Down Syndrome and Decision Theory

I have a wonderful 11-month-old daughter, who thankfully is entirely healthy. During the pregnancy, my wife and I were of course worried about the possibility of a congenital defect, of which the most prominent is Down Syndrome. Today, couples must make a series of complex decisions — whether to have a screening test for Down Syndrome, whether (based on its result) to have a more risky diagnostic test, and of course, what to do if the final result is that the fetus has Down Syndrome. These decisions depend on moral judgements, on various facts regarding the nature of the fetus at various ages, regarding the nature of Down Syndrome, and regarding the reliability and dangers of the tests, and finally, on the proper way to use this information to make a decision.

This last aspect is in the domain of decision theory, and will be the main focus of this post. Decision theory purports to show how a decision-maker should use the probabilities of the various possible outcomes along with their personal “utilities” for these outcomes to make a rational decision, which maximizes their expected utility. The validity of decision theory as a guide to rational action has often been challenged. The Allais Paradox describes one situation where decision theory does not accord with the judgements of many people, and some argue that the fault is not with these people, but rather with decision theory. Interestingly, Down Syndrome testing involves an analogue of the Allais Paradox.

For readers who aren’t familiar with pre-natal tests for Down Syndrome, I’ll first present the main facts:

• Down syndrome results from a chromosomal abnormality, which causes cognitive impairment and a wide range of physical problems. Both the degree of cognitive impairment and the severity of the physical problems are highly variable.
• The risk of Down Syndrome increases with maternal age, from less than 1 i 1000 for young women, to 1 in 100 for women age 40, to 1 in 30 for women age 45, and to 1 in 12 for the rare birth to a woman age 49.
• Whether a fetus has Down Syndrome can be determined to high accuracy between 16 and 22 weeks into the pregnancy by performing amniocentesis, which is an invasive procedure that has about a 1 in 200 chance of causing the fetus to miscarry. Results are available after 2 to 4 weeks.
• Several non-invasive screening procedures (blood tests and ultrasound examination) that are performed at various times from 11 weeks to 16 weeks into the pregnancy can provide information on how likely the fetus is to have Down Syndrome. Combined with information on maternal age, these can give a probability that the fetus has Down Syndrome.
• The results of these screening tests never definitely indicate Down Syndrome. They are used only to decide whether amniocentesis should be done.

Pretty much the only point of testing for Down Syndrome is to provide the option of terminating the pregnancy if the fetus is confirmed to have Down Syndrome. (The only other purpose I can see would be to prepare mentally or financially for having a child with Down Syndrome, but given the risk of amniocentesis, I think few well-informed couples would regard this as a sensible reason to have it done.) The tests available in Ontario are described at this web site, which gives all the facts above (plus more, I’ve slightly simplified the available options), but which strangely makes no mention of pregnancy termination, except buried in the PDF files of some pamphlets. This page by the American College of Obstetricians and Gynecologists also manages to avoid any mention of pregnancy termination. One has to wonder what the rationale might be for this stunning failure to inform people of the purpose of the tests they discuss.

Clearly, if you are certain that you wouldn’t want to terminate the pregnancy even if you were sure the fetus has Down Syndrome, then you shouldn’t do any of these tests. At least, that’s so if we ignore the complication that some of these tests can also detect some rarer conditions, such as Trisomy 18, which are much more severe than Down Syndrome, as well as some rarer conditions that might be treatable.

I suspect that few people are so certain about what they would actually do if faced with a decision of whether to terminate a Down Syndrome pregnancy. On the question of when a fetus becomes “human” (possessing human rights), most people are not extremists — they neither believe that a fertilized egg is fully human, nor believe that a fetus just about to be born has no moral standing. Instead, most people are unsure when a fetus becomes human, and think in any case that the process is a gradual one. Furthermore, where their views fall within this non-extreme range may well be altered by the experience of pregnancy (especially the first time). Also, on learning that their unborn child has Down Syndrome, most couples are likely to learn more about Down Syndrome before making a decision. I do assume that few people regard Down Syndrome as a desirable condition, and indeed, that most people would consider it unethical to conceive a child if they knew for certain (before conception) that the child would have Down Syndrome. (Note that this is a hypothetical situation which never arises in practice.)

Most people should therefore have the non-invasive tests, and then think about the issue more once they have the results. The first question is whether to have amniocentesis done, which would provide an accurate diagnosis of whether the fetus has Down Syndrome, but which has a 1 in 200 chance of causing a miscarriage.

It’s at this point that decision theory has something to say. Suppose that the non-invasive tests (along with maternal age) give a 1 in 1000 chance of Down Syndrome. You could try to directly weigh the benefit (given this chance) of using amniocentesis to confirm whether the fetus really has Down Syndrome against the 1 in 200 chance that amniocentesis would cause a miscarriage, and come to a decision. But applying the “Independence Axiom” of decision theory may clarify the situation.

Let’s ignore the 1 in 200,000 chance that the fetus has Down Syndrome and would be lost to a miscarriage if amniocentesis were done. We can then visualize the decision in terms of 1000 hypothetical pregnancies. In one of these pregnancies, but not the others, the fetus has Down Syndrome. In 5 of these pregnancies, a miscarriage will occur if amniocentesis is done. In 994 of these pregnancies, the fetus does not have Down Syndrome, and amniocentesis would not cause a miscarriage. For these last 994 pregnancies, it makes no difference whether amniocentesis is done or not. These pregnancies can therefore be ignored when making a decision.

Pretending, therefore, that one of the remaining 6 pregnancies is the real one, the decision looks like this: If you do nothing, there’s a 1 in 6 chance you’ll have a child with Down Syndrome. If you have amniocentesis done, that’s effectively like terminating the pregnancy, since for 5 of the 6 pregnancies miscarriage will result, and for the other (with Down Syndrome) you would likely decide to terminate the pregnancy. The decision whether or not to have amniocentesis when there’s a 1 in 1000 chance of Down Syndrome is therefore equivalent to a hypothetical decision whether or not to terminate a pregnancy when there is a 1 in 6 chance of Down Syndrome and no further diagnostic test is available. Of course, if the non-invasive tests produced a different probability, we’d have a different equivalent problem — for example, with a 1 in 2000 probability of Down Syndrome, the equivalent decision is whether to terminate a pregnancy when there’s a 1 in 11 chance of Down Syndrome.

Is making a hypothetical equivalent decision of this sort any easier than making the original decision? I think so, because the probabilities are less extreme, and the decision is more similar to other decisions that you may have already considered.

One highly relevant comparison is that about 1 in 30 children are born with some sort of serious congenital defect, most of which can’t be diagnosed before birth. If you don’t find this level of risk acceptable, you shouldn’t be thinking of having children. The chance of Down Syndrome in the hypothetical decision described above will often be close enough to this that you can think about the risk in the same way, and decide whether you regard it as also being acceptable.

A few years ago, before any prenatal tests were available, a pregnant woman age 49 would have faced the choice of whether to terminate her pregnancy based simply on the overall risk of 1 in 12 of Down Syndrome at her age. This is about equivalent to the choice of whether to have amniocentesis done when the non-invasive tests (plus age) give a 1 in 2000 probability of Down Syndrome.

It may also be helpful to compare with the current world-wide infant mortality rate (deaths in the first year) of around 1 in 20. Infant mortality is around 1 in 200 in developed countries, and around 1 in 6 in a few countries (such as Angola and Afghanistan). Infant mortality in the United States in 1950 was about 1 in 30. These figures tell you something about what other people have regarded as acceptable risks.

Ultimately, of course, your decision will still depend on your personal risk tolerance, your view of Down Syndrome, your view of the humanity of a fetus age 16 weeks or more, and the probability of another pregnancy if you terminate this one.

This last point would seem to be the dominant consideration for anyone who does not view a 16-week (or possibly up to 24-week) fetus as human. Its implication is that older women who want a child should be less inclined to have amniocentesis done than younger women, for a given probability of carrying a Down Syndrome fetus. (Of course, maternal age is one factor on which this probability is based.) This recent post (which I found via Marginal Revolution) discusses this issue.

The equivalence I present above depends, of course, on the validity of the Independence Axiom. In my view, it is obviously correct, even if its implications are not all obvious. The situation with Down Syndrome testing is very analogous to that in the Allais Paradox, which has been taken by some as a refutation of the Independence Axiom, though such a conclusion seems unjustified to me. I think the Down Syndrome testing situation is more interesting, and more real, than the gambling scenario in the typical presentation of the Allais Paradox. (Down Syndrome and decision theory has also been discussed in a comment by A. P. Dawid in Statistical Science, November 1986.)

You will have to judge for yourself whether your intuition satisfies the Independence Axiom, or whether the decision you would intuitively favour for the original problem — whether to have amniocentesis with a 1 in 200 chance of miscarriage if there’s a 1 in 1000 chance of Down Syndrome — differs from the decision you would intuitively favour in the “equivalent” problem — whether to terminate a pregnancy due to a 1 in 6 chance of Down Syndrome.

Suppose that you do find a difference in your intuitions. Those who argue against decision theory (and the Independence Axiom in particular) assume that such differences cast doubt on its validity. But what would be the purpose of developing a theory of decision making if everything it told you was intuitively clear to you anyway?

It’s actually a great benefit of decision theory that it demonstrates that problems which seem different to some people are actually equivalent. This provides an opportunity for further thought, leading to a more satisfactory decision. Analogous situations arise with probability theory, where inconsistent subjective probability judgements indicate that more thought is needed. One should note, however, that sometimes the resolution of such inconsistencies is not that one or both judgements are wrong, but that both are right, with the apparent conflict being due to a failure when formalizing the problem to include some non-obvious but relevant aspects (such as the effect of the decision made on the decision-maker’s reputation for good decision-making).

Some recent studies have shown much lower risk of miscarriage from amniocentesis than 1 in 200 (1 in 1000 or lower), but caution in interpreting these results is needed, since they may not apply to the particular facility where you would have amniocentesis done. Better non-invasive tests, such as ones that look at fetal cells in the mother’s blood, may also become available. We can hope that this interesting decision theory problem will soon cease to be real.