The Value of Life, III

The New York Times had an article in the Sunday Magazine about why we must ration health care. The author, Peter Singer a Princeton bioethecist, wrote more cogently on many of the same issues that I tried to develop in previous posts. One interesting point that he made with some statistics to back up his statement, is that we are rationing health care currently by our access to health care. He points out that the big difference between the rationing in Britain is that we know the names of the people dying due to the denial of care, while in our system, the people who die are unnamed and unknown.

Professor Singer points out that there is a clear bias to save a named person, so rationed national health care is a hard sell. He also notes that it is hard to be sure exactly how many people are dying due to lack of insurance, since this population has many confounding variables. In particular, people without insurance tend to smoke more than those with insurance, and the additional mortality masks other subtler effects.

Both of these points also raise another difficult issue. You might not like all of the people who do better under a national health care system. Your mother or spouse may have treatment denied in favor of someone with unhealthy habits or with a lifestyle you object to. Physicians (ideally) treat all patients equally and don't make moral judgments. A national health care system must do the same.

The method Professor Singer proposes for making the choices required is the Value of a Statistical Life and the Quality Adjusted Life Year (QALY). The first is the amount of money people would be willing to spend to lower the number of fatalities in the population by 1 person, and the second is a portion of a completely healthy life available to a person for one year. Professor Singer acknowledges that both measures of value have serious issues and that they give an appearance of precision where there is none. However, he argues that they are the least bad methods for apportioning medical care. He also notes that various value judgments society makes, e.g., the life of a teenager is worth more than the life of an 85-year old, can be incorporated into adjusted versions of these measures.

I am not sure that I agree with the least bad argument. An imperfect measure of the value to place on a medical treatment will warp how health care is dispensed. It is clear that there is already warping in health care, but we don't know a-priori that we will have a more acceptable warping with a bad but different procedure. This gets back to one of the questions of fundamental interest to me. Is there an appropriate way to determine whether we are making a good decision when we are making that decision in the absence of knowledge?

Decision Analysis

I have taught a business statistics course for about two years at Southern New Hampshire University, a small private school in Manchester. The course covers confidence intervals, hypothesis testing, regression analysis, forecasting, etc. All of these techniques have been applied poorly, even disastrously, at times. I try to stress to my students that a quantitative technique pointing to a nonsensical decision may be wrong, and they should check their assumptions and their arithmetic again. (They should be very skeptical of a quantitative analysis that seems to justify an immoral decision.) However, the lecture which always makes me feel dirtiest is when I explain decision analysis.

One aspect of decision analysis lays out the choices which face you on the left side of a table and the possible futures you envision on the top of the table. For every entry, corresponding to a particular decision and a particular future, you determine a cost or a payoff. There are a number of methods for deciding which choice will most likely lead to the best outcome. These methods can take into account how much risk you are willing to accept or how probable you view a particular outcome. There are alternate methods for laying out more complex decision paths, but at its heart, decision analysis quantifies the payoff or cost of your decisions.

It is very hard to argue that a careful ordering and consideration of your choices and their likely outcomes is a bad way to approach decision making. In fact, when Israel was readying for negotiations after the 1973 War, they used decision analysis to prepare the negotiating team. The participants didn't view the payoffs listed in their tables as particularly useful; however, the process of preparing such a table also forced careful consideration of all options and what their global and regional implications were. The decision analysis was constantly updated during negotiations, and the participants also discovered a lot of value in seeing how their estimations of payoffs changed as decisions were made and events moved forward.

So why don't I like decision analysis?

I find it objectionable to reduce a complex process to a single quantity. There are many reasons as a mathematician I find this incorrect and unjustifiable. The claim/caveat is that you shouldn't pay too much attention to the exact numbers you get when performing decision analysis and that the process is the important part. It is even provable that you will reach the optimal decision when your payoffs are accurate. However, accuracy is very hard to guarantee when you are estimating the impact of an advertising campaign on potential market share. If people spend significant time on an analysis leading to a particular number, then it is hard to argue that number should be ignored. It also appears very easy to structure the analysis so that the favored decision is the one with the highest score.

I explain to my students that they should always document their analyses thoroughly, so that others can look at their assumptions and see whether they agree with the inputs, and therefore the outcome. For decision analysis, this documentation seems most useful as a way to show why you made an incorrect decision when things go wrong. Just as it seemed wrong for judges to choose nits in the statutory language to justify a ruling, it seems wrong for an analyst to justify their decisions with an easily gamed process whose documentation serves mostly as cover if your decision is wrong.

I try to find examples of improper use of all the techniques I teach, so that I can make students wary of non-intuitive decisions justified solely by a single numerical method. I have yet to find a documented instance of badly used Decision Analysis. There are a huge number of websites, organizations, and consultants extolling the virtues of Decision Analysis. This also bothers me, since I don't believe any technique is infallible.

We should also keep in mind the comment of an Israeli friend. He said the government spends a lot of effort on Game Theory and Decision Analysis to determine how to deal with the other players in the region. However, it is not at all clear that their adversaries are playing the same game.

Making Decisions

One of my favorite lecturers at Michigan was Professor Igor Dolgachev. He was one of the many talented people we were fortunate enough to inherit from the former Soviet Union (and its allies.) He seemed unsure of the US approach to education and its wide ranging requirements. "In Moscow," he told us, "once we decided we were studying math, we studied math. Nothing else!" Then he looked a bit sheepish and bobbed his head, "OK, also Marxism-Leninism, but the rest was math!"

I think what upset him was Michigan's requirement that you take two senior or graduate level courses in a department other than the one granting you your degree. The first course I took to fulfill this requirement was Southeast Asian History. Interestingly, it was taught by a Czech who studied that region because it was one of the few places sufficiently far removed from the concerns of the Czechoslovakian Communist party that he could engage in reasonably honest historical inquiry. It seems that one of the reasons why former Soviet professors and students were such excellent physicists and mathematicians is that it was relatively hard to politicize these disciplines, so the brightest people who wanted intellectual freedom were attracted.

The second course I took was in Industrial and Environmental Health Policy. This course was part of the School of Public Health, and the professor had actually been one of the architects of the Material Safety Data Sheet approach to dealing with toxic industrial chemicals. He contrasted this approach favorably with the more draconian and bureaucratic tack taken by the Superfund Legislation.

At one point in the class, we were talking about the process of legislation, rule making, and inevitably litigation which characterizes health policy in the US. When a rule finally makes it to court, the judge looks at precedent, and then he looks at the legislative history to determine whether the Government's interpretation of a rule is legal (and appropriate.) The actual phrasing of the legislation is also very important when there are confusing, ambiguous, or missing elements for interpreting the law.

When I heard this, I was thunderstruck. I don't spend a great deal of care on choosing prepositions when I write, but this could have a huge effect on how a judge interprets a rule. When you consider the size of some bills, or the generic patriotic, Mom and apple pie style of much legislation, I can't believe that Congress spends as much time as it should choosing its words carefully.

I was studying to be a mathematician when I heard this. My time was spent developing exacting proofs of the truth of exact statements. Natural language is too fluffy and ambiguous to easily lead to an understanding of truth (try reading the original statements of Newton's Laws), yet words carelessly chosen ten or twenty years earlier by a Congressional staffer at 2AM would decide the outcome of a $10billion lawsuit or the fate of a land preserve bigger than Rhode Island.

When I expressed this sentiment to the professor, he was sympathetic, but he pointed out that judges don't have the luxury of not making decisions. All parties expect a resolution in the courts, and the judge has to find some justification for their decision. If all else fails, they will fix on the wording and its legal interpretation, whether or not that was the interpretation of Congress.

I am still uncomfortable with this approach to making decisions, and I will return to it in the future. There are times when we are forced to make decisions without having all of the knowledge we require. This was just the first approach to making a choice I encountered where the goal seemed to be providing a plausible cover for the choice made.