Oh shit. You may have come across this already -- it seems the kinks in the riser pipe of the Deepwater Horizon well are the only thing preventing an uncontrolled gusher, and the pipe is steadily being eroded by sand carried in the escaping crude oil. If the wellhead blows wide open, according to one expert, the hole could gush 150,000 barrels of oil a day. That would be the equivalent of the Exxon Valdez spill every two days, and there is no way they are going to be able to stop this for weeks, if not months. And it seems pretty clear to me from reading the account that this possibility is not remote. In fact, it sounds as though it's almost inevitable.
If that happens. . . but let's not go there yet. Let's just talk about something I think about quite a bit, which is how us foolish humans ought to think about events that have immense consequences, but which we believe to be of low probability. While there are actually a few reasons why I have been against offshore oil exploration for quite a while now, having to do with taking a long view of a finite petroleum resource and a finite atmosphere, most people who have opposed offshore drilling were mostly worried about an event such as this -- an environmental catastrophe. And of course the experts all said pish tosh, we know what we're doing, it's perfectly safe.
Politicians don't have any expertise about these matters, but they do know that the world's largest multinational corporations, with tens of billions of dollars to spend on PR, advertising, and campaign contributions, are in favor of drilling; and so are a lot of people in coastal states who want jobs, and legislators who want tax revenue with low political cost. Opponents don't have anything to offer but basically unsupportable fears. Except it turns out they were right.
There might be a few other questions we should rethink.
Friday, April 30, 2010
Oh shit. You may have come across this already -- it seems the kinks in the riser pipe of the Deepwater Horizon well are the only thing preventing an uncontrolled gusher, and the pipe is steadily being eroded by sand carried in the escaping crude oil. If the wellhead blows wide open, according to one expert, the hole could gush 150,000 barrels of oil a day. That would be the equivalent of the Exxon Valdez spill every two days, and there is no way they are going to be able to stop this for weeks, if not months. And it seems pretty clear to me from reading the account that this possibility is not remote. In fact, it sounds as though it's almost inevitable.
Because you're going to have to keep a couple of ideas straight -- concepts that are kind of similar but aren't the same. This part tends to confuse people so you've been warned.
So I'll start with what I hope is a fairly simple idea that will be a half step toward the slightly harder one. If we don't know anything about a population, and then we take a sample from it, the sample is our best estimate of what the population is like. We know the mean and standard deviation of the sample, but we don't know for sure how similar that is to the population. But suppose we do know the distribution of a population, and we want to know if a sample somebody gave us is likely to have come from that population or not.
Suppose we had the medical records of of a whole lot of children, 1,795 of whom had asthma, and .55 were male and .45 were female. We happen to know that .51 of all children are male, and .49 of all children are female. (It’s true! There are slightly more boys born than girls. However, the men start to die off so eventually there are more women than men.) So the question is, does this mean that boys are more likely to have asthma than girls? (These numbers are just made up by the way. I probably shouldn't have used a real disease.)
What we need to do in this case is compute a number called "Z". I don't know why they call it Z, they just do. This is the distance of an observation from the mean, measured in standard deviations.
In this case, the standard error for a sample of 1,795 children of whom .51 are male is approximately .012. (Actually it's 0.011799154872714672808505450202002, but close enough.) How do I know that? Because the standard deviation of a binomial distribution, as you may recall from last time, is the square root of P*Q/n. P is .51, and Q is .49. n is 1,795. Get out your calculator and try it! The difference between .55 and .51 is .04, which is more than 3 times .012. In other words, the observed outcome is more than 3 standard deviations from the expected outcome. The probability of this happening is so small – less than .001 – that it is extremely unlikely that boys have the same risk of asthma as girls. We say in this case that Z= 3.3333 etc. Z is also called the standard normal deviate.
Yup, it's normal and it's standard and it's deviate, all at the same time. What's the world coming to?
But notice something else, which is also very important - the difference is not very large. It's highly unlikely to arise just by chance, because we have a large sample. With big samples, you can detect small differences. But that doesn't mean they necessarily matter very much.
Anyway, hang onto that idea -- how many standard deviations are you from the mean? -- because it is very useful.
Thursday, April 29, 2010
I don't know why I don't write about these issues more -- I actually have a master's degree in urban and environmental policy, I am involved in a study of near highway pollution, and I am an activist on the issue of healthy communities and environmental justice. Most of the e-mails I get from publicists go straight to the trash, but for some reason a flack sent me a link to this article by Jonathan Lerner which I recommend. (I don't see who's making a profit from this so that's why it's a bit unusual.)
The fact is our civilization is not sustainable on the premise that we need to surround ourselves with two tons of steel and propel it down a highway at 70 miles per hour using fossil fuel for two hours a day to get to work and back, and many more hours each week to buy groceries, take Buffy to her flute lessons, and oh yeah, get the car repaired. We can't keep turning farmland and woodland into suburban sprawl to give more and more people a chance to live that way. This entire way of life is doomed -- and maybe a lot sooner than most people think. (The preceding link is from the Apocalypse Now party, but if Richard Branson is right and peak oil is now, well ... tell me why they are wrong. And the well blowout in the Gulf of Mexico is going to throw a big spanner into the plans to stave it off by drilling in the ocean. Just sayin'.)
Most people are just going to have to live in urban or urban-style communities that are dense enough to support walkable shopping and have mass transit connections to the rest of the world. Those communities can work -- I live in Jamaica Plain which is jes' fine, let me tell you, with two of the world's greatest urban parks, great shops and restaurants, safe streets and a strong, welcoming and diverse community. But plenty of our urban areas are social and physical wastelands where it is not good for people to live. Transportation is the foundation on which successful 21st century communities can be built. Not just the Supertrains! between cities that Atrios is so enthusiastic about -- although those are good -- but well designed, accessible local webs of light rail and LNG-powered buses to fill in the places between, along with sidewalks and bike paths.
Tie the people to great grocery stores, farmers' markets, jobs, educational opportunities, recreational opportunities, and get them out of their cars, and you can have a healthy community anywhere. If we're going to have a future, that's it.
Wednesday, April 28, 2010
It has received very little attention in the mass media, but a lot of attention in the circles where I travel, that the president has nominated Donald M. Berwick to direct the Centers for Medicare and Medicaid Services. Apparently Dr. Berwick engaged in lengthy discussions, possibly negotiations, with the administration before agreeing to be nominated. I was initially surprised because I didn't think the CMS director had much of a policy portfolio, that it was essentially an administrative job. That Berwick accepted is a signal that we will see substantial innovation and experimentation in health care financing and organization in Medicare, which the federal government controls directly. CMS can encourage and support the states in redesigning Medicaid, though it has less direct influence.
Berwick, who now runs the Institute for Healthcare Improvement, located in the People's Republic of Cambridge, Massachusetts, is well known as a health care (I still prefer it as two words) visionary and advocate for patients. You can learn his basic schtick here, it's called The Triple Aim. If you've been reading Stayin' Alive, you already know that the goal of universal coverage is inseparable from cost containment. But rather than defining universal coverage per se as part of the triple aim, Berwick allows it to fall out as a consequent, if that. The triple aim is better experience of health care, improving the health of populations, and reducing per capita costs. If universal coverage serves those ends, so be it, but he doesn't try to prove that theorem.
He does argue, however, that the triple aim requires eliminating the fragmentation of our present system, and the misalignment between the incentives of individual institutions and his social goals. This means large scale integration through some sort of authority or another -- a national health service or single payer works, but he's willing to tolerate smaller scale systems -- that is dedicated to these goals, rather than, say, the enrichment of executives or the prestige and market share of an academic medical center. He pretty much concludes that global budgets are necessary, within which resources can be allocated to optimize the first two goals; and that the goal of population health requires redirecting funds away from medical services to more primary public health.
All of this is true, but it means goring many a large and powerful ox. While I believe it is very much pro-liberty, it doesn't sound very libertarian. In fact, some will detect a pinkish hue over the whole thing. I am curious as to how the Confederate Party will approach his confirmation hearing. I hope we'll find out soon.
Tuesday, April 27, 2010
Maybe so but the Central Limit Theorem is the key to Gaussian statistics. The theorem states:
The distribution of sample means from any population, regardless of the population distribution, will be normal, with a mean equal to the population mean.
By a "sample," we mean cases from the population, be it individual people or whatever else the population consists of, chosen at random, or at least in a way that is unrelated to the probability of having the characteristic we are interested in. That is what we call an "unbiased" sample. Bias in this context doesn't have anything to do with prejudice, it's just question of whether our probabilities are somehow distorted.
For this to be true, the sample also has to be large enough. It doesn't really start to work until you have samples of at least 30 and you really need bigger samples than that to do anything useful.
So I supposed you would like me to explain the theorem. Well okay then. One way of looking at it is to go back to our coin flips. The underlying distribution of coin flips in the world is not a normal distribution. It looks like this:
For obvious reasons, we call that a "rectangular" distribution. Half the flips are heads, and half the flips are tails. What our normal curve was actually showing us was the distribution of sample means from many samples of arbitrarily large size. The most likely result is half tails and half heads, with results farther and farther from the population mean increasingly unlikely.
In my magic bag, I have an infinite number of green and blue marbles; 80% are green. Obviously, this is not a normal distribution, but, if I take a million samples . . .
I get this distribution. Yep, it's a normal distribution with a mean of .8, the population mean.
The standard deviation of this curve is called the “standard error of the proportion.” The bigger the sample, the smaller it is. We could figure it out by using the binomial formula, computing the proportion of all possible values of the sample mean, and plugging them into the formula for the standard deviation . . . But there is a much simpler way. The formula for the Standard Error of the Proportion is:
As you may recall, p is the probability of one outcome, q the probability of the other, and what you don't know yet is that n is the sample size. So, bigger samples mean smaller standard errors, which is another way of saying that you can have more confidence that your sample mean is close to the population mean. Big samples are good but they cost more. So they're a luxury we don't always have.
Soon, I will march on with this. It will get more interesting, I hope, when we actually put it to use for a good cause.
Monday, April 26, 2010
or stupid, or perverse. It's downright ugly and evil. I am proximally inspired to these sentiments by this article into today's All the News that Fits, about the efforts of the South African government to ramp up HIV prevention and treatment. The best effort is that 365,000 South Africans died unnecessarily while former president Thabo Mbeki was under the thrall of AIDS denialist Peter Duesberg and other cranks. The harm done to innocent children and families by the deluded cult that blames vaccines for autism belongs to the scientific fraudster Andrew Wakefield and narcissistic upper class twit Robert Kennedy Jr. The catastrophe that looms for the entire planet from anthropogenic climate change might have been averted but for Rush Limbaugh and another crank scientist, Dixie Lee Ray. (Most people don't know about Vulgar Pigboy's seminal role in AGW denialism -- it's well worth publicizing.)
What RFK Jr. and Rush Limbaugh have in common is that they both saw a chance to promote themselves, build a following, and ultimately make money by pretending to be lone crusaders against a deceitful scientific establishment. These "science as conspiracy" theories are nothing but repulsive slurs against people who work hard, generally for quite modest incomes, and who share a culture of dedication to truth. Really. The whole stance is nothing but a scam designed to separate people from their senses as well as their money. Unfortunately, while Kennedy and Limbaugh are just charlatans, they have managed to catch a lot of innocent victims in their net of true belief, and we all have to suffer the consequences. Meanwhile, they go on being rich and influential.
Ana writes, "One of the BIG problems of statistics is that analysts use and abuse measures and stats developed for the ‘normal’ curve, applying them when not appropriate." I'm going to get to critical perspectives on the use and abuse of statistics, which I hope will be more interesting, but I hope people will be patient while I continue my march through the basics.
We derived the normal curve from a binomial distribution, but of course we aren't only interested in binomials -- variables that can take only two values, such as coin flips or whether or not somebody tests positive for a disease, for example. We're also interested in the distribution of variables that can have many values, or even continuous values such as height, weight and blood pressure. Our binomial distribution started out as coin flips, but what we actually wound up charting was a continuous variable -- the proportion of heads in an arbitrarily large series of coin flips.
In the Real World, it's quite rare to find a distribution that is perfectly normal like our coin flip example. Some real world distributions look sorta kinda normal, and many do not. (The reason that the distribution of IQs appears very close to normal is because they intentionally design and score the test so that it will be, BTW. Many of the normal looking curves you will see are really artificial.) Nevertheless, the normal distribution can be useful in thinking about real world populations that aren't normally distributed. We're heading toward the explanation for that but first we need a few more basic ideas.
The Standard Deviation is a measure of dispersion – the tendency of values to cluster near the mean, or be more spread out. You can calculate it regardless of whether a distribution is normal, but for really weirdly skewed distributions it might be misleading, or at least not very informative. Here's how you compute it:
- Calculate the mean: Add up all of the values in your population or sample, and then divide by the number of cases. The "mean" is a synonym for what we ordinarily call the average. We can abbreviate it "M". (Sometimes the Greek letter μ (mu) is used, but why be pretentious?)
- For each case in your sample, subtract M from its value -- X. The result could be a negative or a positive number, obviously, depending on whether X is larger or smaller than M. Then square the result, i.e. calculate (X-M) * (X-M). This way, you'll convert all the numbers into positive numbers.
- Add up all the resulting numbers, then divide by the total number of cases, N. You have now computed a new kind of average, the average of the squared distances from the mean of all your cases.
- This is called the variance. Usually, people then take the square root of the whole thing, to make up for the fact that the original values were all squared. The result is called the Standard Deviation, abbreviated sd
We can write the formula for this easily enough. If formulas make you sick, just avert your eyes.
The thing that looks like a big "E" is actually the Greek letter sigma, which is like our "S". It stands for sum. That means you add up the values of each individual case, just like I said. The rest of it is also just like I said -- what you are adding up is X-M squared, then dividing by N, then taking the square root of the whole thing. Tah Dah! Now you can read a fancy mathematical formula.
MAJOR IMPORTANT FACT: In a normal distribution, about two thirds (.6826) of all values are within one sd of the mean; about 95% (.9545) are within two sd of the mean; more than 99% (.9973) are within three sd of the mean. This is true of all normal distributions.
Now we are getting close to the magical key. Next time!
Friday, April 23, 2010
As I assume you have noticed, a major bloc of opposition to the recent health care reform legislation consists of Medicare beneficiaries who have been convinced by Faux News and Rush Limbaugh that it will cut their benefits and shove them out to die on an ice floe. Of course, as always when referring to Faux News and the Vulgar Pigboy, the opposite is true.
Right now, Medicare beneficiaries get a single "welcome" checkup when they first sign up. After that, Medicare pays for "treatment of disease" plus limited, specific preventive services such as mammograms. But under the reform legislation, they'll now get an annual visit, absolutely free, including 100% of the screening tests, vaccinations and every other service recommended by the U.S. Preventive Services Task Force. They'll also get a personal prevention plan, and a personal health risk assessment. Once the seniors realize the legislation didn't cut their benefits, but actually increased them, and in a really great way, they'll come back to the Democratic Party in droves and the threat of losing control of the House in November will be over.
Oh wait. The new benefits take effect on January 1, 2011. #%$!#%%^ brilliant, Harry.
If you're a curve, that is. The world famous normal curve is:
- A continuous, symmetrical curve w/ both tails extending to infinity.
- The mean, median and mode -- which I will now explain are the same.
- Described by two parameters (i.e., numbers that can vary): arithmetic mean, and standard deviation -- which I will also explain.
As you may recall, we got our normal curve from a binomial distribution -- heads and tails. So what does it mean, to talk about the mean? (Or to miss New Orleans?) Easy. Just assign a numerical value to heads and tails. Usually in the case of a binomial people use 1 and 0. So the value of the most common result -- half heads and half tails -- is going to be .5 = 1/2. It should be easy to see why. Let's say we flipped our coin 100 times. The most frequent result, which is called the mode or modal value, is going to be 50 heads and 50 tails. 50 * 1 = 50, and 50 * 0 = 0, and 50 = 0 = 50. So the total numerical score for that result is 50. The arithmetic mean, or average, is the total numerical value divided by the number of cases, i.e. coin flips. 50/100 = .5. You can see that all the values on each side of the curve have to average out to .5 as well because they cancel each other out. 49 heads and 51 tails cancels out 51 heads and 49 tails, and so on. Therefore .5 is both the mean and the mode of our curve.
The median is the number in the middle: half the values are lower, and half the values are higher. Basically, you can see that the median is also .5 for the same reason the mean is .5: the curve is symmetrical. Half the values are to the left, and lower than .5; and half the values are to the right, and higher than .5. So there you go. To review:
- The mean is the sum of all values, divided by N (N is the size of the population).
- The median is that value which divides the population in half – 50% are greater, 50% are less.
- The mode is the most common value.
A normal curve doesn't have to describe a binomial distribution. It can also describe a distribution of some continuous value with a real numerical meaning, such as people's height or weight. Such real world values wouldn't often be exactly normal but let's pretend they are for the sake of argument. (We'll get to why this is worth doing later.) Then the mean, median and mode, while still the same as each other, would be whatever value happened to pertain in reality, such as 5'7" and 165 pounds.
Enough of this for now. Any questions will gladly be accepted.
Thursday, April 22, 2010
but subjectively shrinking. Many people have wondered if all the recent news about earthquakes, and now a volcano, means that something unusual is happening to the thin skin of solid rock we all float around on. (I have read that if the earth were shrunk to the size of a basketball, the solid crust would be the thickness of a postage stamp.) According to the U.S. Geological Survey, the frequency of strong earthquakes around the world has not been increasing.
However, the human population has gotten a lot bigger, and a lot more urban, in more places, in a very short time. Remember, earthquakes don't kill people: buildings do, when they shake and fall down. The result is that a lot of cities are now more or less in the situation of Port au Prince, including Tehran, as Robin Pomeroy reports for Reuters. You may have read about the Friday prayer leader last week who blamed earthquakes on scantily clad women, but Mahmoud Ahmedinejad, whatever craziness may pertain to him, knows better. Quoting Pomeroy's story,
Like the people of San Francisco, Tehranis know their sprawling metropolis is due for a massive earthquake. In Iran, where building standards have not advanced as quickly as the population, some estimate millions could be killed or maimed. In an Islamic society where disasters are often seen as acts of God, Ahmadinejad told housing officials they could no longer rely on the power of prayer to save Tehran from annihilation.
"Tehran has 13 million inhabitants. If an incident happens, how can we manage it? Therefore, Tehran should be evacuated," said Ahmadinejad, a former mayor of the city, announcing financial aid for people who move to towns with a population of less than 25,000. "At least 5 million people should leave Tehran," he said.
Obviously this is not going to happen, but if it were somehow enforced, it would be an economic, social and ecological catastrophe in itself. The fact of the matter is that we humans have gotten ourselves stuck, badly jammed up in a lot of ways all at once. There are just too damned many of us and we can't make it work.
That's a cold fact.
Oh yeah, there's also this: The combined global land and ocean surface temperature anomaly for March 2010 was 0.77°C (1.39°F) above the 20th century average, resulting in the warmest March since records began in 1880. Of course, this is all a fraud -- it's part of Obama's secret plot for Communist world domination.
Wednesday, April 21, 2010
Heads are H, and tails are T. That's easy. And we know that if you flip a coin once, the probability is 50% heads, and 50% tails, so P(H)=.5 and P(T)=.5
So what if you flip a coin twice? What's the probability of getting two heads? (Jeopardy! music plays for 15 seconds.)
Okay, as you remember from last time, the two coin flips are independent events -- the first one has no influence over the second one. (Believing otherwise is called the "gambler's fallacy" -- you start to think your number is "due" because it hasn't hit for a while.) So you get the probability of two independent events both occurring by multiplying the individual probabilities together. The probability of heads the first time is .5, and the probability of heads the second time is .5:
P(H H)= .5 * .5 = .25
It will happen 1/4, 25%., .25 of the time. Two tails in a row will also happen 1/4 of the time. As you may also remember, the probability of either one of two mutually exclusive events happening is the sum of the probability of each.
P (H H) + P (T T) = .25 + .25 = .5
As we also know, something has to happen, which means that all the probabilities have to add up to one, which means that what is left -- 1 heads and 1 tails -- must have a probability of .5. That makes it, obviously, twice as likely as TT or HH. Why is that? Because there are two ways it can happen: tails then heads; and heads then tails.
P (T H) = .25 and P (H T) = .25, so the probability of either one happening is .25 + .25 = .5. I'll even show you a graphical representation:
Okay, let's keep going. Let's do four coin flips.
You should be able to figure out for yourself how to compute the probability of each possible combination. There is a general formula for this, which is called the Binomial Distribution -- binomial meaning "two names," or "two things." I will show it to you just for the halibut, but it isn't necessary and you don't need to know it. (I can't show it in this post because I haven't been able to get the terms in the formula to line up correctly. Blogger is not very math friendly.) What you do need to know is the limit of the binomial distribution, i.e., what it starts to look like as the number of coin flips gets very large. Here it is:
I put some real data under the curve just to show you that in the real world, it never comes out exactly right -- that's the way it is with probability. But do you recognize that curve? Yes, it's the world famous Normal Curve, the Bell Curve. It is the basis for an entire approach to statistics. It was discovered by a guy named Gauss, so when we do statistics based on the normal curve, we call it "Gaussian statistics." That is the adventure on which we will now embark. Meanwhile, here are some equations for you to ignore.
This is the shortest way to represent the computations concerning 3 coin flips. "P" is the probability of heads, and "Q" is the probability of tails. They happen to be the same in this case.
2T, 1H=HTT, THT, TTH=3pq^2=3(.5)^3=.375
1T, 2H=HHT, HTH, THH=3p^2q=3(.5)^3=.375
Tuesday, April 20, 2010
Apparently not. Sample:
I don’t know if I should Buenos Aires or Bonjour, or... this is such a melting pot. This is so beautiful. I love this diversity. Yeah. There were a whole bunch of guys named Tony in the photo line, I know that. And in the introduction too, in the instructions to you all, I got a kick out of the instruction “No heckling.” I am so used to the heckling, it’s okay! We’re used to it. They just hit you into the boards and maybe get called for a penalty or whatever, but we can handle that too. . . .
I’m wanting to, though, kind of shift away from the political. I’m just getting off the trough from doing a lot of Tea Parties across the US, man those are a blast. [applause] They’re rowdy and they’re wild and it’s just another melting pot, there’s just diversity there and all walks of life and all forms of partisanship and non partisanship just wanting good things to happen in this part of the world. It’s been a blast. The shift from the political, so now that I have that shift from the political but still have that desire to talk about the economy and talk about energy and resources and national security and all those things. I was telling Todd, okay, this is like [inaudible] on the vice presidential campaign trail, where you never really knew what you were getting into when you get into that line before you were interviewed. Obviously, sometimes I never knew what I was getting into in an interview. Obviously!
And on and on and on it goes unto ever more profound depths of stupidity until the brain turns to lemon jello. Who needs The Onion any more?
I was considering another diversion into philosophyland, with a post yammering about the limitations of data and reification and all that jive, but I just know y'all are out there salivating to get to the damn probability and statistics already. So okay.
As I have already said, the very idea of probability is somewhat philosophically intractable but we just have to live with that. In public health, we live in a probabilistic world as a function of the limitations of our knowledge. So there you are.
Probabilities are closely related to the idea of rates. For example, the probability of death (in a given population) during a given year is the same as the death rate (i.e., incidence of death). Of course we didn't know the death rate until after the year was over; but we often use the idea of probability in connection with a prediction about the future. That means we have to estimate the probability of dying based on prior experience, if we want to look forward. We'll be talking a lot about estimates and errors as we go on.
Probabilities can be expressed as fractions where the denominator is the total population, and the numerator the number of events. That's just a way of repeating myself -- they are similar to incidence rates. However, because incidence rates can include events that happen two or more times to the same person, the probability of the event befalling a single person can be somewhat less than the incidence rate for the event. With death, obviously, this doesn’t matter, but it could with say, ear infections. We'll see how it gets tricky sometimes, in this and other ways.
Probabilities can range from zero (no way, never happen, not a chance) to 1 (happens every time, mortal lock, death and taxes). For you gamblers out there, keep in mind -- and this is important -- that probabilities expressed this way are different from odds. A probability of .75 -- which you can also call 75% -- represents odds of 3 to 1. That's easy to figure out. Let's say there's a 25% chance of winning on a scratch ticket. That means there's a 75% chance of losing, because the percentages have to add up to 100. Something has to happen! 75/25=3. You're three times as likely to lose as you are to win, that's 3 to 1. A probability of .5, obviously, represents 1 to 1 odds. And so on. We won't go back to odds until much later, because for most of what we're going to do, it's much easier to work with probabilities.
You can do arithmetic with probabilities to figure out more complicated situations. Suppose you have a situation in which there are 3 possible outcomes, and they are mutually exclusive. That means only one of them can happen. For example, you apply to college. You might get admitted with a scholarship, you might get admitted without a scholarship, or you might get rejected. If you want to know your chance of getting admitted, with or without a scholarship, just add together the probabilities of each outcome. Again, here is a simple formula:
P(X) + P(Y)=P(X or Y)
If X means getting a scholarship, and Y means getting in without a scholarship, there you have it. As you can also figure out, if Z means not getting in at all, P(Z)=1 - P(X or Y), because one of those three outcomes must happen and the sum of all three probabilities must be 1. But remember, this only works if the events are mutually exclusive!
What if they aren't? What if we're worried about two things happening, such as you get into Harvard and you get into Yale? (No endorsement implied.) In this situation, you have to assume that the events are independent, which means the admissions offices aren't talking to each other and saying we'll take Joe and you can have Sally, which would totally mess it up. In this case, you multiply the two probabilities together:
P(X) * P(Y)= P(X andY)
We like to use "*" to mean multiplication, instead of "X" as you might have learned in school, because, obviously, we also use "X" a lot to mean "whatever," so we try to minimize confusion. We don't always succeed, as you will see. Unfortunately there are symbols that get used for two or more purposes, but I'll try to keep it to a minimum.
So, if your chance of getting into Harvard is 20%, and your chance of getting into Yale is 50% because your father went there, your chance of getting into both is
.2 * .5 = .1
That's 10%. If you want to make sure to get into Yale, ask your father to give them a million bucks.
Next time, I'll get to more complicated situations. If anything is unclear, or you have suggestions for making it more clear, please let me know.
Monday, April 19, 2010
First we need a bit of vocabulary -- what we call some of the kinds of rates or proportions that we commonly talk about in public health. Last time, I said that "rate" and "proportion" basically mean the same thing, and they do; but we tend to use them in slightly different contexts. We can say that:
A “rate” means the proportion of a population which either 1) has some characteristic at a given time, or 2) to which some event occurs during a given period.
In public health, a “population” normally means some defined group of humans – but in statistics, a “population” can consist of anything, and sometimes our units aren’t people – they might be hospitals, or procedures, or laboratory rats, for example.
To compute a proportion, divide the number of “cases” (people with the characteristic) by the total population of interest. If you have 18 people, and 3 of them have nose rings, the nose ring proportion is 3/18=.167=16.7%. As I said last time, all three ways of writing it mean exactly the same thing.*
There are two major kinds of rates:
Prevalence means the proportion of people who have the characteristic at a specific point in time. So, in our group of 18 people, the prevalence of nose rings is .167, or one out of six if you prefer.
The incidence is the proportion of people who acquired the characteristic within a specified period of time. Usually, it's calculated for a calendar year, but it certainly doesn't have to be! If it turns out that 2 of our 18 people already had nose rings as of January 1, 2009; and 1 of them got a nose ring for the first time during 2009, the incidence of nose rings for 2009 is 1/18=.055555555555555555555 and on to infinity which we would probably round off as .056 or 5.6%. Next time, I'll use 20 people with a prevalence of 5 nose rings and an incidence of 2 so you'll get nice simple fractions and snappy finite decimals. But the idea is the same. And now I'm going to write a dreaded formula!
# of people who
When we write formulas we like to save space by using short symbols in place of long phrases so we might write this as:
where R=number of people
*3/18 happens to be the same as 1/6, and one sixth can't actually be written as a decimal because it would be infinite, so 1.67 or 67% is only a close approximation. Not worth worrying about.
This isn't even the first installment in the curriculum. It's something I'm going to hand out to read before the first class. Many of you will find it completely unnecessary. Some may feel insulted by it, but please don't be: lots of people out there actually, truly need to read this. If you feel you don't, read it anyway as a lesson in what lots of people actually need to read. If you are matho-phobic or hate math or think you just can't possibly understand it, this will help. I hope.
In public health science, and for that matter in most fields of scientific inquiry, we frequently talk about proportions, rates or percentages.
These all mean exactly the same thing!
When people speak of proportions, there is a tendency to represent them as decimals, like this: .9 (pronounced "point nine.") When people speak of rates, they are probably a bit more likely to represent them as fractions, like this: 9/10 (pronounced "nine tenths," or "nine out of ten.") To get the percentage, you just multiply by 100: 90% (pronounced "ninety percent.")
They all mean exactly the same thing! There is no difference at all. I would not be doing any violence to the English language or to mathematics to speak of a proportion of .9, a proportion of 9/10, or a proportion of 90%. There is no difference at all, not even a little tiny difference. None.
For some reason, when I show people a percentage -- 90%, 87%, whatever -- they usually say that's fine, they get it. But when I show them .9, or .87, the very same people often say they don't get it, they can't possibly understand it, it's math and it's just too confusing. That is like saying you understand me perfectly well when I say a Ford is a car, but it's impossible to understand or follow what I'm saying if I say a Ford is an automobile.
There's nothing to understand. There's nothing to "get." There is no deep meaning or special attribute of the symbol .9 that makes it any different from the symbol 90%. If you are at all confused, just keep in mind that the space just to the right of the decimal point is 10ths. .9 = 9 tenths = 9/10 = 90/100 = 90%. The next space is hundredths. .97 = 9 tenths + 7 100ths = 90 100ths + 7 100ths = 97 100ths = 97%. That's all there is to it. If you still think you don't get it, it's because you are convinced there must be more to it than that, that there must be something I'm not telling you, some deeper secret. There isn't.
Probabilities: Probabilities are a lot like proportions. If 90% or .9 or 9/10ths of the people in the room are right handed, and I pick somebody at random, the probability that person will be right handed is 90%, .9, or 9/10. We will often say "nine out of ten" for a probability but it means exactly the same thing to say .9 or 9/10 or 90%. It obviously saves space to write .9 and it makes calculations easier, so that's what I will do most of the time. If this bothers you, you can think "ninety percent" every time you see .9, and it will be just fine.
Formulas and equations: Mathematical formulas and equations give lots of people the heebie jeebies. As soon as they see one, they stop reading and they stop thinking. One reason for this, I think, is the convention, when writing about mathematical subjects, of first writing down the equation, and then telling the reader what the symbols mean. The result is that you'll see a bit fat equation sitting in the middle of the page, and you have no idea what it means, so you feel stupid. But remember, at this point, even Einstein has no idea what it means. You have to read the next sentence, where the person tells you what it means, and look up at the equation and back and forth between the equation and the sentence underneath it to get what all the symbols mean. For example, suppose I write this:
P(RH) = .9
You're baffled and you're mad at me because you don't know what that means. But all you had to do was wait for me to tell you. "P" means the probability of whatever term is enclosed in the parentheses right after it. "RH" means being right-handed. So P(RH)=.9 means "The probability of being right-handed is point nine" (or ninety percent if you prefer).
Why didn't I just say so in the first place? Because I want to use this idea more generally: I want to use this structure in arguments and equations where I'm not just talking about being right-handed and .9, but whatever phenomenon and whatever probability happens to apply. The equation is a handy structure that doesn't take a lot of space to write down and captures the ideas I want to talk about, not just the specific case.
So what I am going to do is first, discuss concepts qualitatively, in prose, with as little use of mathematical symbols as I can get away with. I'll only use mathematical symbols when I'm pretty sure it will make it easier, but we're going to be talking about mathematics so it will be impossible to avoid referring to mathematical concepts such as one thing being equal to another.
Then I'll use one or more specific examples and maybe do some arithmetic with them to show you how the idea works.
Then, and only then, I will present general formulas that embody the idea. If you don't like that part, you can skip it. It doesn't need to turn you off to the rest of it.
Any questions? Are we ready to begin?
Saturday, April 17, 2010
No, the title does not signal an inane quip, I really do want to start my discussion of probability and statistics with some musings on the philosophy of science. I'll try to keep it all as clear and bullshit free as possible. Let me know if I fail.
For a long time, as people did what we today recognize as science or something like it, philosophers didn't fire up any neurons worrying about what they were doing. Archimedes, Eratosthenes, Galileo, Newton, Herschel, Darwin, pretty much just did their thing, while philosophers worried about the moral virtues and the noumenon and what not. By the 20th Century, however, distinguishing between scientific and unscientific beliefs and methods of inquiry had obviously gotten to be important. Philosophers came up with an idea called positivism, which in a nutshell held that a statement is meaningful only if it can be verified, and that it's meaning is equivalent to the means by which it can be verified.
This would seem to imply that there is some stuff that we can totally know -- assertions that can be fully established as true -- and that any other kind of assertion is just gobbledygook of no interest to those who wish to live by the light of reason. However, it soon became clear that this doesn't really work. The kinds of general statements about the world that constitute interesting science are difficult or maybe even impossible to prove in a formal sense. Newton's theory of gravitation, as a matter of fact, was not exactly true. It was true as far as anyone could tell with the accuracy of measurement and the conditions available to Newton's scrutiny but then along came Einstein and with better instruments we found that his theory is more accurate.
But does that mean that Einstein's theory is proved, or that even in principle we will ever have the means to demonstrate as a matter of formal certainty that it isn't wrong somehow, somewhere? Not at all. In fact physicists have been working very hard for a long time to do Einstein one better, and develop a theory that unifies gravity with the other cosmic forces. So they certainly don't think Einstein's theory is a settled matter. But does that mean it is not a scientific theory? Obviously not.
So Karl Popper proposed that at the very least, even if we couldn't really prove anything, a scientific proposition had to be falsifiable. There had to be tests available to show that it was not so. But that turned out to be a bit of an oversimplification as well. One spanner was thrown into the works by the Austrian mathematician Kurt Goedel, who proved that in any logical system at least as complicated as number theory -- basically everything you can say about numbers using arithmetic -- there are true propositions that can never be proved, which implies that their negations -- false propositions -- can never be falsified. To be sure, he's talking about abstract systems of deduction, not empirical investigation per se, but scientists use mathematical reasoning all the time to describe the world, plugging empirical entities into formal systems of logic. So Goedel's theorem (called the Incompleteness of First Order Arithmetic) was a bit disturbing.
Another problem was that physicists discovered that the world at very small scales -- where the electrons and protons and photons disport themselves -- is not deterministic, but can only be described in terms of probabilities. By the time you pile up enough atoms to make an object apprehensible to the senses, those probabilities average out so that it is extremely unlikely your coffee cup will suddenly jump off the table. But it is only extremely unlikely, it is not officially impossible.
Since the very tiny quantum world and the larger scale world are linked, this means that the universe as a whole does not have the deterministic quality that animated positivism and related philosophical schools. People used to think that if you could know the position and momentum of every particle in the universe, and you had a sufficiently powerful computer, you could know the future. But it turns out that you can't simultaneously know the position and momentum of even a single particle, nor can you know when it might decay or change its energy state. You can only make a probabilistic statement about such events. If you wanted to assure the unpredictability of the future, you could rig up a detector that would respond to a radioactive decay event by tripping a switch that would do something really, really big, like blow up a dam; and you could have it wait for an event with a 50% probability of happening at any time within 100 years. Hmmm.
Absent such exotic experiments, the macro world is not so uncertain. If you knew all of the forces acting on a roulette wheel and the ball -- the precise coefficient of friction of the bearings, if you could map out the turbulence of the air around it and precisely how it affects the motion of the ball and the slowing of the wheel, the coefficient of restitution of the ball vis a vis whatever parts of the wheel it might touch, and so on, and the exact vector of the ball and speed of the wheel at the beginning of the spin, in principle you could predict what number will come up. But you can't possibly know all that. The tiniest variation in initial conditions, below what you can possibly measure, will produce a completely different result. Like the weather, it is a so-called chaotic system.
What does it mean when the guy on TV with the perfect teeth and the hairpiece molded from a single piece of plastic says there is a 50% chance of rain tomorrow? How can we verify his statement? Either it rains tomorrow or it doesn't; either way, he was right. So is the statement meaningless? No. What it means is that if he makes that prediction 100 times, we should expect it to rain about 50 times. It might not rain exactly 50 times -- maybe it rains 52 times, or 47 times, and we'll let him get away with it. But if it rains 80 times, we'll decide he's a lousy forecaster.
Similarly, assuming there are 38 slots on the roulette wheel, we'll call it honest if, in a thousand spins, each number comes up about 1/38 of the time. Unfortunately, 1,000 is not divisible by 38, so each number cannot possibly come up the same number of times. We'd like it if most hit 26 times and some hit 27, but that's actually very unlikely to happen. You'll most likely have some 29s or 30s, and some 23s and 24s in there, and maybe even bigger deviations. That's why once in a while, somebody walks away from the table a winner.
It turns out that science depends very heavily on probabilities. When we observe variations in populations -- whether they be of people or of stars -- we can only estimate the probability that the same patterns pertain to the people or stars we haven't observed. We can't really prove anything, or necessarily know how to falsify most of the interesting scientific theories we might come up with. That doesn't mean we might not end up falsifying any of them eventually, it just means we don't have to know how to do it when we first assert them in order for the assertion to be meaningful.
That's more than enough for now.
Friday, April 16, 2010
should I decide to accept it -- actually I have decided to accept it, but I don't yet know if it's Mission Impossible -- is to develop a curriculum in probability and statistics, not for dummies, but for real people who are not math majors, or not necessarily any kind of majors, including people who have not attended college.
Naturally, that means I'll be trying out some stuff here. So you'll have to get used to it. I've thrown up posts from time to time on the subject, but now I'll have to be more systematic and, I also realize, more philosophical. Probabilistic reasoning is pervasive in science. The essentially probabilistic nature of most scientific propositions has essentially overturned the positivist theories of knowledge which once were considered the basic philosophy of science, and has also made the falsification criterion for scientific propositions obsolete, at least in its simple form.
Oh wait, that must seem like word salad to most people. I have to explain really basic stuff. Why do we think we know what we think we know? Why is it not a contradiction to say that science is a path to truth but most scientific findings are false? True fact! But not a defense of Paul Feyerabend, or post-modernism, or creationism or pseudoscience. What is taught in science classes, and the big important stuff that scientists believe, is true, in the sense of being as true as we can make it although probably not exactly true; but new scientific findings are out on the edge of what we don't know, not in the comfortable middle of what we do know. And in order to understand that, you have to understand probability and statistics, including that pesky Bayes fellow.
So I'll do my best.
Thursday, April 15, 2010
Since I've already set you up with one downhead riff for today, here's another from three public health lawyers in the new NEJM. You probably haven't thought much about that pesky Citizens United Supreme Court ruling since it came down in January but that's because you're living in a fool's paradise. That's the one about how corporations are people and therefore have the same First Amendment rights as you do to spend a billion dollars on an election campaign. Hey, what are you complaining about? You can spend a billion dollars if you want to, kwitcherbitchin.
Anyhow, they point out that insurance companies can now spend unlimited bucks to run attack ads against candidates they don't like, in the month before the 2010 election. Of course they would never do such a thing, just to protect their pecuniary interests. I mean, come on, corporations have souls, they have moral scruples, they care what happens to you.
If you think about it, drug companies have certain ideas about the FDA, beverage companies have certain ideas about sugar taxes and what's in school cafeterias, Monsanto has certain ideas about what can and cannot be dumped into the river . . . and just like you, they can now spend billions of dollars to elect the candidates they like. Viz the previous post, consider the poor, beleaguered coal companies.
It's gonna be a wonderful second decade of the 21st Century, lemme tell yuh.
Do views no longer differ? Here's a straight-up story from CBS News. March was the warmest on record, and "climate researchers have been reporting rising global temperatures for several years as a result of what is called the Greenhouse Effect, in which rising levels of carbon dioxide and others gases in the atmosphere trap heat instead of allowing it to escape out into space." No qualifiers, no obligatory second opinion from denialists, no bullshit.
On the other hand, it's a pretty low-key report. This is in fact the biggest story of, well, the millennium, and it only gets major attention from the corporate media when the well-funded denialist publicity machine dumps a new load of BS. So please, bring yourself down with this. Do it for the children.
Wednesday, April 14, 2010
KG Smolderen and a multitude of the doctorly host report in the new JAMA that people who lack health insurance, or who are worried about out of pocket costs, delay longer before they show up at the hospital after a heart attack. Actually it's worse than that because they could only study the people who eventually made it there alive.
I would like to say, "Well duhhhh," but keep in mind that a favorite line of people who opposed the reform legislation was that we already do have universal health care when we really need it. Indeed, the greatest president of the 21st Century, the visionary whose portrait will one day be on the $3 bill, said "I mean, people have access to health care in America. After all, you just go to an emergency room."
Maybe so, but if they know it's going to cost them thousands, or tens of thousands of dollars, they are not inclined to do so. They'll hope it's just a bad case of indigestion. When people get there late, they are more likely to be rehospitalized, so it just ends up costing more in the end -- except of course for the people who have the good grace to just drop dead. Of course, the uninsured people are more likely to have a heart attack in the first place because their blood pressure and cholesterol are uncontrolled.
But we can't provide universal coverage because then we'll have rationing. Dumbasses.
Tuesday, April 13, 2010
Despite the serious backsliding of the past few decades, we should remind ourselves that we are still a long way from the 14th Century when our European cultural forebears were ruled by a despotism based in claims of supernatural authority and fundamentally nonsensical mysticism. The institutional church of that era is still around, still just as irrational and oppressive, but far less powerful. Various forms of competing nonsense have arisen to enchain people's minds, but the realm of freedom has enlarged.
Depressing it is, however, for me to realize that I was raised in a bubble of enlightenment and truly, until mid-life, had no idea how deeply our culture is still steeped in anti-rationalism, and how much indoctrination and ideological tribalism still rule political discourse. The ridiculous spectacle of a self-styled revolutionary movement rising up against nothing in particular (as usual, Hunter says it well) has truly impressed me. They claim their elected representatives aren't "listening" to them. Well, what exactly aren't the politicians hearing?
- These people want tax cuts. Well, Obama cut their taxes.
- They want cuts in federal spending, but polls consistently show that they don't want any cuts in programs that constitute any substantial part of federal spending . . .
- E.g., they want the government to keep its hands off of Medicare. Okaaaaayyyy.
- They don't want death panels. Okay, there aren't any.
- They didn't like the bank bailout. That was signed by George W. Bush, who is no longer president.
- They don't want socialism. Not to worry.
- They don't want anybody to take their guns away. The only gun-related legislation under the present administration allows them to carry weapons in national parks.
And so on. Now, some of them want Christian dominion over the earth, which the present government is not delivering, to be sure. Maybe they think the End Times are at hand and Obama, or Javier Salana, or Richard Dawkins, is the Antichrist. I dunno, but that would not suggest to me a situation amenable to political action. Supposedly the Democrats are doomed to lose massive numbers of seats in the fall election because the people are angry damnit, they're mad as hell and they aren't going to take it any more. But why? What exactly is the problem here?
I will be happy to hear a coherent explanation.
Monday, April 12, 2010
It seems that the Marion County, Florida DA is prosecuting Olympic equestrian team member Darren Chiacchia for putting a former lover at risk for contracting HIV. According to this story by NYT's Katie Thomas, 32 states have laws that specifically criminalize transmission of HIV or putting others at risk for HIV.
It so happens I'm just now finishing up a paper about whether and how physicians counsel their HIV+ patients about sexual risk behavior. Our assumption was that it ought to be a goal in HIV care to work with patients to reduce the chances that they will transmit HIV, as well as the chance of their becoming reinfected or acquiring other sexually transmitted infections. (Even if you're already HIV infected, you don't want to be infected again because the new strain of virus might be resistant to the medications you are taking.) A couple of the patients in our data appear to be engaging in risk behavior. Actually one of them definitely is, and he says so, but the doctor doesn't respond with any clear suggestion that he ought not to, or any suggestion about how he could reduce risk to himself and others. My co-authors and I have have considerable discussion about exactly what doctors ought to do in these circumstances, but I must say it never occurred to any of us that there should be a specific law for people with HIV, for many reasons.
I do think that people ought to take responsibility for the safety of their sexual partners, as well as themselves, and that physicians should convey that message.
However . . .
First of all, as some of the law enforcement officials Thomas interviews suggests, it was hard to prosecute people without the laws because you couldn't show malicious intent. Well exactly. The people aren't generally intending to infect anybody, they are just intending to have sex -- in Mr. Chiacchia's case, not casually but in the context of a romantic relationship. There are plenty of ways in which people in sexual encounters, and relationships, fail to take care of each other or to be fully honest. Why single out HIV in this way? It seems to me that if someone becomes HIV infected as a result of irresponsibility or dishonesty on the part of another, they can try a civil suit. And you do bear a part of the blame, if you don't even bother to ask.
Second, what we have here is a spurned lover, who as far as we know did not even become infected, whose motive for going to the Sheriff may well have been revenge. We have a he said/he said situation in which the only evidence that Mr. Chiacchia did not inform the complainant, and/or consistently practice safe sex, is the complainant's word. This seems to be opening up a good deal of room for mischief.
Pragmatically, if people know they can be at legal risk, all they have to do is not get an HIV test. If they don't know, they can't be prosecuted. That's obviously counterproductive. In fact, if you have treated HIV with suppressed viral load, you are at very low risk for transmitting the virus. That's no excuse to have unsafe sex -- you don't know for sure that your viral load is fully suppressed right now, even if it was last time you were tested, you could be reinfected, and there are other STIs out there. But still, from the standpoint of public health, what we want is for people to know their HIV status and get treatment.
Finally, if somebody really does maliciously try to infect someone with HIV, you don't need a special law - it's already plain old assault and battery. Some of these laws criminalize HIV+ people spitting, or biting people, which will not transmit HIV, by the way, so it's just a response to irrational stigma.
We'll get a lot more benefit from education, persuasion and promoting a culture of sexual responsibility than we will from punitive approaches and discriminatory laws. All these laws should be repealed.
What do you think is the lead, screaming, headline top story on the CNN web site right now? With video no less? The shroud of Turin, which some Christians believe is Jesus Christ's burial cloth, went on public display Saturday for the first time since it was restored in 2002. Two million people, including Ratzi himself, are expected to view it. Of course the article is Fair and Balanced concerning the authenticity of the artifact.
Unfortunately if you try to research the shroud using the Internet search engine of your choosing, you will find the first two or three pages of results are dominated by tendentious horseshit. Here's the 4-1-1. I mean come on now. This is a no-brainer. CNN needs to get a grip. It's embarrassing, on the same level as crop circles and the Jersey Devil. Can't we please grow up?
Friday, April 09, 2010
At this week's grand rounds our medical director suggested googling "Czech Republic tobacco New York times" if we wanted a thrill. The hit is a Bob Herbert column that's a few years old but it's still pretty relevant on several levels. It seems that officials over there in Dvorak land were worried about the high medical costs of tobacco-related disease. Philip Morris commissioned a study to prove them wrong.
It turns out that "The premature demise of smokers saved the Czech government between 943 million koruna and 1.19 billion koruna ($23.8 million to $30.1 million) on health care, pensions and housing for the elderly in 1999, according to the report." I believe someone actually made a similar calculation for the United States. Eliminating smoking would mean big costs in future social security and Medicare expenses as people had the temerity to live on into old age.
I point all this out because it is an inconvenient truth: we will never save money in the long run by preventing disease and promoting health unless we somehow achieve a state in which most people live in good health and then quickly drop dead; and more people keep working well past 65. That's not where we're going, unfortunately. The more people live into old age, the more expensive their medical care will be, because we are absolutely nowhere near arresting the aging process.
I realize this is a downer, but it has to be factored into our thinking about the future. We face rising unfunded pension obligations, medical costs, incalculable unfunded need for infrastructure replacement, and a whole lot of other problems we need to solve, and a declining percentage of the population that's of what has traditionally been considered working age. I think we're just going to have to try to encourage more people to defer retirement. That doesn't have to be a drag if work can be rewarding.
Update: I wrote this before I came across this on the front page of Kos. I swear.
Thursday, April 08, 2010
If you happen to like science, and you want a feed of the latest exciting stuff that's going down, Physorg.com shoots it at you through a firehose. It's kind of advertising heavy, so just avert your eyes.
I like this story -- these researchers think high CO2 levels in the blood may be behind so-called "near death" experiences. I'd say we have a long way to go before that's confirmed, but it does remind us that our conscious experience is a manifestation of the physical substrate of the brain. To my mind, there are two great mysteries that science has yet to get close to, which people have such need to understand that they are principal drivers of religious belief. (Fear of death and the inability to accept mortality is another, but death of course is no mystery to science, just an inconvenient truth.)
These are the nature of consciousness; and the origin of our universe. We can describe both of them to some extent, but we cannot explain either one of them. Why is there something rather than nothing? That's the most basic question there is but it is imponderable. Given that there is something, why this, why what actually is? What caused it to come into being?
As for consciousness, it is absolutely compelling to everyone, at least everyone I have ever spoken with, that it somehow transcends physical reality, that it is more than the sum of our neural firings. But what? Why? Is it connected to some deeper truth to which we do not have access?
So far at least, the methods of science bite on granite when it comes to these questions. Just so you know I fully concede that.
Wednesday, April 07, 2010
Paul Kettl, M.D. (yeah, he should get a vowel) writes an important essay in JAMA, unfortunately behind the subscription wall. He's for the Death Panels, or rather what was labeled Death Panels by depraved Republican liars -- the proposal that Medicare pay for end-of-life counseling if people want it. Dr. Kettl is a geriatric psychiatrist who used to work in an inpatient unit where most of the patients had dementia. He writes:
As part of the care . . . we would meet with the patient and then with the family to explain the type of dementia, the typical course that could be expected. . . . Finally, we talked about what the future would bring, usually giving the already-burdened patient and family an explanation of the inexorable downhill course of progressive dementia leading to death. We . . . asked the patient and the family about what care they may want both now and in the days ahead.
... [F]amilies typically said two things to us. First they thanked us for taking the time to share some education and discuss these issues. . . . [T]he second thing the families always told us: "No one has ever sat down with us to tell us what was going on, what we could do."
Dr. Kettl goes own to explain that primary care physicians, with only a few minutes available for each visit, just don't have time to do this. Medicare doesn't pay for it. As you will recall, it was proposed as part of the health care reform legislation, but howling mobs of enraged citizens hurled so much abuse at members of Congress over the proposal that they took it out.
Physicians should ask [patients' wishes], and it is reasonable to submit a bill for this meeting. . . . Patients should expect that care will be available for their illness . . . but they should not have procedures forced upon them out of ignorance of which medical procedures they may have chosen. That's why I'm in favor of 'death panels.' But it won't be in this or any bill in the near future. The proposal was sunk by a phrase. . . .
This was among the most shameful moments in our recent politics, and it has plenty of competition. Sarah Palin has the morals of a tapeworm.
There's an MP3 if you care to listen. I can't figure out a way to embed it here, sorry to say.
Tuesday, April 06, 2010
is that reality will bite you in the ass. And much sooner than knowledgeable people were predicting even a short time ago. As in, approximately right now.
It's not my expertise, so haven't devoted many posts to it, but I do follow this very closely, as should we all. The zeitgeist has yet to catch up with where climate science has gotten to very recently, so I will tell you: it's really, really alarming. As Joseph Romm tells you in the above-linked post, if we go on the way we are now -- not a worst case or unlikely scenario, but what is exactly in the middle of what is likely to happen -- the continental United States will be 10 degrees Fahrenheit warmer by 2090, and the sea level will be 6 feet higher. It could well be worse than that.
But in fact the changes are going to be very obvious much sooner, probably starting right now. We've had a bit of a slowdown in the process for the past few years due to a solar minimum and the state of the southern oscillation, but that is over. We're seeing extreme weather anomalies all over the place, and we're likely to see wildfires in North America this year like never before. Believe me Alexander Cockburn, David Koch and James Inhofe, there is no percentage in what you are doing -- you will very soon be totally exposed as utter fools, and ultimately remembered among histories greatest villains.
I have been asked for further discussion of screening tests and the associated good, bad and ugly. First I'd like to offer a little more math for those who like it -- and I know you're rare and strange. Others can skip this if they like. One way of understanding Bayes' Theorem that may be helpful and accessible to people is the concept of the Likelihood Ratio, which is explained here very well and clearly, I think. The explanation is intended for physicians, who generally speaking aren't math wizards, so it should do well for a general audience as well.
Basically the Likelihood Ratio (which is easily calculated as the sensitivity* of a test divided by 1-the specificity), is the amount by which the probability of actually having the condition changes with a positive test. As you can see, if the probability is quite low to begin with, even multiplying it several times still leaves a low probability. For example, if the Likelihood Ratio is 10, and the prevalence of the condition in the population is 1 in a thousand, then a positive test means you still have only a 1 in 100 chance of having the condition.
The Negative Likelihood Ratio (1-the sensitivity divided by the specificity) is the amount by which the likelihood of not having the condition changes with a negative test. Under some circumstances, it can be just as bad to think you've ruled out something when it's really there as to think you've found something that isn't there. A good example is the Lyme Disease test, which is often negative even when the person does have Lyme Disease.
So a good screening test has to be both highly sensitive and highly specific; if you set a cut off level that is low enough to be highly sensitive, but it's not highly specific, you'll have a lot of overdiagnosis. Conversely, if you set the level high enough to be highly specific, you'll lose sensitivity and you may decide not to worry when you really should. The Prostate Specific Antigen test for prostate cancer is in this category, unfortunately. If you really want to get wonked about it, you can read it here, but I offer this only for the sake of good form.
So what are the harms of overdiagnosis? They are legion. For the sake of good blogging form, I'll tackle that next time.
* Remember that the "sensitivity" is the probability of a positive test if the person actually has the disease; the "specificity" is the probability of a negative test if they do not.
Monday, April 05, 2010
I thought about posting this yesterday. I must tell you that the delay was not about deference to anybody's sensibilities, I just didn't have time until now. I'm going to talk about the Catholic Church, specifically. I could write about other religions -- I have and I will. I don't single out the Roman Catholic Church particularly, I think that all religions are equally ridiculous. It just happens to be my subject today.
We don't know, and we probably never will know, for how long Catholic priests have been raping and otherwise abusing children with the full protection of the institutional church. I expect it's been going on for hundreds of years, actually. Go ahead, show me some evidence that it has not. I had a boarding school roommate who grew up in a Catholic orphanage and he knew exactly what the church was all about. As it happened he was a tough kid who fought them off, but most kids could not, of course. I had another friend who attended a school in Andover run by "Christian" brothers, and he told me that the monks used to beat the crap out of the kids all the time, for kicks. He probably didn't feel comfortable mentioning the rapes, which I'm sure happened as well.
The clergy sexual abuse scandal first erupted here in Boston, but everybody with half a brain already knew that it went on everywhere and had for a long time. Now it's coming out worldwide, and of course the Bishops are reacting the same way they did here -- all this talk about the issue is a malicious attack on the church, it's a conspiracy by the news media, nobody has a right to question our motives or our moral authority which comes from God almighty so we don't have to be accountable to the law or anybody else. Since this blog is about public health, I'm going to do my best to restrict my focus to the impact of the church on the issues we normally discuss here, but I could say a lot more.
The Catholic Church is a force for evil in many very important respects. The idea that people might have sex for reasons other than procreation is more offensive to the Bishops than the idea that they might die a horrible death from AIDS, so they forbid the use of condoms. They actually run hospitals here in Massachusetts where it is forbidden for health care providers to distribute condoms, or to recommend them to people. That is evil.
So is the condemnation of people whose sexuality does not conform to their rigid -- and utterly hypocritical -- bigotry. When sexuality is stigmatized and driven underground, nothing but evil ensues, from the persecution of Oscar Wilde, to the suicide of Alan Turing, to the self-loathing that leads people to like Larry Craig to live their entire lives as lies, to widespread high risk behavior and the near impossibility of engaging people in positive public health programs. The Bishops demand that people live in phony marriages that scar children, that women endure abuse at the hands of men they are forbidden to divorce, that people who have found true fulfillment after one or more failed attempts must live in shame. (Unless, of course, they happen to be politically powerful or wealthy.) It's perfectly okay to be a psychopathic Mafia Don, but it's not okay to be gay, or remarried.
Remember Terry Schiavo? Remember those brainwashed teenagers following some demented monk around with tape over their mouths with "life" written on it? Obviously the church was not defending "human life," in that case, but wallowing in its culture of death. Think of all the good that could be done with the resources squandered on keeping corpses in a state of simulated animation -- and the continual torment and misery of loved ones who believe they have some moral obligation to preserve the mortal tissue of people who are long gone.
The Bishops aggressively inject all of their moral depravity into politics, but when it comes to the supposedly universal messages of the Gospels, they won't abide it. The Pope ordered Fr. Robert Drinan to retire from politics because Drinan was a campaigner for peace, justice and human rights. Not an appropriate role for a priest at all.
Then there is the question of abortion. I've certainly said plenty about it in the past, but I'll just remind everyone of the key points. There is nothing, not one word, anywhere in the Bible that condemns abortion or even mentions it, even though abortion, and for that matter infanticide, were widespread in Biblical times. The obsession of the Church with abortion is a purely modern invention, which has nothing to do with human life and everything to do with fear and loathing of female sexuality. As I wrote earlier, "In fact, if you believe in God, then you also have to believe that God is the most prolific abortionist in history, by many orders of magnitude, because something like 2/3 of "human lives" -- the zygotes created at the moment of conception -- never successfully develop. Most of the time, the woman is not even aware that she was ever pregnant. If abortion is murder, this is the death of tens of millions of innocent children every year. Should it not be the absolutely highest priority of medical research to save those babies' lives? But you never hear a peep from these people about it."
The Bishops are depraved moral idiots. The Catholic Church's doctrines are preposterous, nonsensical. The Church has been an enemy of science, of human rights, of justice, and of human progress throughout its existence. They no longer torture people to death who try to defy them, but that's only because they don't think they can get away with it. The Catholic Church is one of the most profoundly evil institutions on the planet. Humanity, and the rest of the biosphere, will be much better off when it finally withers up and blows away. I hope that will be soon.
Friday, April 02, 2010
It's ridiculous that this is hidden behind the subscription wall, but you can read the first 150 words and I'll say something about the rest of it.
David and Steffie are not at all gruntled by the Big Fucking Deal the president signed last week. As you know, I basically agree but I ultimately decided that it does make it more plausible, not less so, that we'll end up where we need to be.
As D & S point out in the part you aren't allowed to read, "competition" among insurers is based, not on providing at better product at a lower price, but on a) taking your money and then b) finding ways to avoid paying for your health care. While the legislation purports to restrict their ability to do (b) in exchange for more of (a), they will no doubt find all sorts of tricks, dodges and scams to do (b) anyway. Meanwhile, there is no affirmative reason for them to exist.
In spite of "insurers" failing to insure, medical costs will continue to inexorably rise, as more money is pumped into the system, "insurers" will continue to skim their third in exchange for nothing, and no serious efforts are made to rationalize the use of medical resources. As a result, many people will still have inadequate insurance that will leave them financially ruined if they become seriously ill, and many people won't really be able to afford the insurance they are legally required to buy.
All this is true. We need universal, comprehensive, single payer national health care, still, as much as ever. However, we now have a nationwide regulatory regime over insurers. Once the bonds are in place, they can be tightened. And the logic of the situation says they will have to be as the federal government now has more skin than ever in the game. If the people can be helped to understand the issues correctly, they will see that it is their money which is being stolen by the insurance companies, and they will want it to stop. And we now have a structure in place to accomplish that.
That's my plan, anyway.
Thursday, April 01, 2010
on the significance of religion in people's lives. As you may have heard, we've had record rainfall in southern New England and the pathetically tiny state of Rhode Island -- which isn't even an island -- suffered the most. The economic damage is devastating:
Demetri Skalkos, co-owner of McNamara's liquor store, said about 3 feet of water stood in the basement. He said he was worried about losing business over the traditionally busy Easter period. "This is the Holy Week," he said. "If we don't do business now, when are we going to do business?"
At last the true meaning of Easter is made clear to me. None so blind . . .
This is apropos of my project of last evening. Since the Book of Revelation is central to the world view of a large percentage of Americans, I figured I'd read it again just to see what all the excitement is about. I make the following observations:
I didn't know those kinds of mushrooms grew on the Greek islands.
The book was written in the early First Century CE, in other words around the year 130. The author repeatedly purports to describe events which are "at hand," imminent, about to happen. Curious that he meant by that "in a little less than 2,000 years from now."
The author spills some ink near the beginning on individual messages to seven churches around the eastern Mediterranean. Among other idiosyncracies, he really, really doesn't like the Nicolaitans. Nowadays, nobody is quite sure who the heck they were.
The various visions seem to correspond to separate mushroom trips. They don't constitute a coherent chronology. They are linked by some recurrent images and numerology, but in order to develop a narrative you have to go in and arbitrarily rearrange the events in an order that makes sense to you. This is why the End Times believers have varying versions of what is going to happen when. The currently popular idea of "the rapture" -- which is not explicitly described, actually, but more or less reverse engineered from the idea that some people will wind up in the heavenly city -- followed by the tribulation and the thousand year reign and finally the end of the universe as we know it, is not a story actually told in the book.
An inconvenient truth: if there's one thing in the book which is absolutely, incontrovertibly crystal clear -- and there is only one thing, other than not liking the Nicolaitans -- it is the number of the elect. There are precisely 144,000 of them. Even more precisely, they consist of 12,000 people from each of the 12 tribes of Israel. Of this, there can be no doubt, it's right there. That would seem to be bad news for the overwhelming majority of Christians, no?
None of this was ever supposed to make any sense, but still, the question is compelling. Why in the delta quadrant of the galaxy do millions of Americans believe in this apocalypse crap? What is the psychology or sociology that drives this idiotic nonsense in the same era when we are actually unraveling the deep secrets of the universe and really can glimpse the future, at least dimly? Just exactly what the hell is this wackiness all about?