Mammograms, Drug Tests, and Bayes

Mammograms, Drug Tests, and Bayes

The nation has been bombarded with hysteria about the new recommendations for mammograms for the last week or so. The real concern behind the recommendations was the high incidence of false positive results and their costs to the people involved.

As I listened to the debates, I realized two things: first, no one had any idea about the numbers involved in the analysis of the problem; and second, the same mathematics are crucial in the debate over drug testing in schools and the work place.

The crucial problem in both issues is that of false positive results in the testing: a mammogram showing that a healthy woman has breast cancer or a drug test showing that an abstinent subject has used drugs.

That problem can only be analyzed through the application of a subtle and sophisticated branch of advanced mathematics known as Bayesean analysis, or conditional probability.

The issue, and why it is a problem, can be demonstrated through a simple example that uses nothing more complicated that addition, subtraction, and decimal arithmatic.

However, if anyone gets the urge to present this information to a school board, get a statistics or probability instructor from the local college to help you. Very few high school math or science teachers are familiar with it, and the chance of finding a school board member who knows anything about it is about the same as that of finding a penguin on Miami Beach.

 * * *

Assume that a drug test is to be given to 10,000 high school students. Before the test is given, two things are known:

1. The test is 95% accurate, or on the average, out of every 100 tests given, 5 of the results will be wrong. (Most of the available tests are advertised as 99% accurate, but that figure is derived from rating the test in carefully controlled laboratory situations with randomized samples. In real life, with poorly trained part-time administrators, poorly handled specimen cups, bad sanitation conditions, sloppy records, uncalibrated lab equipment, and out-of-date or impure reagents, almost all of them will perform at less than a 95% level).

2. Only 5% of the group to be tested will have used the drug in question. (In actuality, only marijuana use will have reached the 5% level -- and it presents other, different problems). No other illegal drug is use levels nearly that high.

Based on these assumptions, of the 10,000 people tested, 9,500 will be non-users and 500 will be drug users.

When the 500 drug users are tested, 5% of the test results, or 25, will be incorrect. The other 475 results will be correct. The result is:

475 true positives (drug users found to be drug users)

25 false negative (drug users found to be non-users).

These results, by themselves, are harmless and probably acceptable. But what happens when the test is administered to the non-users?

The 9,500 tests administered to non-users will also be right in 95% of the cases, or 9025 correct results. Wrong results will appear in 5% of the cases, or 475 cases. The results of testing the non-users are:

9025 true negative (non-users identified as non-users)

475 false positives (non-users identified as users).

Now combine the two sets of results:

475 true positives (drug users correctly identified as drug users)

475 false positives (non-users incorrectly identified as drug users).

In other words, if someone fails the drug test, she is just as likely to be a non-user as she is to have used drugs. This result is the same as that one would get by tossing a coin – and the coin toss costs less and doesn’t invade anyone’s privacy. Any test that can get a student kicked off the football team, forced into rehab, or even expelled from school should be more reliable than a coin toss.

The story of mammograms is more complex. The consequences of false negatives – undetected cancers – and of false positives – anxiety, more testing, or even surgery, chemotherapy, or radiation – are much more severe. The test itself is not a simple yes/no like the drug test and the reliability is much less than 95% and depends partially on the skill and experience of the examiner. I will have to leave the full explanation to a professional statistician in another forum.

Toward a More Civil Government

Toward a More Civil Government

For well over a decade the nation’s government has been scarred by acrimony, distrust, bitterness, and strident partisanship. The result has been a marked decrease in the quality of society. Something needs to be done to reconstruct civility. I have a idea…

What if all politicians – both candidates and holders of elective office at all levels – were required to spark a j and mellow out before any public appearance or meeting? No longer would speeches be interrupted by angry shouts of “You Lie!” At worst, there would be giggles and “Love ya, Bro.” The Capitol dining room could quit serving Senate Bean Soup and just put out bushel baskets of Kit Kats and every flavor of Doritos. Think of the difference in senators’ opening statements in committee hearings. They would still be long and rambling, but they would not be harsh, self-serving and untruthful.

The work would still get done. The pols don’t trouble themselves with the details anyway. All the work is done by staffers and attorneys, who would still have to stay sober during work hours. Committee meetings and debates would still be lively, but less rancorous. The risk would be that they could degenerate into food fights. Probably the Democrats should be limited to Ho-Hos and the Republicans to Twinkies so the television cameras could keep things straight. (I originally assigned the snacks arbitrarily, but if someone wants to assign symbolic values to them, that is The Reader’s choice.)

When I first broached this idea, one colleague objected on the grounds that susceptibility to marijuana is genetic and some people would not mellow out. But that’s actually another ground for insisting that candidates toke up in public. What better way is there to exclude congenital curmudgeons and eternal pessimists from positions in which their nay-saying can create major harms?

What is sauce for the congresscritter should probably be applied to those testifying in committee as well. The O.S.S. was testing weed as a truth drug as early as the 1940s. Anyone who has been there knows how hard it is to tell a convincing lie while wasted. Turning a witness on should be at least as effective as making them swear to tell the truth. The problem would be that the truth would be buried under an endless stream of babble. Imagine three wasted automotive executives trying to explain why they flew three private jets to Washington so that they could ask congress for money to help their broke companies.

If congress is mellow, so should be the broadcast political commentators who talk about them. A mellow Bill O’Reilly might make more sense, but the world may not be ready for a stoned Glen Beck. The Limburger could be more believable if grass were substituted for his Oxy. Who would be liable if a wacked Lou Dobbs tried a faint smile and his face shattered into a thousand granite shards? Keith Olberman? I suspect he is already following the program at least part of the time.

The rule would have to include Sunday morning talk shows – hosts, guests, and panelists. The schedule for these shows would have to be extended to accommodate the much more drawn out questions and answers, but they don’t have much competition in those time slots anyway. The panelists present a different problem. My mind boggles at even the idea of a giggling George Will. Perhaps if that frozen-in-place hair were a little mussed and that little bow tie somewhat askew (and who can tie one of those damn things anyway?), a real human might emerge from that bloodless automaton.

This kind of radical change could cause social and economic changes as well. Recent studies indicate that increased marijuana use is coupled with decreased alcohol use. If the Washington power class becomes a stoner caste, what will happen to their booze consumption – now at astronomical levels? Will the top-tier watering holes become taco stands? Will Jack Daniel have to ask for a federal subsidy to avoid bankruptcy? Will K Street become the world’s largest AA group?

If the plan works for the political side of government, perhaps it can also be applied to parts of the administration. The top administrators of the DEA and ONDCP need to be more familiar with the subject matter of their jobs if they are to do them well. As soon as they are confirmed, these top people should be put through a training program in which they experience recreation-level doses of at least the four most common drugs subject to their administration: marijuana, heroin, cocaine, and the amphetamines. These doses should probably be administered over the course of a month to avoid the shock that a more concentrated introduction would cause. These people don’t have the resiliency of teenagers any more.

The training for working DEA agents should be more intense, including at least some of the psychedelics. This training should help to weed out the inherently paranoid and overly suspicious, resulting in a more compassionate and cooperative force. One beneficial side effect could be substantial revenue to the government. Just imagine the earnings of that new reality tv show: “Narcs on Acid.”

Okay, you’re right. This is just a pipe dream. But I think I’ll hold on to the fantasy just a bit longer. As Axl Rose told us, when you’re high, “you never ever wanna come down, come, down, come do-ow-ow-own!

Fig-Leaf Legalization

Fig-Leaf Legalization

In my last posting, I referred to California’s medical marijuana system as “fig-leaf legalization”. The more I think about it, the better that idea looks.

The idea, as pointed out in a recent issue of Fortune among other places, is that the limits and qualifications of the Californian medical marijuana program are so liberal that virtually anyone can qualify. The result is that the medical dispensaries are in fact nothing but retail marijuana outlets – pot shops.

Several factors contribute to this laissez faire operation.

The first is that the state law places no direct limitation on the medical conditions for which a doctor may recommend the use of marijuana. A doctor may recommend its use, not only for relief of chronic pain or adjunct therapy for cancer patients, but for minor conditions like headaches, mild insomnia, or even mild feelings of malaise. (In its first life as a legal medicine before 1937, two of the main uses of cannabis were for migraine headaches and PMS, two conditions for which newer drugs often provide insufficient relief.)

The second factor is that, in American law in general, only a doctor exercising his professional judgment in the treatment of a patient may determine what does or does not have medical value. Subject only to state licensing and disciplinary rules and malpractice laws, that doctor may recommend, dispense, or prescribe any substance or course of treatment he thinks will be of value to the patient. A small exception exists in the case of heroin, which the federal government persuaded many states to ban outright in the 1920s and 30s.

California doctors are now charging $150 for a consultation for a marijuana recommendation. The consultations usually last no more than ten minutes and rarely involve an actual physical examination. They have become a ready source of additional income for a large number of California doctors.

The third factor is that the federal government has no jurisdiction to determine the medical value, or its lack, of any substance. This limit on federal power has been recognized since the mid-1920s and was reaffirmed as recently as Gonzales v. Oregon. (2006) Three major federal statutes are concerned with the way in which drugs are marketed – The Food, Drug, and Cosmetics Act (as amended), which establishes the Food and Drug Administration, The Controlled Substances Act, which regulates the way in which scheduled drugs are marketed, and the Dietary Supplement Health and Education Act of 1994, which grants the FDA oversight of the marketing of herbal remedies and dietary supplements – but none of these authorize any federal agency to determine whether or not any substance has medicinal value.

Many think that the FDA “approves” new medicines, but it does not. The FDA, acting under the Interstate Commerce clause, prevents misleading or deceptive marketing of drugs by requiring that each drug bear an approved “label” [1] .

Once the drug is sold, the FDA has no control over how doctors use that drug. A doctor may then prescribe the drug for other diseases, a practice known as “off-label” uses. For instance, amphetamines are approved for the treatment of narcolepsy, a rare disease, but physicians prescribe them for attention spectrum disorders as well; and now some doctors are prescribing them for patients to use as “brain-boosters”.

The Dietary Supplement Act is also a marketing act, preventing deceptive or misleading marketing of supplements, vitamins, and herbal preparations. The distinction is that the FDA may intervene only after a product is marketed using methods that make unsubstantiated health claims.

Contrary to popular perception, the Controlled Substances Act is also a marketing control act, not one determining the medicinal value of any substance. It divides all drugs with psychoactive effects into two broad categories: Schedule I and Schedules II-V. The Drug Enforcement Administration establishes regulations for the ways in which doctors may prescribe drugs in Schedules II-V (duplicate forms, non-refillable, limits on amounts for each prescription, etc.), but it may not limit the uses for which a doctor may prescribe that drug.

Schedule I drugs seem to be an exception to the general scheme in that those drugs (including heroin, marijuana, MDMA, and most psychedelics) may not be manufactured, distributed, or possessed. However, a close reading of the statutory language reveals that Schedule I drugs are not defined by their medical effectiveness (reserved by the Constitution to the states), but by whether they have “currently accepted medical use in the United States.” In other words, the DEA is not to determine medical effectiveness, but is only allowed to conduct a survey as to whether the drug is currently used by doctors.

In the first rescheduling action (MDMA), the Administrative law Judge recommended placement on lower than Schedule I on the grounds that the drug was in fact used by doctors with the approval of reviewing peers. The Administrator refused to accept the petition and placed the drug in Schedule I. In that case and the two other cases decided by the Courts of Appeals that issue was not presented to the court and the courts made no finding on that definition. The Iowa Supreme Court, using this interpretation of equivalent language in the state law, has ordered the State Board of Pharmacy to reconsider the scheduling of marijuana. The first federal law suit based on this interpretation is now pending in the U.S. District Court in New Mexico. The result could be to force the federal government to follow the lead of the states.

If that legal interpretation controls, the federal government will have no legal force against state medical marijuana, and the AG’s decision not to prosecute compliant medical marijuana distributors suggests that it has also lost its moral and political backing.

One result is appearing that, at first sight, looks surprising, but is predictable in hindsight. With the risk premium for unlawful conduct removed from their cost structure, medical marijuana distributors are lowering their prices. Market rules apply here as they do elsewhere. Reports show some illegal street dealers lowering their prices by up to 20% in order to compete. Illegal dealers have inherently higher cost structures than do legal ones; the illegal dealers and distributors will be forced from the market. Al Capone cannot compete with Anheiser-Busch.

Colorado is rapidly following in California’s footsteps, and three other states have approved distribution systems. Legislative action on medical marijuana is heating up to unprecedented levels, with nation-wide popular support running over 70% in recent polls. Editorial support is also uniformly high.

Outright legalization of marijuana is still too frightening and too radical for many, and therefore probably politically impossible in the immediate future. Decriminalization has its fans and provides some relief for the consumer, but it does nothing to combat the violence, corruption, and harms of the black market; it may even strengthen them by increasing demand. Fig-leaf legalization, following in the steps of California and Colorado, may be an acceptable compromise. It furnishes an excuse to those whose morals may be offended by a pleasure-driven search for chemical happiness while also furnishing a loosely regulated market, avoiding the excesses and harms of full legalization. Paying a hundred dollars a year for a license from a doctor is a small price to pay for demolishing a major part of the War on Drugs.
-----------------------------------

[1]  The label is all of the text, and only that text, which the FDA has approved and which must be included when the drug is sold or advertised. The label must include at least one medical use for which the drug has been scientifically shown to be safe and effective. The label is actually several pages long and is presented as the package insert, which the pharmacist will give to you if you ask for it. It is also included in compendia like Physician’s Desk Reference.