Heterogeneity

The Social Science Statistics Blog has an interesting entry today on heterogeneity in observational studies. Below is an excerpt:

"Imagine you are asked to conduct an observational study to estimate the effect of wearing a helmet on the risk of death in motorcycle crashes. You have to choose one of two different data-sets for this study: Either a large, rather heterogeneous sample of crashes (these happened on different roads, at different speeds, etc.) or a smaller, more homogeneous sample of crashes (let's say they all occurred on the same road). Your goal is to unearth a trustworthy estimate of the treatment effect that is as close as possible to the `truth', i.e. the effect estimate obtained from an (unethical) experimental study on the same subject. Which sample do you prefer?

Naturally, most people tend to choose the large sample. Larger sample, smaller standard error, less uncertainty, better inference…we’ve heard it all before. Interestingly, in a recent paper entitled "Heterogeneity and Causality: Unit Heterogeneity and Design Sensitivity in Observational Studies" Paul Rosenbaum comes to the opposite conclusion. He demonstrates that heterogeneity, and not sample size matters for the sensitivity of your inference to hidden bias (a topic we blogged about previously here and here). He concludes that:

“In observational studies, reducing heterogeneity reduces both sampling variability and sensitivity to unobserved bias—with less heterogeneity, larger biases would need to be present to explain away the same effect. In contrast, increasing the sample size reduces sampling variability, which is, of course useful, but it does little to reduce concerns about unobserved bias.”

...

Now you may say: well it all depends on the estimand, no? Do I care about the effect of helmets in the US as a whole or only on a single road? This point is well taken, but keep in mind that for causal inference from observational data we often care about internal validity first and not necessarily generalizability (most experiments are also done on highly selective groups). ...

So finally back to the helmet example. Rosenbaum cites an observational study that deals with the heterogeneity issue in a clever way: “Different crashes occur on different motorcycles, at different speeds, with different forces, on highways or country roads, in dense or light traffic, encountering deer or Hummers. One would like to compare two people, one with a helmet, the other without, on the same type of motorcycle, riding at the same speed, on the same road, in the same traffic, crashing into the same object. Is this possible? It is when two people ride the same motorcycle, a driver and a passenger, one helmeted, the other not. Using data from the Fatality Analysis Reporting System, Norvell and Cummings (2002) performed such a matched pair analysis using a conditional model with numerous pair parameters, estimating approximately a 40% reduction in risk associated with helmet use.”

Type I and II Error Movie

Here is an old silent movie describing Type I and Type II errors.

High Octane Gasoline

Scientific American: Fact or Fiction?: Premium Gasoline Delivers Premium Benefits to Your Car
Exploding the myth that premium gasoline delivers better performance in the average automobile

Positional Goods

Economist discuss positional goods, which are goods that are in fixed supply. People can only enjoy these goods if others do not. Some examples include the best education, best jobs, and best home locations.

Positional goods for previous generations have become commonplace for this generation. For example, having central air conditioning was maybe a positional good 40 years ago. However, air conditioning is now much more common (at least in the United States). So luxuries of years ago are becoming necessities in the present.

Gregg Easterbrook in his book, 'The Progress Paradox' describes a paradox in which or standard of living has improved greatly, while our levels of happiness have stayed about the same. Maybe this paradox can be partly explained by the wanting of positional goods. As soon as enough people have attained positional goods, the goods no longer provide the satisfaction they used to provide. Thus, new items become positional goods and people strive for these new positional items (while their overall happiness remains unchanged).

Student and Guinness

In the beginning of the 20th century, the Guinness Brewing Company made an innovative move that changed the world of statistics. They hired William Gosset, a mathematician and chemist (they actually hired him for his chemistry skills, but it was his mathematical abilities that changed the field of statistics).

One of his first contributions to the Guinness Company was in the process of measuring the number of yeast cells that needed to be added to ferment the mash to make beer. Too much yeast led to bitter beer and too little led to incomplete fermentation. Prior to his techniques, people would try to count the number of yeast cells in a sample under the microscope. Gosset determined that the cells could be modeled with a probability distribution. Guiness was then able to able to more accurately measure how much yeast to use based on Gosset’s probability functions.

Guiness had a strict rule about publishing results in scientific journals (so company secrets would not be given away). Karl Pearson, the editor of Biometrika, worked out a deal with Gosset to publish his papers under the name, Student. Over the next thirty years, Student wrote many influential papers on statistical topics. One of the most famous papers, was on comparing small samples. This statistical test is know known as the Student’s t-test and is one of the most widely used tests.

Gosset was able to keep his identity secret for many years. One story suggests that when the Guiness family first found out about Gosset’s secret identity, Gosset died of a sudden heart attack.

Guiness chemist by day, Super Statistician by night. A statistical Clark Kent?

Nonlinear Science

The Mahalanobis Blog has an interesting comment on nonlinear relations (the blog is actually on a much different topic). His example is uses a straight line to describe a relationship, when the relationship is much more complicated. Rather than summarizing it, here is an excerpt:

"An analogous scientific consensus was the belief that nuclear testing caused millions of cancer deaths, popularized by scientific heavyweight Linus Pauling. High levels of radiation will certainly kill you, and lower levels will harm you. Linus Pauling calculated the damage at minuscule levels by extending that graph back in a straight line to zero. Zero radiation, obviously, causes no harm. At low levels not many would be harmed, but multiplying that low level by the population of the world, as Pauling did, allowed him to claim that continued nuclear testing would kill millions of children. So it should be stopped. Pauling organized a petition against nuclear testing signed by 11,000 scientists and presented to the United Nations, for which he won the Nobel Peace Prize (to add to his Nobel in chemistry). It was all science and logic. Naysayers were anti-scientific ideologues. But with poisons dosage is key, and highly nonlinear. The graph of radiation mortality does not go straight back to zero. It goes down to about 700 millirems a day, then heads back up again, like a hook. Low background levels of radiation seem to be good for you. The evidence that the "linear extrapolation to zero" is wrong, in that while bad for you in large doses, radiation does some good in small doses. It seems to keep the DNA repair mechanisms in good working order. The same principle is observed with alcohol, a potential poison: heavy drinking will kill you, but a glass of wine a day is good for you.

Theories that are really compelling are often wrong, because all theories are simplifications to a more complicated reality. So the fact that 90% of the population believe X causes Y and can be fixed by Z makes me highly skeptical. When in history has something complicated, true, and important, been so agreed upon prior to definitive evidence? It suggests the facts have little to do with it."

Free Software

Softwarefor.org has made a compilation download of free software for students. The software is for Windows and Mac operating systems.

One of the most important pieces are Openoffice.org's suite of office applications. These programs are very similar to Microsoft Office and for the most part completely compatible with Microsoft Office.

Another great piece of free software is R. R is statistical software that is similar to the S-Plus programming language.

Latex is a typesetting program that is used by many scientist. It is a very powerful language for typesetting.

StatTalk Part 3

I have recently found a replacement for the StatTalk podcasts. It is the StatTalk Blog. I am (honestly) extremely excited.

Fairness

A paper recently appeared in the December issue of Notices of the American Mathematical Society, entitled "Better Ways to Cut a Cake." Science News has an interesting review of this article describing how people can split cake. Here is an excerpt:

a division is fair if, after it's made, each person's assessment of the value of his or her piece is the same...The classic way for two people to share a cake without argument is known as "I cut, you choose." To divide an elaborately decorated sheet cake strewn with nuts and coconut, I'd cut the cake into two pieces that seem to me to be of equal value, though not necessarily equal size. If I particularly like nuts, for example, I would divide the cake into unequal pieces, the smaller piece getting more nuts, to make sure that I'm satisfied with whichever slice remains after you've made your choice.

Scientific American also has an article describing this research. Here is a quote that sums the research: "under special circumstances, two people can split something up and both feel like they got more than half."

Health Guarantees and Risk Reduction

Christopher Wanjek, a writer for Livescience.com has an interesting article on risk reduction in health outcomes. Here is an excerpt:
"Risks are established in health studies. For example, doctors will study thousands of patients with circulatory disease and look for commonality. They find that many of these patients have high levels of a certain kind of cholesterol or fatty acid in their blood, have high blood pressure, or smoke. Through medication or lifestyle change, a patient can lower these risks but never eliminate them. Conversely, these risks are merely known indicators; the absence of these indicators doesn't mean disease won't develop. Risk reduction is the essence of public health. The message goes out to stop smoking, to eat more vegetables and to exercise more in order to reduce risks across the entire population. Nationwide, the rate of circulatory disease will fall. But that doesn't mean you won't get it if you follow the marching orders. For example, most adults with diabetes are overweight. So, sure, lose weight. But skinny people do get diabetes."

StatTalk Part 2

Earlier I wrote about a great Podcast from the UCLA Statistical Consulting Group. Unfortunately, they have not made any new podcasts in some time. I would like to urge a write-in campaign so that they know they are missed. You can write them at StatTalk@ ats.ucla.edu.

Grades, Performance, and Poop

Tim Harford write an excellent column for Slate.com (He also has a great book). In this column, he discusses how a person in charge of providing incentives determines what good performance is. In his example, he discusses determining his daughter's performance in using the toilet. I find the difficulty of determining performance to be very similar to how professors deal with determining grades. Here is an excerpt:

"She has the capacity to use the potty, so all that is now required is the right incentive. Chocolate coins turn out to be the sort of currency a 2-year-old understands. Successful use of the potty earns a chocolate coin. It works, and is money well spent.

Yet two days into the contract, problems are emerging. What is "successful use of the potty"? This morning, my nose alerted me to a borderline case: an enormous turd on the sitting room floor, and a tiny rabbit-dropping in the potty. At this early stage, we chose to accentuate (and reward) the positive. In a month's time, I will be less impressed, but can we really move the goal posts then?

Even straightforward incentives can be manipulated. The great pole-vaulter Sergei Bubka repeatedly broke the world record by a centimeter and earned a cash bonus every time. I have visions of a near future in which Miss Harford empties her bladder one drop at a time in order to scoop bagfuls of chocolate coins.

As we are discovering, apparently black-and-white matters of performance can quickly become shades of gray. It is much more tempting to resort to discretion: If we're happy with Miss Harford's potty performance, chocolate coins will be forthcoming.

This sounds a bit like your boss's vague promise of a salary review sometime the year after next. Employees know that bosses are lying weasels and wisely ignore such empty gestures. Daughters know that parents are lying weasels too, and that is why we must keep our incentive payments as unambiguous as possible.

Employers want to offer incentives for good behavior, just as parents do. But how to combine the oh-so-important discretion with the credibility needed to make the promises persuasive?

One possibility is to rely on relative performance. The boss can announce that the best three performers in the office will receive a $1,000 bonus at the end of the year. There is no weaseling out of such a promise, and there is no incentive to give the bonus to bad workers instead of good ones, but the boss retains the flexibility to decide what a good performance actually means."

Higher Oil Prices Making People Skinnier

The Freakonomics Blog has an interesting scientific question:

"Will the High Price of Oil Make Americans Skinnier?
Not because higher gas prices will spur people to walk or ride bicycles instead of driving. No, I’m thinking it might work like this:

– Notwithstanding the recent drop, high oil prices have driven a demand for ethanol made from corn.

– Accordingly, the price of corn is rising fast, with July contracts at $4/bushel, about 60 percent higher than last summer.

– With corn so much more expensive, food manufacturers who use corn in so many forms in so many foods will look for substitutes. As the writer Michael Pollan puts it, “Corn is the keystone species of the industrial food system… If you are what you eat, and especially if you eat industrial food, as 99 percent of Americans do, what you are is corn.”

– Because corn was so cheap for so long, high-fructose corn syrup has become a common substitute for cane sugar. Pollan and others have argued that corn syrup is a great contributor to national obesity.

– Already, one boutique soda company has trumpeted its return to using cane sugar instead of corn syrup. “It’s better for you, it’s better-tasting and, overall, it’s better for the environment,” says the CEO of Jones Soda.

So, as higher oil prices continue to drive demand for corn-based ethanol, which drives the price of corn higher, which makes cheap corn syrup more expensive, which leads food manufacturers to seek out potentially less fattening sweeteners, will American get skinnier?"

Milk Decreasing the Benefits of Tea Use

Researchers have found that the addition of milk reduces the benefits of tea in an experiment. The researchers investigated the effect of blood flow in arteries using ultrasound. This measurement of artery functioning is thought to be related to long-term heart disease. This experiment is a prime example of an interaction. That is, milk interacts with tea to attenuate the artery functioning.

(Reuters News has an article describing the research if the above article is unaccessible.)

Things You Never Knew You Wanted

Gregg Easterbrook's book, the Progress Paradox discusses how our living standards have improved greatly, but out levels of happiness have stayed the same.

Many economists and psychologists are now trying to measure happiness and look at determinants of happiness. A great book from a psychologist's perspective is Daniel Gilbert's "Stumbling on Happiness."

The Economist discusses this paradox in the following quote:

"Capitalism, it notes, is adept at turning luxuries into necessities--bringing to the masses what the elites have always enjoyed. But the flip side of this genius is that people come to take for granted things they once coveted from afar. Frills they never thought they could have become essentials that the cannot do without"

Scientific American Skeptic: Is religion good for society?

Scientific American: Bowling for God
Is religion good for society? Science's definitive answer: it depends

Monkey Troops

From the Dec 19 edition of The Economist:

"Tyler Cowen of George Mason University points out that America has more than 3,000 halls of fame, honouring everyone from rock stars and sportsmen to dog mushers, pickle-packers, and accountants. In such a society, everyone can hope to come top of his particular monkey troop, even as the people he looks down on count themselves top of a subtly different troop."

Rental Car Upgrades

Today I rented a car. I reserved a subcompact because I generally like small cars and I am rather thrifty (wanting to spend less on gas). However, at the Avis counter, I was told that my reservation was upgraded. I found that upgrade meant they were giving me a Lincoln Towncar. Not wanting to drive this big of a car, I asked for a different vehicle. I was told there were no small cars and that my only other option was a SUV or a convertible. I took the convertible thinking it would be smaller and cheaper on gas. The convertible is a Ford Mustang (MPG 18 to 25). Now I know that I am probably lucky to be driving this 'American Classic' that I will never own, but I feel that their 'upgrade' is really a downgrade when it comes to my preference.

I remember reading a comment on the Freakonomics Blog on how the car companies are having a difficult time selling their gas inefficient cars. Thus, they have given rental companies good deals on them. The rental car company can provide consumers with 'upgrades', but in actuality the consumer is getting a car that the average car buyer does not want (because it is gas inefficient).

Folate and Distortion of Science

MSNBC.com has an article titled "Could low-carb diets lead to birth defects?" The interesting thing about the article is that it is lack of folate that can lead to birth defects. Many breads and cereals are fortified with folate. Thus, if you are a pregnant woman who does not eat folate fortified foods then birth defects could arise.

However, there is no study saying that low-carb diets lead to more birth defects. Someone made a speculation and MSNBC used that speculation as a headline. Might it be better if they highlighted that pregnant woman need to get their folate (especially those not eating folate fortified foods)?

Diagnoses

Wired Magazine has an interesting article titled: "The Thin Pill. How Big Pharma turned obesity into a disease – then invented the drugs to cure it."

Here is an excerpt:

"Metabolic syndrome is characterized by five risk factors: high blood pressure, high blood sugar, high triglycerides (fatty acids in the bloodstream), low HDL ("good") cholesterol, and obesity. Of the five, obesity – which is itself often referred to as an epidemic – is the most important, because the rise of the morbidly overweight is directly driving the rise in the syndrome. Metabolic syndrome is, in fact, almost indistinguishable from obesity – at least 85 percent of those who have the syndrome are obese or overweight.

The tidiness of that correlation makes it tempting to view metabolic syndrome not as an emerging fact of medicine, but as a fiction, wholly devised and disseminated by the pharmaceutical industry. After all, drug companies have long eyed obesity as the ultimate growth market – and they just happen to have an arsenal of pills poised to target it. Such cynicism isn't misplaced. The drug industry is among the most profitable in the world; pharma's knack for generating money makes oil companies look like lemonade stands. Drug firms owe their prodigious success to doing one thing exceptionally well. R&D? No – marketing. And as perfect an opportunity as obesity might be, it's also a legitimate health crisis that's only getting bigger. The one snag is that most people don't consider being fat a disease, they see it as a lifestyle problem. Which explains the appeal of metabolic syndrome. It's a simple, compelling concept that reframes the issue in scientific terms.

But is it real? In some ways, no. You can't see metabolic syndrome through a microscope, or detect it through a single blood test. Since it's a checklist of risk factors rather than symptoms, it stretches the way we think of disease. It's very much a human invention, a "syndrome" – that term researchers assign to things they don't quite understand. But in other ways, it's absolutely real. Though championed by drug companies, it's been defined and recognized by legitimate health organizations. And it's definitely unhealthy. You can't die of metabolic syndrome, but you can die of what it leads to: diabetes and heart disease.

And even if metabolic syndrome is just another term for obesity, it wouldn't be the first condition of daily life to become a disease. Alcoholism, clinical depression, and gastritis were all once considered personal problems that are now recognized as legitimate medical disorders, with all the trimmings of diagnosis, treatment, and pharmaceuticals. Many of these new illnesses, like osteoporosis, are widely accepted. Others, like fibromyalgia and female sexual dysfunction, remain fuzzy quasi diseases with shaky standing in the medical community."

State and Traits

Individuals are considered to have stable personality traits. There is much research on how these traits affect many different outcomes, such as health, relationships, and finances. However, one long-term debate is whether people actually have any stable traits. This debate is due to the immense variability in how people act in different situations. That is, a individual’s behavior can be seen to be incredibly variable depending on the situation A colleague, Ellen Hamaker, writes about a very interesting approach to modeling the interaction of states and traits using structural equation modeling.

Another approach is taken by Walter Mischel and Yuichi Shoda. They investigate a single person with an intensive measurement approach (i.e., many measurements over time). Rather than averaging the person’s data into an average personality, they use the ‘noise’ that comes from the situation-individual interaction to create a behavior signature. That is, by determining how people act in different situations, a behavioral signature is created that is a stable pattern within that individual. Both of the above approaches are unique means to investigate the dynamics of personality. Both are mathematically intensive and have not yet been popularized as much as traditional personality models.

Below are some references to papers describing these techniques:

Hamaker, E. L., Nesselroade, J. R. & Molenaar, P. C. M. (in press). The integrated trait-state model. Journal of Research in Personality.

Hamaker, E. L., Dolan, C. V. & Molenaar, P. C. M. (2005). Statistical modeling of the individual: Rationale and application of multivariate stationary time series analysis. Multivariate Behavioral Research, 40(2), 207-233.

Mischel, W., Shoda, Y., & Mendoza-Denton, R. (2002). Situation-behavior profiles as a locus of consistency in personality. Current Directions in Psychological Science, 11, 50-54.

Shoda, Y. & LeeTiernan, S. (2002). What remains invariant?: Finding order within a person's thoughts, feelings, and behaviors across situations. In D. Cervone & W. Mischel, Advances in Personality Science, 1, pp. 241-270.