Wednesday, November 25, 2009

RDU: where the wild things are

From this morning's News Observer:
RDU officials have noted a marked increase in recent months in the number of coyotes crossing the paths of taxiing airplanes. The critters can wreak havoc, causing delays in takeoffs and landings. In September, an American Eagle jet struck a coyote on a runway. No one was injured.
A coyote was struck by a jet, and no one was injured. That's some coyote.

Friday, November 20, 2009

Applying Bayes' theorem to breast cancer screening

Bayes' theorem gives the formula that statisticians use for calculating conditional probabilities.

Suppose that you have two events A and B that have joint probabilities. From Bayes' theorem, the probability that A occurs given that B has occurred, Prob(A|B) is

Prob(A|B) = Prob(B|A)*Prob(A)/Prob(B)

where Prob(B|A) is the probability that B occurs given A, Prob(A) is the unconditiional probability of A occurring, and Prob(B) is the unconditional probability of B occurring.

Let's apply this to cancer screening. According to the American Cancer Society, the unconditional probability that a woman who is age 40 develops breast cancer by the time she is 50 is 1.44 percent.

Suppose that we had a screening test for breast cancer that gave a positive result 100 percent of the time that breast cancer is present. That is, let's assume that the test never generates a false negative. However, let's also assume that there is a small chance, say 5 percent, of false positives.

From these figures, the probability of a randomly screened 40-year-old woman receiving a "positive" result is

Prob(Pos. test) = Prob(Pos. test|Cancer)*Prob(Cancer)
+ Prob(Pos. test|No cancer)*Prob(No cancer)
= 1.0*.0144 + .05*(1-.0144) = .0637

And the probability that a woman with a positive test has cancer is
Prob(Cancer|Pos. test) = Prob(Pos. test|Cancer) * Prob(Cancer) / Prob (Pos. test)
= 1.0 * .0144 / .0637 = .226

In this case, a positive test means that the woman has only a one-in-four chance of actually having cancer. She is much less likely to have cancer than to not have it.

The test provides information. Without the test, the woman would have only known about a 1-in-70 chance.

However, because of the very low underlying rate of cancer, the test yields many more false positives than true positives (three times as many). Many, many more women without cancer are tested and subject to false positives.

Suppose that the same test is used for a 50 year old woman. According to the American Cancer Society, the woman would have a 2.39 percent chance of developing cancer over the next ten years. The probability that she has cancer given a positive result from our hypothetical test is 33 percent. So, the rate of false positives drops from one in four to one in three.

To be clear, these examples are not arguments for doing away with testing. However, they do show some of the limitations associated with even a very good test and some of the excess costs associated with routine testing.

Tuesday, November 17, 2009

You've come a long way baby

You needed that college admission. And you were the best qualified. But they had to give it to a man because of a gender quota. Is that really fair?
Inside Higher Ed reports
The U.S. Commission on Civil Rights has started an inquiry into the extent to which liberal arts colleges discriminate against female applicants in an attempt to minimize gender imbalances in the student body. On Friday, the commission agreed on a set of colleges -- primarily in the Washington area -- to investigate, but declined to release a full list.

The issue is an extremely sensitive one for liberal arts colleges, many of which in recent years have worried about their gender ratios reaching points (60 percent female is commonly cited) where they face difficulty in attracting both male and female applicants. Generally private undergraduate colleges have the legal right to consider gender in admissions. They were specifically exempted from the admissions provisions of Title IX of the Education Amendments of 1972.

Cost benefit in cancer screening

The U.S. Preventive Services Task Force has issued a stunning recommendation. It recommends against routine screening mammographies for women 40-49 years old with no other risk factors for breast cancer and recommends only biennial mammographies for women 50-74 years old. It also recommends against teaching women how to self-examine.

The recommendations reverse those made by the same group in 2002.

The task force reviewed evidence from numerous studies in making its recommendation.

It concluded that there is a benefit to regular screening mammographies; the evidence demonstrates that they reduce cancer mortality among women aged 40 and over. The benefits increase with age. So, the task force's recommendation will likely contribute to a higher death rate.

However, the task force cited new evidence that the mortality benefits were exceedingly small. For every 1,903 women aged 40-49 who were given the opportunity for annual screening, only one cancer death would be avoided. For women aged 50-59, the ratio was 1,339 to one. The new evidence was largely responsible for the change in recommendations.

The task force balanced this small but undeniable benefit against "moderate" costs and harms from screening.
The harms resulting from screening for breast cancer include psychological harms, unnecessary imaging tests and biopsies in women without cancer, and inconvenience due to false-positive screening results. Furthermore, one must also consider the harms associated with treatment of cancer that would not become clinically apparent during a woman's lifetime (overdiagnosis), as well as the harms of unnecessary earlier treatment of breast cancer that would have become clinically apparent but would not have shortened a woman's life. Radiation exposure (from radiologic tests), although a minor concern, is also a consideration.
The task force found no benefit from self-exams but some of the same harms as mammographies.

An interesting thought experiment is to consider how the recommendations might change yet again if a less expensive but more accurate screening technology is developed (the recommendations do compare film, digital, and MRI screenings). A technology that reduced the screening costs and led to more true positives and fewer false positives could well tip the balance back in favor of additional screenings.

With the current technology, however, the "rational" approach is to cut back on screeings.

What's not in my wallet

I got home last night to find a letter from Sears kindly informing me that the interest rate on my seldom-used Sears card was going up to "the U.S. Prime Rate plus 21.99%." Effectively, that was going to make the interest rate just a bit over 25% and well into usury territory, so much for the "softer side of Sears."

I can take a hint. I cancelled the card shortly thereafter.

This morning reports
One in four consumers plan to pay with cash this holiday season, according to a new survey by the National Retail Federation. That's up 9.1% from a year ago.

That's not too surprising considering both credit card companies and consumers have reined in usage during the Great Recession.

Another 42.5% of holiday shoppers plan to use primarily debit or check cards, a 2.5% increase from last year, the survey found.

Credit card usage, meanwhile, is expected to fall by 10.1% to 28.3%.
The story doesn't mention changes in rates but does mention that "credit usage will remain weak until unemployment starts to fall, economists say." Credit usage will also remain weak while interest rates are sky high.

Many other card customers will see notices like this as a result of the Credit Card Accountability, Responsibility, and Disclosure Act of 2009, which bans some types of rate increases and "gotcha" fees. Issuers are rushing to raise rates before the provisions kick in this winter (or sooner if Congress gets its way).

It just goes to show that these types of regulations are like squeezing on a balloon. Squish down on one fee and another pops out. At least the new rules have the benefit of simplifying card provisions and making usurious rates easier to spot.

Thursday, November 12, 2009

CNN at 7 p.m. may soon be worth watching again

Hurray! The grouch is gone.

No, not Oscar, that other trashy malcontent, Lou Dobbs.

Dobbs has quit CNN, raising the channel's on-air IQ by several points in the process.

Dobb's ill-informed rants (he calls it "advocacy journalism") have grated for years and made the 7 p.m. CNN slot unwatchable. His screeds against immigration and trade were bad enough. But this year, the emperor was laid bare when he persisted in questioning President Obama's citizenship.

Maybe it's time to tune into CNN after dinner again.

Wednesday, November 11, 2009

Veterans Day 2009

It's raining, windy and gray in Greensboro this morning, somber weather for an especially sad Veterans Day. This year's remembrance occurs with battles in Afghanistan growing bloodier, with troops still serving in large numbers in Iraq, and in the wake of the senseless tragedy at Ft. Hood.

A memorial service was held yesterday at Ft. Hood. The President attended and gave a wonderful speech that focused less on the terrible violence and more on the lives and contributions of the troops themselves.
Your loved ones endure through the life of our nation. Their memory will be honored in the places they lived and by the people they touched. Their life's work is our security, and the freedom that we all too often take for granted. Every evening that the sun sets on a tranquil town; every dawn that a flag is unfurled; every moment that an American enjoys life, liberty and the pursuit of happiness -- that is their legacy.
Later in the speech, he linked the sacrifices of the Ft. Hood victims with a more general charge for Veterans Day.
It's a chance to pause, and to pay tribute -- for students to learn the struggles that preceded them; for families to honor the service of parents and grandparents; for citizens to reflect upon the sacrifices that have been made in pursuit of a more perfect union.

For history is filled with heroes. You may remember the stories of a grandfather who marched across Europe; an uncle who fought in Vietnam; a sister who served in the Gulf. But as we honor the many generations who have served, all of us -- every single American -- must acknowledge that this generation has more than proved itself the equal of those who've come before.

We need not look to the past for greatness, because it is before our very eyes.

This generation of soldiers, sailors, airmen, Marines and Coast Guardsmen have volunteered in the time of certain danger. They are part of the finest fighting force that the world has ever known. They have served tour after tour of duty in distant, different and difficult places. They have stood watch in blinding deserts and on snowy mountains. They have extended the opportunity of self-government to peoples that have suffered tyranny and war. They are man and woman; white, black, and brown; of all faiths and all stations -- all Americans, serving together to protect our people, while giving others half a world away the chance to lead a better life.
If you have the time, I encourage you to read the speech in its entirety.

Thursday, November 5, 2009

Census shenanigans blocked

The Washington Post reports

Senate Democrats Thursday blocked a GOP attempt to require next year's census forms to ask people whether they are U.S. citizens.

The proposal by Louisiana Republican Sen. David Vitter was aimed at excluding immigrants from the population totals that are used to figure the number of congressional representatives for each state. Critics said Vitter's plan would discourage immigrants from responding to the census and would be hugely expensive. They also said that it's long been settled law that the apportionment of congressional seats is determined by the number of people living in each state, regardless of whether they are citizens. A separate survey already collects the data.
The article quotes Sen. Vitter,
"The current plan is to reapportion House seats using that overall number, citizens and noncitizens ... I think that's wrong. I think that's contrary to the whole intent of the Constitution and the establishment of Congress as a democratic institution to represent citizens."
Instead of "thinking" that he knows what the Constitution says, Sen. Vitter should actually read the document, specifically the 14th Amendment, which states
Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed.
The word "persons" is purposeful. Other language in the 14th Amendment, including language that describes how representatives and electors may be proportioned in other ways, explicitly mentions citizens.

The decennial census is due to go out early next year. Sen. Vitter's proposal would have increased the cost of the count, delayed the census, and reduced compliance (further raising costs). Moreover, citizenship information is already asked of 3 million households from all 50 states and DC each year (including census years) as part of the American Community Survey (ACS).

Although the proposal was blocked, Sen. Vitter had the support of 38 other Republican senators who were equally willing to waste money and monkey with the decennial census.

This is the best the Republicans could offer?

Last Friday, Rep. Boehner, the Republican minority leader, promised "over the coming days, you're going to hear an awful lot about the specifics of what we would do to lower the cost of health insurance in America and really do this in a step-by-step gradual process."

In the same interview, Rep. Boehner went on to discuss differences in the Democratic and Republican approaches to expanding coverage and addressing pre-existing conditions, saying
Most of the 36 million that they say they're going to cover already have access to some type of government program, or even their employer program, or have chosen just not to have health insurance. When you really boil this down, there are about seven or eight million people in America, those with pre-existing conditions, those who are what I would describe as the working poor, and some early retirees who have a difficult time getting health insurance. We can help those people get health insurance and still bring down the cost of health insurance for the 85 percent of Americans who have it and think they pay too much for it.
Well the specifics are now here. Rep. Boehner and the Republicans this week unveiled their bill, the preamble of which states
The purpose of this Act is to take meaningful steps to lower health care costs and increase access to health insurance coverage (especially for individuals with preexisting conditions)...
For a bill that's supposed to help 7-8 million vulnerable people, the bill at best does precious little and at worst actually harms those who need insurance most.

First, the 219-page bill only uses the word "preexisting" three times: in the preamble, in a section title, and in a provision ordering the General Accountability Office to do a study. You would think that legislators concerned "especially for individuals with preexisting conditions" could bring themselves to mention those conditions a few more times.

Second, a CBO analysis of the bill indicates that by 2019 (ten years from now) it will only increase insurance coverage "by about 3 million relative to current law," far short of the 7-8 million cited by Rep. Boehner. The legislation would leave 52 million people uninsured; one out of every six nonelderly residents would lack insurance. Rep. Boehner did promise a "gradual" approach, but this is ridiculous.

Third and most importantly, the bill will likely hurt many of those who need help the most. From the same CBO analysis
...some provisions of the legislation would tend to decrease the premiums paid by all insurance enrollees, while other provisions would tend to increase the premiums paid by less healthy enrollees or would tend to increase premiums paid by enrollees in some states relative to enrollees in other states.
As an example of how the distribution of costs and enrollment might change under the Republican plan, the CBO states
For example, states that loosened rating rules in the market for individually purchased insurance to allow premiums to vary more on the basis of age would cause premiums for older people to increase and premiums for younger people to decrease. With other factors held equal, fewer older people (who tend to have higher health care costs) and more young people (who tend to have lower health care costs) would then sign up for coverage, and the improved average health status of insured people would lower average premiums; at the same time, the pool of people without health insurance would end up being less healthy, on average, than under current law.
The Republican plan does lower average costs for people who will have insurance. However, it does this in part by changing the mix of people with insurance, bringing in people who are younger and healthier and driving out people who are older and unhealthier.

Fourth, the Republican plan also reduces average premiums by reducing the types of services that would need to be covered in plans--that is, by reducing the quality of coverage. The CBO writes that provisions in the plan would
encourage states to reduce the number and extent of benefit mandates that they impose, and provisions that would allow individuals or affiliated groups to purchase insurance policies in other states that have less stringent mandates.
In short, insurance premiums go down because the insurance covers less.

The plan does have some good features, such as requirements for the government to improve electronic record-keeping and some extra funding for fraud investigations. However, in keeping with the Republicans' gradual and incremental approach, these could be enacted subsequently.

The bottom line is that the Republican plan is no substitute for the Democratic plan. The Republican plan doesn't even live up to Rep. Boehner's own diminished promises or its own preamble.

Wednesday, November 4, 2009

U.S. lags further behind in infant mortality

The Centers for Disease Control (CDC) have released figures that show that infant mortality rates in the U.S. exceed many other countries in the world. In the latest CDC analysis, which uses 2005 data, the U.S. ranked a disappointing 30th. So much for our world-leading medical expenditures buying us better health outcomes.
The United States international ranking in infant mortality fell from 12th in the world in 1960, to 23rd in 1990 to 29th in 2004 and 30th in 2005. After decades of decline, the United States infant mortality rate did not decline significantly from 2000 to 2005.
Some have argued that infant mortality rates cannot be compared across countries because of differences in the ways that births are registered (some countries don't count very early or very low weight births as "live" births).

The CDC report acknowledges these differences but concludes
There are some differences among countries in the reporting of very small infants who may die soon after birth. However, it appears unlikely that differences in reporting are the primary explanation for the United States’ relatively low international ranking. In 2005, 22 countries had infant mortality rates of 5.0 or below. One would have to assume that these countries did not report more than one-third of their infant deaths for their infant mortality rates to equal or exceed the U.S. rate. This level of underreporting appears unlikely for most developed countries.
Even so, the detailed analyses in the CDC report focus on European countries, most of whom use the same reporting standard that the U.S. does, and limit the comparisons to mortality among infants with a gestational age of 22 weeks or more.

The CDC analyses indicate that
The main cause of the United States’ high infant mortality rate when compared with Europe is the very high percentage of preterm births in the United States.
However, the report also shows that the U.S. has one of the highest mortality rates for infants born at or near full term (after 36 weeks). For instance, the report compares births between the U.S. and Sweeden. If the U.S. had Sweeden's gestational age distribution, the U.S. infant mortality rate would be about a third lower than it is. However, even this adjusted birth rate would be 30 percent higher than Sweeden's. Put another way, differences in gestational age distributions account for two-thirds of the difference in infant mortality rates between the U.S. and Sweeden, but the remaining one-third is due to higher gestation-specific mortality rates in the U.S.

Tuesday, November 3, 2009

Lunch with Paul Krugman

I type this post with the hand that just shook Paul Krugman's hand...

Krugram is in town to give a talk as part of the Bryan Lecture Series. He also gave a lecture on the current economic crisis this morning at UNCG and then went out to lunch with faculty from the Economics Department.

The talk this morning began with a discussion of how the trends in world output in the current crisis initially mirrored those from the late 1920s but subsequently recovered (unlike the earlier decline). Krugman then moved on to discuss how the failure of the financial system, especially the "shadow banking system," contributed to the crisis, how the crisis was similar to Japan's lost decade, how we managed to avoid even worse outcomes, and how hard the recovery is likely to be.

The talk followed a lot of what Krugman has written in his columns. For instance, he discussed the important roles of deposit insurance, conventional monetary policy, and automatic fiscal stabilizers. There was a lot of emphasis on the limits of monetary policy--the liquidity trap--and how the Fed has adopted some unconventional policies, such as buying commercial paper in addition to government securities. Although Krugman also predicted a slow employment recovery, he didn't spend a lot of time talking about a follow-on stimulus package. He did, however, discuss how difficult it would be to return to healthy employment numbers with the policy tools that were currently being deployed.

Lunch afterward was an absolute blast. With all the questions being fired at him, it was a wonder that he got any time to eat.

All-in-all, it was the sort of day economists really enjoy.

Sickening employment policies

The New York Times reports this morning on how the spread of H1N1 and other illnesses is assisted by crummy sick leave policies.
Public health experts worried about the spread of the H1N1 flu are raising concerns that workers who deal with the public, like waiters and child care employees, are jeopardizing others by reporting to work sick because they do not get paid for days they miss for illness.
Firms clearly face a dilemma with these policies. On the one hand, sick leave helps to curb the spread of illnesses among employees, possibly raising output (or at least reducing losses associated with illness). On the other hand, sick leave promotes absenteeism (e.g., people calling in "well"). Economists call this "moral hazard," which in this case translates loosely as "if you offer it, they will cough."

An underlying problem is that firms cannot completely observe employees' health. It's difficult for a firm to determine whether an employee really is sick, and requiring employees to submit independent documentation of an illness is costly and impractical.

There is also a good possibility that firms and employees undervalue this benefit. A contagious disease is a classic example of a negative externality--a economic harm whose costs aren't fully borne by the immediate parties. Workers fail to consider the harm that they are causing their coworkers and others by showing up sick; firms fail to consider the harm that their sick employees may be causing customers, commuters, and others.

As an estimated 39 percent of workers lack sick leave, there's some evidence that sick leave is under-provided.

Even when sick leave is available, firms sometimes discourage its use. The Times article describes the policies of, who else, Walmart.
At Wal-Mart, when employees miss one or more days because of illness or other reasons, they generally get a demerit point. Once employees obtain four points over a six-month period, they begin receiving warnings that can lead to dismissal.

In addition, when Wal-Mart employees call in sick, their first day off is not a paid sick day (although workers can use a vacation day or personal day), but the second and third days are paid.
In this case, Walmart imposes a cost in terms of demerit points and lost personal/vacation leave for sick days, creating a clear disincentive to using those days.

In the end, the choices come down to having employees use too many sick days or too few. This employee's vote would be for too many.