The China Study again: A multivariate analysis suggesting that schistosomiasis rules!

In the comments section of Denise Minger’s post on July 16, 2010, which discusses some of the data from the China Study (as a follow up to a previous post on the same topic), Denise herself posted the data she used in her analysis. This data is from the China Study. So I decided to take a look at that data and do a couple of multivariate analyzes with it using WarpPLS (warppls.com).

First I built a model that explores relationships with the goal of testing the assumption that the consumption of animal protein causes colorectal cancer, via an intermediate effect on total cholesterol. I built the model with various hypothesized associations to explore several relationships simultaneously, including some commonsense ones. Including commonsense relationships is usually a good idea in exploratory multivariate analyses.

The model is shown on the graph below, with the results. (Click on it to enlarge. Use the "CRTL" and "+" keys to zoom in, and CRTL" and "-" to zoom out.) The arrows explore causative associations between variables. The variables are shown within ovals. The meaning of each variable is the following: aprotein = animal protein consumption; pprotein = plant protein consumption; cholest = total cholesterol; crcancer = colorectal cancer.

The path coefficients (indicated as beta coefficients) reflect the strength of the relationships; they are a bit like standard univariate (or Pearson) correlation coefficients, except that they take into consideration multivariate relationships (they control for competing effects on each variable). A negative beta means that the relationship is negative; i.e., an increase in a variable is associated with a decrease in the variable that it points to.

The P values indicate the statistical significance of the relationship; a P lower than 0.05 means a significant relationship (95 percent or higher likelihood that the relationship is real). The R-squared values reflect the percentage of explained variance for certain variables; the higher they are, the better the model fit with the data. Ignore the “(R)1i” below the variable names; it simply means that each of the variables is measured through a single indicator (or a single measure; that is, the variables are not latent variables).

I should note that the P values have been calculated using a nonparametric technique, a form of resampling called jackknifing, which does not require the assumption that the data is normally distributed to be met. This is good, because I checked the data, and it does not look like it is normally distributed. So what does the model above tell us? It tells us that:

- As animal protein consumption increases, colorectal cancer decreases, but not in a statistically significant way (beta=-0.13; P=0.11).

- As animal protein consumption increases, plant protein consumption decreases significantly (beta=-0.19; P<0.01). This is to be expected.

- As plant protein consumption increases, colorectal cancer increases significantly (beta=0.30; P=0.03). This is statistically significant because the P is lower than 0.05.

- As animal protein consumption increases, total cholesterol increases significantly (beta=0.20; P<0.01). No surprise here. And, by the way, the total cholesterol levels in this study are quite low; an overall increase in them would probably be healthy.

- As plant protein consumption increases, total cholesterol decreases significantly (beta=-0.23; P=0.02). No surprise here either, because plant protein consumption is negatively associated with animal protein consumption; and the latter tends to increase total cholesterol.

- As total cholesterol increases, colorectal cancer increases significantly (beta=0.45; P<0.01). Big surprise here!

Why the big surprise with the apparently strong relationship between total cholesterol and colorectal cancer? The reason is that it does not make sense, because animal protein consumption seems to increase total cholesterol (which we know it usually does), and yet animal protein consumption seems to decrease colorectal cancer.

When something like this happens in a multivariate analysis, it usually is due to the model not incorporating a variable that has important relationships with the other variables. In other words, the model is incomplete, hence the nonsensical results. As I said before in a previous post, relationships among variables that are implied by coefficients of association must also make sense.

Now, Denise pointed out that the missing variable here possibly is schistosomiasis infection. The dataset that she provided included that variable, even though there were some missing values (about 28 percent of the data for that variable was missing), so I added it to the model in a way that seems to make sense. The new model is shown on the graph below. In the model, schisto = schistosomiasis infection.

So what does this new, and more complete, model tell us? It tells us some of the things that the previous model told us, but a few new things, which make a lot more sense. Note that this model fits the data much better than the previous one, particularly regarding the overall effect on colorectal cancer, which is indicated by the high R-squared value for that variable (R-squared=0.73). Most notably, this new model tells us that:

- As schistosomiasis infection increases, colorectal cancer increases significantly (beta=0.83; P<0.01). This is a MUCH STRONGER relationship than the previous one between total cholesterol and colorectal cancer; even though some data on schistosomiasis infection for a few counties is missing (the relationship might have been even stronger with a complete dataset). And this strong relationship makes sense, because schistosomiasis infection is indeed associated with increased cancer rates. More information on schistosomiasis infections can be found here.

- Schistosomiasis infection has no significant relationship with these variables: animal protein consumption, plant protein consumption, or total cholesterol. This makes sense, as the infection is caused by a worm that is not normally present in plant or animal food, and the infection itself is not specifically associated with abnormalities that would lead one to expect major increases in total cholesterol.

- Animal protein consumption has no significant relationship with colorectal cancer. The beta here is very low, and negative (beta=-0.03).

- Plant protein consumption has no significant relationship with colorectal cancer. The beta for this association is positive and nontrivial (beta=0.15), but the P value is too high (P=0.20) for us to discard chance within the context of this dataset. A more targeted dataset, with data on specific plant foods (e.g., wheat-based foods), could yield different results – maybe more significant associations, maybe less significant.

Below is the plot showing the relationship between schistosomiasis infection and colorectal cancer. The values are standardized, which means that the zero on the horizontal axis is the mean of the schistosomiasis infection numbers in the dataset. The shape of the plot is the same as the one with the unstandardized data. As you can see, the data points are very close to a line, which suggests a very strong linear association.

So, in summary, this multivariate analysis vindicates pretty much everything that Denise said in her July 16, 2010 post. It even supports Denise’s warning about jumping to conclusions too early regarding the possible relationship between wheat consumption and colorectal cancer (previously highlighted by a univariate analysis). Not that those conclusions are wrong; they may well be correct.

This multivariate analysis also supports Dr. Campbell’s assertion about the quality of the China Study data. The data that I analyzed was already grouped by county, so the sample size (65 cases) was not so high as to cast doubt on P values. (Having said that, small samples create problems of their own, such as low statistical power and an increase in the likelihood of error-induced bias.) The results summarized in this post also make sense in light of past empirical research.

It is very good data; data that needs to be properly analyzed!

What is a reasonable vitamin D level?

The figure and table below are from Vieth (1999); one of the most widely cited articles on vitamin D. The figure shows the gradual increase in blood concentrations of 25-Hydroxyvitamin, or 25(OH)D, following the start of daily vitamin D3 supplementation of 10,000 IU/day. The table shows the average levels for people living and/or working in sun-rich environments; vitamin D3 is produced by the skin based on sun exposure.

25(OH)D is also referred to as calcidiol. It is a pre-hormone that is produced by the liver based on vitamin D3. To convert from nmol/L to ng/mL, divide by 2.496. The figure suggests that levels start to plateau at around 1 month after the beginning of supplementation, reaching a point of saturation after 2-3 months. Without supplementation or sunlight exposure, levels should go down at a comparable rate. The maximum average level shown on the table is 163 nmol/L (65 ng/mL), and refers to a sample of lifeguards.

From the figure we can infer that people on average will plateau at approximately 130 nmol/L, after months of 10,000 IU/d supplementation. That is 52 ng/mL. Assuming a normal distribution with a standard deviation of about 20 percent of the range of average levels, we can expect about 68 percent of those taking that level of supplementation to be in the 42 to 63 ng/mL range.

This might be the range most of us should expect to be in at an intake of 10,000 IU/d. This is the equivalent to the body’s own natural production through sun exposure.

Approximately 32 percent of the population can be expected to be outside this range. A person who is two standard deviations (SDs) above the mean (i.e., average) would be at around 73 ng/mL. Three SDs above the mean would be 83 ng/mL. Two SDs below the mean would be 31 ng/mL.

There are other factors that may affect levels. For example, being overweight tends to reduce them. Excess cortisol production, from stress, may also reduce them.

Supplementing beyond 10,000 IU/d to reach levels much higher than those in the range of 42 to 63 ng/mL may not be optimal. Interestingly, one cannot overdose through sun exposure, and the idea that people do not produce vitamin D3 after 40 years of age is a myth.

One would be taking in about 14,000 IU/d of vitamin D3 by combining sun exposure with a supplemental dose of 4,000 IU/d. Clear signs of toxicity may not occur until one reaches 50,000 IU/d. Still, one may develop other complications, such as kidney stones, at levels significantly above 10,000 IU/d.

Chris Masterjohn has made a different argument, with somewhat similar conclusions. Chris pointed out that there is a point of saturation above which the liver is unable to properly hydroxylate vitamin D3 to produce 25(OH)D.

How likely it is that a person will develop complications like kidney stones at levels above 10,000 IU/d, and what the danger threshold level could be, are hard to guess. Kidney stone incidence is a sensitive measure of possible problems; but it is, by itself, an unreliable measure. The reason is that it is caused by factors that are correlated with high levels of vitamin D, where those levels may not be the problem.

There is some evidence that kidney stones are associated with living in sunny regions. This is not, in my view, due to high levels of vitamin D3 production from sunlight. Kidney stones are also associated with chronic dehydration, and populations living in sunny regions may be at a higher than average risk of chronic dehydration. This is particularly true for sunny regions that are also very hot and/or dry.

Reference

Vieth, R. (1999). Vitamin D supplementation, 25-hydroxyvitamin D concentrations, and safety. American Journal of Clinical Nutrition, 69(5), 842-856.

The lowest-mortality BMI: What is the role of nutrient intake from food?

In a previous post (), I discussed the frequently reported lowest-mortality body mass index (BMI), which is about 26. The empirical results reviewed in that post suggest that fat-free mass plays an important role in that context. Keep in mind that this "BMI=26 phenomenon" is often reported in studies of populations from developed countries, which are likely to be relatively sedentary. This is important for the point made in this post.

A lowest-mortality BMI of 26 is somehow at odds with the fact that many healthy and/or long-living populations have much lower BMIs. You can clearly see this in the distribution of BMIs among males in Kitava and Sweden shown in the graph below, from a study by Lindeberg and colleagues (). This distribution is shifted in such a way that would suggest a much lower BMI of lowest-mortality among the Kitavans, assuming a U-curve shape similar to that observed in studies of populations from developed countries ().

Another relevant example comes from the China Study II (see, e.g., ), which is based on data from 8000 adults. The average BMI in the China Study II dataset, with data from the 1980s, is approximately 21; for an average weight that is about 116 lbs. That BMI is relatively uniform across Chinese counties, including those with the lowest mortality rates. No county has an average BMI that is 26; not even close. This also supports the idea that Chinese people were, at least during that period, relatively thin.

Now take a look at the graph below, also based on the China Study II dataset, from a previous post (), relating total daily calorie intake with longevity. I should note that the relationship between total daily calorie intake and longevity depicted in this graph is not really statistically significant. Still, the highest longevity seems to be in the second tercile of total daily calorie intake.

Again, the average weight in the dataset is about 116 lbs. A conservative estimate of the number of calories needed to maintain this weight without any physical activity would be about 1740. Add about 700 calories to that, for a reasonable and healthy level of physical activity, and you get 2440 calories needed daily for weight maintenance. That is right in the middle of the second tercile, the one with the highest longevity.

What does this have to do with the lowest-mortality BMI of 26 from studies of samples from developed countries? Populations in these countries are likely to be relatively sedentary, at least on average, in which case a low BMI will be associated with a low total calorie intake. And a low total calorie intake will lead to a low intake of nutrients needed by the body to fight disease.

And don’t think you can fix this problem by consuming lots of vitamin and mineral pills. When I refer here to a higher or lower nutrient intake, I am not talking only about micronutrients, but also about macronutrients (fatty and amino acids) in amounts that are needed by your body. Moreover, important micronutrients, such as fat-soluble vitamins, cannot be properly absorbed without certain macronutrients, such as fat.

Industrial nutrient isolation for supplementation use has not been a very successful long-term strategy for health optimization (). On the other hand, this type of supplementation has indeed been found to have had modest-to-significant success in short-term interventions aimed at correcting acute health problems caused by severe nutritional deficiencies ().

So the "BMI=26 phenomenon" may be a reflection not of a direct effect of high muscularity on health, but of an indirect effect mediated by a high intake of needed nutrients among sedentary folks. This may be so even though the lowest mortality is for the combination of that BMI with a relatively small waist (), which suggests some level of muscularity, but not necessarily serious bodybuilder-level muscularity. High muscularity, of the serious bodybuilder type, is not very common; at least not enough to significantly sway results based on the analysis of large samples.

The combination of a BMI=26 with a relatively small waist is indicative of more muscle and less body fat. Having more muscle and less body fat has an advantage that is rarely discussed. It allows for a higher total calorie intake, and thus a higher nutrient intake, without an unhealthy increase in body fat. Muscle mass increases one's caloric requirement for weight maintenance, more so than body fat. Body fat also increases that caloric requirement, but it also acts like an organ, secreting a number of hormones into the bloodstream, and becoming pro-inflammatory in an unhealthy way above a certain level.

Clearly having a low body fat percentage is associated with lower incidence of degenerative diseases, but it will likely lead to a lower intake of nutrients relative to one’s needs unless other factors are present, e.g., being fairly muscular or physically active. Chronic low nutrient intake tends to get people closer to the afterlife like nothing else ().

In this sense, having a BMI=26 and being relatively sedentary (without being skinny-fat) has an effect that is similar to that of having a BMI=21 and being fairly physically active. Both would lead to consumption of more calories for weight maintenance, and thus more nutrients, as long as nutritious foods are eaten.

Looking for a good orthodontist? My recommendation is Dr. Meat

The figure below is one of many in Weston Price’s outstanding book Nutrition and Physical Degeneration showing evidence of teeth crowding among children whose parents moved from a traditional diet of minimally processed foods to a Westernized diet. ()

Tooth crowding and other forms of malocclusion are widespread and on the rise in populations that have adopted Westernized diets (most of us). Some blame it on dental caries, particularly in early childhood; dental caries are also a hallmark of Westernized diets. Varrela, however, in a study of Finnish skulls from the 15th and 16th centuries found evidence of dental caries, but not of malocclusion, which Varrela reported as fairly high in modern Finns. ()

Why does malocclusion occur at all in the context of Westernized diets? Lombardi () put forth an evolutionary hypothesis:

“In modern man there is little attrition of the teeth because of a soft, processed diet; this can result in dental crowding and impaction of the third molars. It is postulated that the tooth-jaw size discrepancy apparent in modern man as dental crowding is, in primitive man, a crucial biologic adaptation imposed by the selection pressures of a demanding diet that maintains sufficient chewing surface area for long-term survival. Selection pressures for teeth large enough to withstand a rigorous diet have been relaxed only recently in advanced populations, and the slow pace of evolutionary change has not yet brought the teeth and jaws into harmonious relationship.”

So what is one to do? Apparently getting babies to eat meat is not a bad idea (). They may well just chew on it for a while and spit it out. The likelihood of meat inducing dental caries is very low, as most low carbers can attest. (In fact, low carbers who eat mostly meat often see dental caries heal.)

Concerned about the baby choking on meat? See this Google search for “baby choked on meat”: (). Now, see this Google search for “baby choked on milk”: ().

What if you have a child with crowded teeth as a preteen or teen? Too late? Should you get him or her to use “cute” braces? Our daughter had crowded teeth as a preteen. It overlapped with the period of my transformation (), which meant that she started having a lot more natural foods to eat. There were more of those around, some of which require serious chewing, and less industrialized soft foods. Those natural foods included hard-to-chew beef cuts, served multiple times a week.

We noticed improvement right away, and in a few years the crowding disappeared. Soon she had the kind of smile that could land her a job as a toothpaste model:

The key seems to be to start early, in developmental years. If you are an adult with crowded teeth, malocclusion may not be solved by either tough foods or braces. With braces, you may even end up with other problems ().

We share an ancestor who probably lived no more than 640 years ago

We all evolved from one single-celled organism that lived billions of years ago. I don’t see why this is so hard for some people to believe, given that all of us also developed from a single fertilized cell in just 9 months.

However, our most recent common ancestor is not that first single-celled organism, nor is it the first Homo sapiens, or even the first Cro-Magnon.

The majority of the people who read this blog probably share a common ancestor who lived no more than 640 years ago. Genealogical records often reveal interesting connections - the figure below has been cropped from a larger one from Pinterest.

You and I, whoever you are, have each two parents. Each of our parents have (or had) two parents, who themselves had two parents. And so on.

If we keep going back in time, and assume that you and I do not share a common ancestor, there will be a point where the theoretical world population would have to be impossibly large.

Assuming a new generation coming up every 20 years, and going backwards in time, we get a theoretical population chart like the one below. The theoretical population grows in an exponential, or geometric, fashion.

As we move back in time the bars go up in size. Beyond a certain point their sizes go up so fast that you have to segment the chart. Otherwise the bars on the left side of the chart disappear in comparison to the ones on the right side (as several did on the chart above). Below is the section of the chart going back to the year 1371.

The year 1371 is a little more than 640 years ago. (This post is revised from another dated a few years ago, hence the number 640.) And what is the theoretical population in that year if we assume that you and I have no common ancestors? The answer is: more than 8.5 billion people. We know that is not true.

Admittedly this is a somewhat simplistic view of this phenomenon, used here primarily to make a point. For example, it is possible that a population of humans became isolated 15 thousand years ago, remained isolated to the present day, and that one of their descendants just happened to be around reading this blog today.

Perhaps the most widely cited article discussing this idea is this one by Joseph T. Chang, published in the journal Advances in Applied Probability. For a more accessible introduction to the idea, see this article by Joe Kissell.

Estimates vary based on the portion of the population considered. There are also assumptions that have to be made based on migration and mating patterns, as well as the time for each generation to emerge and the stability of that number over time.

Still, most people alive today share a common ancestor who lived a lot more recently than they think. In most cases that common ancestor probably lived less than 640 years ago.

And who was that common ancestor? That person was probably a man who, due to a high perceived social status, had many consorts, who gave birth to many children. Someone like Genghis Khan.

The Friedewald and Iranian equations: Fasting triglycerides can seriously distort calculated LDL

Standard lipid profiles provide LDL cholesterol measures based on equations that usually have the following as their inputs (or independent variables): total cholesterol, HDL cholesterol, and triglycerides.

Yes, LDL cholesterol is not measured directly in standard lipid profile tests! This is indeed surprising, since cholesterol-lowering drugs with negative side effects are usually prescribed based on estimated (or "fictitious") LDL cholesterol levels.

The most common of these equations is the Friedewald equation. Through the Friedewald equation, LDL cholesterol is calculated as follows (where TC = total cholesterol, and TG = triglycerides). The inputs and result are in mg/dl.

    LDL = TC – HDL – TG / 5

Here is one of the problems with the Friedewald equation. Let us assume that an individual has the following lipid profile numbers: TC = 200, HDL = 50, and TG = 150. The calculated LDL will be 120. Let us assume that this same individual reduces triglycerides to 50, from the previous 150, keeping all of the other measures constant with except of HDL, which goes up a bit to compensate for the small loss in total cholesterol associated with the decrease in triglycerides (there is always some loss, because the main carrier of triglycerides, VLDL, also carries some cholesterol). This would normally be seen as an improvement. However, the calculated LDL will now be 140, and a doctor will tell this person to consider taking statins!

There is evidence that, for individuals with low fasting triglycerides, a more precise equation is one that has come to be known as the “Iranian equation”. The equation has been proposed by Iranian researchers in an article published in the Archives of Iranian Medicine (Ahmadi et al., 2008), hence its nickname. Through the Iranian equation, LDL is calculated as follows. Again, the inputs and result are in mg/dl.

    LDL = TC / 1.19 + TG / 1.9 – HDL / 1.1 – 38

The Iranian equation is based on linear regression modeling, which is a good sign, although I would have liked it even better if it was based on nonlinear regression modeling. The reason is that relationships between variables describing health-related phenomena are often nonlinear, leading to biased linear estimations. With a good nonlinear analysis algorithm, a linear relationship will also be captured; that is, the “curve” that describes the relationship will default to a line if the relationship is truly linear (see: warppls.com).

The Iranian equation yields high values of LDL cholesterol when triglycerides are high; much higher than those generated by the Friedewald equation. If those are not overestimations (and there is some evidence that, if they are, it is not by much), they describe an alarming metabolic pattern, because high triglycerides are associated with small-dense LDL particles. These particles are the most potentially atherogenic of the LDL particles, in the presence of other factors such as chronic inflammation.

In other words, the Iranian equation gives a clearer idea than the Friedewald equation about the negative health effects of high triglycerides. You need a large number of small-dense LDL particles to carry a high amount of LDL cholesterol.

An even more precise measure of LDL particle configuration is the VAP test; this post has a discussion of a sample VAP test report.

Reference:

Ahmadi SA, Boroumand MA, Gohari-Moghaddam K, Tajik P, Dibaj SM. (2008). The impact of low serum triglyceride on LDL-cholesterol estimation. Archives of Iranian Medicine, 11(3), 318-21.

Do prominent health gurus live longer?

Many years ago, when I started blogging about health issues, I noticed a couple of interesting patterns. The first pattern is that prominent health “gurus” often talk about having had serious health problems in their past, which they describe as having motivated them to do research on health issues – and thus become health gurus. Frequently these problems pop up before 45 years of age; this is a threshold beyond which there is a clearly noticeable increase in severity of health problems.

In fact, I remember being somewhat surprised by one such “guru” (I will not name him), who would regularly write posts saying something to the effect that “… finally, my health is now on the right track …” In other words, every few months or so this person had to deal with serious health problems, always coming up with reasonable knowledge-based solutions. The knowledge seemed to be of good quality, but this guy’s health was poor to say the least.

The second pattern, related to the above, is that prominent health gurus seem to have a below average life expectancy. The life expectancy for the general population is around 79 years of age in the USA at the time of this writing, according to the World Health Organization (). Anthony Colpo has written an interesting post about this below average life expectancy pattern among health gurus ().

To better understand and illustrate this situation to our blog’s readers, I created a dataset with 100 records, corresponding to 100 health gurus, with various variables interacting in ways that reflect the above observations. The observations are summarized as assumptions, listed later. The following variables are on a scale from 1 to 7; in real life they would have been measured retrospectively, looking back at a guru’s entire life:

- The guru's health before age 45 (BEF45).

- The guru's knowledge about health issues (KNOWL).

- The guru's health after age 45 (AFT45).

- The guru's prominence (GPROM).

Finally, the variable below is on a continuous scale of years, with an average of 79 and a standard deviation of 10. As mentioned earlier, 79 is the life expectancy for someone living in the USA at the time of this writing. The standard deviation of 10, which approximates that figure in the USA, means that approximately 68 percent of the individuals in the simulated dataset will have a life expectancy between 69 and 89. That is 79-10 and 79+10, respectively.

- The guru's age at the time of death (GAGED).

This experimental exercise with simulated data can be seen as a simulation “game”, where various variables interact to generate results that are not obvious. A widely used process to create data is known as the Monte Carlo method (), which is what we used here. I also made the following assumptions in the data creation process:

- That the poorer is the guru's health before age 45 (BEF45), the greater is the guru's knowledge about health issues (KNOWL). The reason for this is that poor health compels the person to study about health issues.

- That the poorer is the guru's health before age 45 (BEF45), the poorer is the guru's health after age 45 (AFT45). This assumes that the person has an underlying condition that causes the poor health in the first place, and that can be exacerbated by a poor diet and lifestyle.

- That the greater is the guru's knowledge about health issues (KNOWL), the better is the guru's health after age 45 (AFT45). This counteracts the effect above, and assumes that the knowledge is put to good use and contributes to improving the person’s health.

- That the greater is the guru's knowledge about health issues (KNOWL), the greater is also the guru's prominence (GPROM). In other words, a guru’s status among followers is enhanced by the guru’s knowledge.

- That the better is the guru's health after age 45 (AFT45), the higher is the guru's age at the time of death (GAGED).

A final assumption made is that the causal relationships laid out above have a small effect size (more technically, that they are associated with f-squared coefficients slightly below 0.1), meaning that random influences are not only present but also play a big role in what happens in the simulation. The causality links are summarized in the graph below, created with WarpPLS (). We also used this software to analyze the data.

Note that in our simulated data the guru's prominence (GPROM) does not directly influence the guru's age at the time of death (GAGED). Stated differently, there is no causality link between GPROM and GAGED, one way or the other, even though these two variables are likely to be correlated due to the network of causality links in which they exist. Nevertheless, it is by looking at the relationship between these two variables, GPROM and GAGED, that we can answer the question in the title of this post: Do prominent health gurus live longer?

And the answer appears to be “no” in our simulation. The plot below shows the relationship between a guru's prominence (GPROM), on the horizontal axis, and the guru's age at the time of death (GAGED), on the vertical axis. Each data point refers to a guru. On average, the greater a guru's prominence, the lower seems to be the guru’s life expectancy. Each one-point increase in prominence is associated, on average, with approximately a one-year decrease in life expectancy.

Note that there is one very prominent guru whose age at the time of death was around 95; the data point at the top-right corner (GPROM=7, GAGED~95). This happened largely by chance in our data. Nevertheless, assuming that our data somewhat reflects what could happen in real life, the followers of the guru would probably point at that longevity as being caused by the guru’s knowledge about health issues. They would likely be wrong.

Our dataset also allows us to estimate the probability that a fairly prominent guru (GPROM greater than 4, on a 1-7 scale) would have a below average life expectancy (GAGED lower than 79). That conditional probability would be approximately 60 percent.