Which Controlling Variables Mattered Most in Determining COVID19 Mortality?
And, which members of a subset of these variables have the greatest effects on normal life expectancy?
Introduction
This is the last (part 5 of the series) public posting on the subject of the most frequently employed non-pharmaceutical work-around methods of minimizing COVID19 mortality. The analytical approach so far has generally been to first obtain US state level proxies for such work-arounds as supplementation with zinc and its ionophores (e.g., hydroxychloroquine, quercetin, various plant flavonoids), antioxidants like melatonin, vitamins like vitamin C and D, and exercise frequency. Each proxy was then taken as an independent variable and graphed against CDC reports of state level COVID19 mortality rates per 100,000 people. Nearly all the resulting scatter plots illustrating the association (versus causation) of each of these independent variables with COVID19 mortality rate, the dependent variable, were consistent with the results and findings of previous biochemical research, and recent and ongoing medical practice.
These simple two-factor graphical correlation analyses suggest, as previously indicated by the findings and experience of many biochemical and medical researchers, that background, pre-COVID19 state average intakes of nutraceuticals, food, and drink supplying zinc, its ionophores, vitamins A, C, D, E, melatonin, all significantly helped reduce COVID19 mortality in the US and elsewhere. In addition to background, everyday levels of nutritional augmentation present in each state because of dietary habits and environment, the regularity of physical exercise of state residents was graphically shown to be especially predictive of state population COVID19 mortality rates.
What Factors Exerted the Strongest Influence of COVID19 Mortality?
The current posting provides the results of rudimentary mathematical modeling of the relative effectiveness of immune response of state populations to COVID19 infection. The modeling employs the production function systems theory model developed in economics to estimate the relative importance of nine (9) major controlling (independent) variables or “inputs” in determining the COVID19 death rates (the “output”) in each of the lower 48 states. Keep this in mind – this rudimentary mathematical work shown here is very much like a preclinical study in medicine, or like an early exploration drilling program exploring a newly discovered mineral deposit in the mining industry: the results provided are preliminary and approximate.
Variables employed for this modeling work included:
1 LOB – natural log of percentage of obesity in each state;
2 LCBG – natural log of product of per capita craft breweries/state times state per capita annual gallons craft brew consumption. This is a proxy for state adult population exposure to beer- and ale-contained plant flavonoids with antioxidant and possible zinc ionophore activity;
3 LAT – natural log of average state latitude. This is a complex proxy for both flu season nighttime exposure to endogenously produced melatonin and the latitude-limited level of vitamin D endogenous production. According to the modeling results provided in the next section, under normal (non-pandemic) circumstances, the positive effect of nightly melatonin production for people dwelling in more northerly states seems to be more important than the negative effects otherwise caused by their endogenous, sunlight- and latitude-limited vitamin D production. In the COVID19 environment, the vitamin D production-limiting effect of increasing latitude appears to have been more important in determining state level of COVID19 mortality. This last result is consistent with observations and conclusions reported here.
4 LVC – natural log of percent of state population eating at least one serving of vegetables per day;
5 LFC – natural log of percent of state population eating at least one serving of fruit each day;
6 LA – natural log of percent of population getting physical exercise on a regular basis;
7 LZN – natural log of average state soil zinc concentration in parts per million (ppm);
8 LLD – natural log of a third-party ranking of strictness and duration of lockdown procedures in each state. A low whole number represents a low level of lockdown during 2019-2020, while a high whole number denotes a high degree of lockdown rigor in a given state.
9 LE – natural log of actuarially-estimated average life expectancy in years for a state’s residents. This variable is used as a proxy for average overall long run robustness and resilience of health of an average state citizen before the onset of COVID19.
10 LCD – natural log of CDC-reported state average mortality rate (deaths per 100,000 people) due to COVID19. It is important to note that, very unfortunately, this most critical variable in the model is reported to have a measurement uncertainty on the order of plus or minus 30% due to arbitrariness of criteria used to classify COVID19-associated deaths in the US. This variable is the dependent variable, that produced by the actions of the 9 independent or controlling variables.
The economic production function (or equation) used to estimate the relative effects of each apparently controlling variable on state level COVID19 is the Cobb-Douglas function. As an example, for a two controlling variable case, v1 and v2, the Cobb-Douglas function can be written as:
Q = Output or product = C*(v1)^a*(v2)^b
where C is a constant, v1 is independent/controlling variable 1, and v2 is independent/controlling variable 2. The exponent “a” is a constant whose value reflects the amount of change in v1 has on the amount of change in output or product (“Q”) produced by the system, while exponent “b” does the same thing for variable 2. As an example, if exponent “a” for v1 = 2, then a 10% increase in v1 would produce a 20% increase in output or product Q.
The same mathematical model can be used for any number of additional controlling variables just by adding variables and their exponents. This mathematical form is consistent with systems theory in that change in any one of the inputs and its exponent affects the output of the whole system.
Provided the data sample is reasonably accurate and contains enough cases, the values of the exponents for each controlling variable can be estimated quite easily by using ordinary least squares linear multi-variable regression software (e.g., Excel), as the log-transformed form of the equation is linear:
Ln(Q) = a*ln(v1) + b*ln(v2) + C. C is the error or residual term in the linear regression output.
As it will later be explained, it is important to note here that the exponents “a” and “b” cannot change in the Cobb-Douglas production model from one sample case to another. So, using this mathematical model in multivariable linear regression to estimate the relative importance of different controlling variables in producing some result (like the COVID19 mortality rate), tacitly assumes that the variable exponents are constant with any increases or decreases in the level of output whatsoever. This is an inaccurate assumption in many, if not most, natural systems, but it is a ‘good enough’, simplifying assumption for exploratory work.
A second assumption implicit in the use of the Cobb-Douglas model of production for this sort of exploratory analysis is that there are no complementary synergies among the controlling variables. That is, the mathematical assumption of the Cobb-Douglas model is that each variable or imput exerts influence on the product of the system (COVID19 mortality rate in this case) wholly independently of the influences from all other variables or inputs. This also, of course, is an inaccurate assumption in most natural systems.
Table I below shows regression results for the Cobb-Douglas model of the Lower state level mortality rate (e^LCD) for the Lower 48 States using the 9 controlling variables defined above:
According to this modeling work, the three most influential variables on state level COVID19 mortality rates are citizen average level of physical activity, frequency of vegetable eating in the diet, and the long run life expectancy of the people living in any given state. Increases of any of these three variables with negatively signed coefficients (Table “coefficients” = the exponents in the Cobbs-Douglas function), would have been expected to very significantly reduce the state’s COVID19 death rates. The state physical activity level coefficient of -4.74 indicates a 10% increase in the average physical activity level of the residents of a state would have resulted in an extremely significant 47.4% decrease in the state’s COVID19 mortality rate. A 10% increase in the background level of vegetable consumption in any given state population would be expected to reduce COVID19 death rates by 47.3%, and states with an established 10% greater life expectancy than another state would have been expected to experience about 31.9% less deaths from the virus than the other state.1
Other factors estimated to reduce COVID19 mortality rates include (surprisingly) obesity, craft beer and ale ingestion, lockdown measures, and soil zinc concentrations. Ten percent increases in the background state levels of these controlling variables would have been expected to reduce COVID19 mortality rates by 9.0%, 0.74%, 0.68%,2 and 0.06%, respectively. It’s notable that, according to Table I linear regression results, the life-preserving effects of pleasurably drinking craft brews slightly exceeded the similarly small benefits obtained by suffering through unpleasant lockdown measures.
The obesity result seems counterintuitive on first glance, but see previous comments and possible explanation provided here. Indeed, it seems altogether possible – given the high degree of infectiousness of the COVID19 viruses and the clear ineffectiveness of ‘masking’ in preventing viral spread – that the government lockdown measures did not gain their effectiveness by reduction of viral transmission but by the unintended ‘fattening’ of usually skinnier people made subject to the enforced inactivity consequent of lockdown regulations.
Two of the 9 controlling factors appear to have actually increased COVID19 mortality rates. These are state average fruit consumption level and latitude. A 10% increase in state level of fruit consumption frequency prior to and/or during the COVID19 event would have been expected to produce a 17.5% increase in COVID19 mortality, while a 10% increase in state average latitude of residence would have been expected to correspond to a 2.9% greater frequency in COVID19 mortality rate. These last two result reverse the earlier scatter plot interpretations reported elsewhere in this posting series because the effects of confounding variables that strongly co-vary with fruit consumption frequency and residential latitude have here been removed and accounted for by the least squares mathematical regression process. In the case of latitude, determinations made elsewhere on the basis of lesser sunshine exposure and vitamin D generation in people living at higher latitudes are consistent with modeling results reported here. In the case of fruit consumption, regression results are consistent with scientific observations regarding fruit sugar consumption, consequently increased inflammation, and poorer health results with COVID19 infection discussed in this paper.
Takeaways from the modeling work shown provided above are that future viral threats from COVID19 or other respiratory viruses are best met with individual habits of frequent vegetable eating and regular exercise >> maintaining or acquiring slight obesity and avoidance of fruit (fructose) consumption during viral infectious activity. Craft brew drinking and government shutdowns apparently conferred much less protection from the virus, while zinc supplementation seems to provide even less defense.
Additional Evidence that CDC-Reported COVID19 Mortality Rates are Inaccurate: the State Level Life Expectancy Modeling Comparison
The same Cobb-Douglas mathematical model was used to conduct ordinary least squares regression of the state level, actuarially-determined, average life expectancies (i.e., the variable LE above now functions as dependent variable “Q”) against the controlling variables of obesity (LOB), physical activity (LA), frequency of vegetable consumption (LVC), frequency of fruit consumption (LFC), residential latitude (LAT), soil zinc values (LZN), and level of craft brew consumption (LCBG). As you can see below in Table II from the much increased significance of each of the coefficients/exponents of the controlling variables in this predictive model of state average life expectancy, it was not the model specification (i.e., the choice of variables) or the accuracy of the variable values that caused the relatively poor prediction power (R-squared and adjusted R-squared values) of the Table I COVID19 mortality rate model. Rather, it was the imprecision and inaccuracy of the output or product measure of the CDC COVID19 mortality rates for the states that partially fouled the COVID19 death rate modeling work (GIGO).
According to the Table II modeling results, dietary and living habits have much less decisive and much less pronounced effects on life expectancy than they do on survival during such exigent events like viral invasion. You can see, by examining the coefficients in Table II, that four different variables – obesity, vegetable eating, zinc ingestion, and craft brew drinking – have slightly negative effects on state resident average life expectancy under normal, everyday (non-pandemic) conditions.
In contrast to the obesity-related finding in the Table I, obesity under long run normal conditions actually has a slightly negative effect on long run life expectancy. A 10% increase in average obesity of a state’s residents is predicted to cause a small 0.35% decrease in state average expected life expectancy. This finding is qualitatively consistent with conventional medical belief.
Surprisingly, a 10% increase in state population frequency of vegetable consumption is predicted to result in a 1.9% decrease in average life expectancy. Perhaps this small predicted decrease is a result of the presence of phytotoxins in many vegetable foods — especially those generally popular vegetables of the nightshade family like potatoes, tomatoes, and peppers. (Non-fruit-bearing plants ‘prefer’ not to be eaten by animals and produce poisons to discourage such activity.)
Both soil zinc values and craft brew drinking evidently exert even slighter negative effects on state population life expectancies. A 10% increase in zinc consumption and craft beer consumption are both predicted to result only in about a 0.02% reduction in state citizen average life expectancy.
According to the Table II model, increases in physical activity, fruit consumption, and residential latitude all are predicted to lead to small increases in average life expectancy. A 10% physical activity increase would be expected to generate a 0.79% average increase in life expectancy. A 10% percent residential latitude increase, on the other hand, is predicted to cause a 0.14% increase in longevity. Possibly this slight increase in longevity is related to the nightly increase in antioxidant melatonin generation consequent of longer flu season nights at higher latitudes.
The life expectancy data regression unexpectedly yielded a relatively high coefficient or exponent for fruit consumption. According to Table II, a 10% increase in average fruit consumption frequency would produce a 2.60% extension of average life expectancy. Given that fruits are rich in antioxidants and vitamins, and relatively poor in phytotoxins (fruit bearers, after all, ‘want’ animals to eat their seed-bearing fruits as a means of propagating their species), this surprising result could make sense – despite the evident acute health harm fruit-eating causes under disease infection conditions.
Apparent takeaway from this second model is that longevity is generally a harder needle to move by habit and dietary manipulation than is avoidance of abrupt death by infection using the same health management tools. Note here, however, the use of the word “apparent”. Successful application of a more advanced mathematical systems theory model for the life expectancy case, the translog3 production function, suggests that the exponents for certain variables that seem to increase and decrease longevity are considerably stronger than otherwise indicated by multivariable regression completed following the simple Cobb-Douglas systems model (Table II). These strikingly different results are believed to be the result of the removal of the implicit assumptions of lack of scalability and synergy (complementarity) associated with use of Cobb-Douglas-based multivariable linear regressions.
The analytical results of the translog model of Lower 48 state life expectancy will be provided in the next Grundvilk post. This translog model of the US human longevity system is not only considerably more predictive (higher R-squared value) than the Table II Cobbs-Douglas model, but its exponent/coefficient results are also much more promising and encouraging as far as carrying out the productive task of increasing both health-span and life-span is concerned.
Anyone interested in duplicating the regression analyses discussed here can contact the author for copies of the (messy) Excel files used by him in his regression work supporting this post. For original data sources, see the previous posts in this series, especially the scatter plots provided.
Showing that a strong, long run state of good physical health as indicated by life expectancy is like ‘money in the bank’ when human populations are exposed to external stressors like widespread virus infections.
See https://granitegrok.com/wp-content/uploads/2022/02/A-Literature-Review-and-Meta-Analysis-of-the-Effects-of-Lockdowns-on-COVID-19-Mortality.pdf. The incremental effectiveness of lockdowns in reducing COVID19 mortality indicated in Table I is of the same magnitude estimated in the John Hopkins report.
https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7976.1981.tb02155.x This advanced, potentially more useful model could not be applied to the COVID19 mortality rate case because of the inaccuracy of the CDC COVID19 mortality data. (I tried and tried, and got nothing but theoretically and numerically inconsistent garbage for my pains.)