institute of Health Metrics and Evaluation, the World Health Organization, or anywhere.; data source; set IHME2017.source; label BMI17f1=20 foods combined risk factor; BMI17f1= + pmeat17KCsW * 5.49 * 0.3649 + rmeat17KCsW * 50.70 * 0.4380 + fish17KCsW * 10.01 * 0.0105 + milk17KCsW * 25.37 * 0.4682 + poultry16KCsW * 45.06 * 0.6611 + eggs16KCsW * 19.47 * 0.4731 + Alcohol17KCsW * 81.71 * 0.0277 + Sugarb17KCsW * 297.65 * 0.0142 + corn16KCsW * 34.67 * 0.0053 + potatoes16KCsW * 84.16 * 0.0443 + SFA16KCsW * 191.27 * 0.5038 * 0.477 + PUFA17KCsW * 82.24 * 0.5431 * 0.477 + TFA17KCsW * 13.40 * 0.2379 * 0.477 - fruits17KCsW * 40.39 * 0.3873 - Vegetables17KCsW * 80.14 * 0.270 - nutsseeds17KCsW * 8.51 * 0.2367 - wgrains17KCsW * 55.65 * 0.0402 - legumes17KCsW * 51.66 * 0.1477 - rice16KCsW * 141.23 * 0.3144 - swtpot16KCsW * 22.67 * 0.0230 ; run; quit; *The first BMI versus risk factors multiple regression includes the composite dietary variable, physical activity, and sex; Proc reg data=source; model BMI17msW=BMI17f1 PAMets17msW sex_IDsW / selection=STEPWISE slentry=.25 slstay=.25; run;quit; * Results BMI17f1 0.00545 0.00004933 3843.16145 12213.9 <.0001 PAMets17msW -0.13763 0.00710 118.27826 375.90 <.0001 sex_IDsW 0.12293 0.00662 108.47074 344.73 <.0001 1 BMI17f1 foods combined risk factor 1 0.6446 0.6446 1023.48 14300.9 <.0001 2 PAMets17msW Physical activity METs 2 0.0271 0.6717 346.730 650.39 <.0001 3 sex_IDsW sex male 1 female 2 3 0.0138 0.6855 4.0000 344.73 <.0001 * ; *First step BMI formula with dietary variables, physical activity and sex R2=0.6855; data source; set source; label BMI17f2="combo diet, physical act, and sex"; BMI17f2= + BMI17f1 * 0.00545 - PAMets17msW * 0.13763 + sex_IDsW * 0.12293 ; run; quit; *VIF testing of the three variables: Proc reg data=source; model BMI17msW=BMI17f1 PAMets17msW sex_IDsW / selection=STEPWISE slentry=.25 slstay=.25; run;quit; *Results Parameter Estimates Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Variance Inflation Intercept Intercept 1 -1.6351E-13 0.00632 -0.00 1.0000 0 BMI17f1 20 foods combined risk factor 1 0.00545 0.00004933 110.52 <.0001 1.18131 PAMets17msW Physical activity METs 1 -0.13763 0.00710 -19.39 <.0001 1.26268 sex_IDsW Sex male 1 and female 2 1 0.12293 0.00662 18.57 <.0001 1.09860   *The second step of the entire multiple regression includes childhood severe underweight, discontinuation of breast feeding before 6 months and total kilocalories available; Proc reg data=source; model BMI17msW=Childunwt17msW discbreastF17msW kcal2016msW / selection=STEPWISE slentry=.25 slstay=.25; run;quit; * Results Childunwt17MsW -0.38646 0.00841 354.66255 2111.00 <.0001 discbreastF17msW 0.08612 0.00960 13.51799 80.46 <.0001 kcal2016msW 0.54075 0.00673 1085.87775 6463.29 <.0001 1 kcal2016msW Total Kc/d avail 1 0.7112 0.7112 5671.77 19415.9 <.0001 2 Childunwt17MsW Child/infant 2SD underweight 2 0.1191 0.8303 82.4609 5535.51 <.0001 3 discbreastF17msW Discontinued breast feeding <6 mo 3 0.0017 0.8321 4.0000 80.46 <.0001 ; *VIF testing the second step; Proc reg data=source; model BMI17msW=Childunwt17msW discbreastF17msW kcal2016msW / VIF; run;quit; *Results   Parameter Estimates Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Variance Inflation Intercept Intercept 1 -1.3083E-13 0.00462 -0.00 1.0000 0 Childunwt17MsW Child/infant 2SD underweight 1 -0.38646 0.00841 -45.95 <.0001 3.32051 discbreastF17msW Discontinued breast feeding <6 mo 1 0.08612 0.00960 8.97 <.0001 4.32648 kcal2016msW Total Kc/d avail 1 0.54075 0.00673 80.39 <.0001 2.12331 *Second step BMI formula R2=0.8321; data source; set source; label BMI17f3="combo child underweight, discontinued breast feeding before 6 mo, and kcal"; BMI17f3= - Childunwt17MsW * 0.38646 + discbreastF17msW * 0.08612 + kcal2016msW * 0.54075 ; run; quit; *The third step to create the BMI formula is to combine the first two steps; Proc reg data=source; model BMI17msW=BMI17f2 BMI17f3 / selection=STEPWISE slentry=.25 slstay=.25; run;quit; * Results: BMI17f2 0.35423 0.00804 261.63900 1941.01 <.0001 BMI17f3 0.74815 0.00730 1417.51533 10516.1 <.0001 1 BMI17f3 combo childUnWt, disc breast feeding, and kcal 1 0.8321 0.8321 1942.01 39060.5 <.0001 2 BMI17f2 combo diet, physical act, and sex 2 0.0332 0.8652 3.0000 1941.01 <.0001 *Third step VIF analysis results; Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Variance Inflation Intercept Intercept 1 -1.4122E-13 0.00413 -0.00 1.0000 0 BMI17f2 combo diet, physical act, and sex 1 0.35423 0.00804 44.06 <.0001 2.59058 BMI17f3 combo childUnWt, disc breast feeding, and kcal 1 0.74815 0.00730 102.55 <.0001 2.59058 *From the second step BMI formula, we wanted to include only the variance not accounted for by the first step BMI formula. We did this by subtracting the R2 of the first step BMI formula (0.6855) from the combined first step BMI formula and second step BMI formula R2 (=0.8652); BMI17f2 R2=0.6855 BMI17f2 + BMI17f3 R2=0.8652 BMI17f3 - BMI17f2= 0.8652 - 0.6855=0.1797 ; Proc reg data=source; model BMI17msW=BMI17f2 BMI17f3 / VIF; run; quit; *Final combined BMI formula R2=0.775438; data source; set source; label BMI17f4=BMI formula precursor; BMI17f4= + BMI17f2 * 0.6855 + BMI17f3 * 0.1797 ; run; quit; * On an Excel spreadsheet, we divided up the percent weights of all the variables and adjusted them to total the Total BMI formula R2 (= 0.775438); data source; set source; label BMI17f5=Final BMI formula, risk factors expressed as percent weights; BMI17f5= (+ pmeat17KCsW * 0.450 + rmeat17KCsW * 4.991 + fish17KCsW * 0.024 + milk17KCsW * 2.670 + poultry16KCsW * 6.695 + eggs16KCsW * 2.069 + Alcohol17KCsW * 0.509 + Sugarb17KCsW * 0.948 + corn16KCsW * 0.041 + potatoes16KCsW * 0.838 + SFA16KCsW * 10.330 + PUFA17KCsW * 4.788 + TFA17KCsW * 0.342 - fruits17KCsW * 3.516 - Vegetables17KCsW * 4.865 - nutsseeds17KCsW * 0.453 - wgrains17KCsW * 0.503 - legumes17KCsW * 1.715 - rice16KCsW * 9.978 - swtpot16KCsW * 0.117 - PAMETs17msW * 5.675 + sex_idsW * 5.069 - Childunwt17msW * 4.178 + discbreastF17msW * 0.931 + kcal2016msW * 5.845) * 0.05464712 + 21.78981 ; run; quit; proc corr data=source fisher; label BMI17f1=foods combined risk factor BMI17f2="Mult reg: combo diet, physical act, and sex" BMI17f3="Mult reg: combo childUnWt, disc breast feeding, and kcal" BMI17f4=Precursor BMI formula BMI17f5=Final BMI formula, risk factors expressed as percent weights; var PAMets17msW sex_IDsW BMI17f1 BMI17f2 BMI17f3 BMI17f4 BMI17f5; With BMI17m; run; quit; *Results 1 With Variables: BMI17m 7 Variables: PAMets17msW sex_IDsW BMI17f1 BMI17f2 BMI17f3 BMI17f4 BMI17f5   Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum Label BMI17m 7886 21.78981 2.31161 171834 17.94889 29.38579 BMI kg/M2 PAMets17msW 7886 -1.149E-13 1.00000 -9.059E-10 -2.26696 2.16518 Physical activity METs sex_IDsW 7886 0 1.00000 0 -0.99994 0.99994 Sex male 1 and female 2 BMI17f1 7886 0 139.17979 0 -277.97823 429.93603 foods combined risk factor BMI17f2 7886 0 0.82767 0 -1.81719 2.64672 Mult reg: combo diet, physical act, and sex BMI17f3 7886 0 0.91216 0 -1.87979 2.11848 Mult reg: combo child underweight, discontinued breast feeding before 6 months, and kilocalories available/day BMI17f4 7886 0 0.70322 0 -1.42007 2.10069 Precursor BMI formula BMI17f5 7886 21.78981 2.31161 171834 17.12183 28.69532 Final BMI formula, risk factors expressed as percent weights   Pearson Correlation Coefficients, N = 7886 Prob > |r| under H0: Rho=0   PAMets17msW sex_IDsW BMI17f1 BMI17f2 BMI17f3 BMI17f4 BMI17f5 BMI17m BMI kg/M2 -0.44498 <.0001 0.12202 <.0001 0.80288 <.0001 0.82793 <.0001 0.91217 <.0001 0.88060 <.0001 0.88059 <.0001 Pearson Correlation Statistics (Fisher's z Transformation) Variable With Variable N Sample Correlation Fisher's z Bias Adjustment Correlation Estimate 95% Confidence Limits p Value for H0:Rho=0 PAMets17msW BMI17m 7886 -0.44498 -0.47843 -0.0000282 -0.44496 -0.462488 -0.427082 <.0001 sex_IDsW BMI17m 7886 0.12202 0.12263 7.73718E-6 0.12201 0.100206 0.143692 <.0001 BMI17f1 BMI17m 7886 0.80288 1.10668 0.0000509 0.80287 0.794880 0.810574 <.0001 BMI17f2 BMI17m 7886 0.82793 1.18151 0.0000525 0.82791 0.820840 0.834730 <.0001 BMI17f3 BMI17m 7886 0.91217 1.54031 0.0000578 0.91216 0.908379 0.915796 <.0001 BMI17f4 BMI17m 7886 0.88060 1.37845 0.0000558 0.88059 0.875537 0.885453 <.0001 BMI17f5 BMI17m 7886 0.88059 1.37838 0.0000558 0.88057 0.875520 0.885437 <.0001  I'm sorry that I didn't present the problem/question to you this way in the first place. I hope that you will agree that, since 20 dietary variables are combined into one, the VIF test would be better than the PLS test with many variables in a multiple regression. In this analysis none of the 6 variables (not 25) had VIF>5.  What do you think?  Thank you.  David Cundiff  ... View more