Down Syndrome and Decision Theory

2008-09-07 at 1:06 pm 21 comments

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.

Entry filed under: Science, Society, Statistics, Statistics - Nontechnical.

R Design Flaws #1 and #2: A Solution to Both? Amazement

21 Comments Add your own

  • 1. Andrew Gelman  |  2008-09-08 at 1:29 pm

    This problem has been much discussed in the medical decision making literature. There are no easy answers, but such analyses can help answer the question of what is a reasonable age threshold to recommend for the test.

  • 2. ale  |  2008-09-09 at 8:39 am

    There seems to be no utility value assigned above to the “peace of mind” provided by the amniotic fluid test should it come back Down’s-negative. Or the predicted future regret on not having done the test in case the child is Down’s positive (whether predicted future regret should happen to a rational decision maker or not does not prevent it from existing to humans and thus forming part of the real utility function). My guess is that these two would be important.

  • 3. Bman  |  2008-09-09 at 11:35 am

    If “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”, shouldn’t the 16-week old fetus’s utility be given some consideration and the 24-week fetus’s utility be given even more consideration? If it is neither “fully human” nor has “no moral standing”, it should at least get some weight and presumably increasing weight as time passes. What would the fetus think about getting tested, being aborted, etc.? Presumably, it has the will to live.

  • 4. Andrew Gelman  |  2008-09-12 at 9:09 pm

    Ale, Bman: These are good points but I don’t think they refute Radford’s point (which has been made in detail in the medical decision making literature); they just represent additional terms in the utility function.

  • 5. Radford Neal  |  2008-09-13 at 1:01 pm

    Putting a non-negligible value on “peace of mind” would make the Independence Axiom inapplicable. It would no longer be the case that “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.” Doing amniocentesis on these 994 pregnancies would have the good effect of reassuring the parents.

    However, I think it’s crazy to value “peace of mind” enough to make it a signficant consideration. (This isn’t a mathematical judgement, obviously, but rather a moral one.) If some couples have amniocentesis done for this reason (or even if this is a significant factor in their decision), then I think the medical profession has an ethical problem, since these couples’ uneasiness is probably largely iatrogenic – a result of medical professionals having discussed the issue with them, perhaps too much.

    I think “future regret” is not a sensible consideration when making a decision. It’s basically double-counting the bad consequence. To the extent that it might not be explained that way, it’s counting the utility of someone other than the decision-maker, since “you” and “you-in-the-future” are not the same person.

    Andrews comments about the medical decision making literature don’t contian references, but if they are about “what is a reasonable age threshold to recommend for the test”, then I think they are far too simplistic. For one thing, recommendations today should not be based just on age, but on non-invasive tests. For another, it’s medically presumtuous to think that a “threshold” can be decided on by medical ethics people, rather than by the people actually affected.

  • 6. Andrew Gelman  |  2008-09-13 at 9:09 pm


    The focus on the medical decision making literature is on general medical recommendations, in this case what is a good age to recommend testing.

    Nobody’s being presumptuous here. Doctors give recommendations, and it’s reasonable for these recommendations to be evidence-based. Of course the decisions are made by the people affected (well, except for the fetuses involved), but said people might well ask their doctor for advice!

    Researchers in medical decision making are well aware of utility theory and the value of information and the risks of testing and all these other things. It’s fine for you to work this out on your own; I just wanted to let you know that there are people who have been working in this area for awhile, and they’re not as naive or simplistic as you might think.

  • 7. Radford Neal  |  2008-09-13 at 11:29 pm


    I’d be more convinced that they’ve thought of it all already if you gave a reference!

    I did some Google searches on things like “amniocentesis” and “Allias Paradox” before posting this, and about the only relevant result was the comment by Dawid that I mentjion in the post.

  • 8. David  |  2009-02-06 at 6:17 pm

    I seem to recall that there was a nice article in Chance on this topic. Maybe within the last 2 yrs.

  • 9. Corinna  |  2009-04-24 at 3:02 pm

    I just wanted to comment (enjoyed your post very much) that the question is not when the embryo/fetus becomes “human”. It is human right from the sperm & oocyte stage (i.e. it isn’t a dog or a cat or a Martian, it has the exact genetic makeup that causes us to call skin cells or hair “human skin cells” or “human hair”. It is a “human embryo/fetus”). I would say the question is actually when it becomes a person/its own individual…whether its personhood has equal status to the individual carrying it…whether it is a separate being with its own inherent rights, or part of the mother. Anyway, this is tangential to your point :)

  • 10. Adriana  |  2009-09-30 at 5:28 am

    An interesting post!
    Here is a paper related to this subject

    Making Rational Decisions using Adaptive Utility Elicitation (2000)

  • 11. Radford Neal  |  2009-10-03 at 6:21 pm

    Note that I had to resort to the “cached” version to get the PDF of the paper mentioned above.

    From a brief glance, it seems to be flawed. It ends up using the expected value of a utility function, since the utility function is regarded as uncertain. But the mathematical nature of a utility function makes this expectation operation meaningless. Utility functions are defined only up to an arbitrary affine transformation, which destroys the ability to take expectations.

    I mentioned this problem to my colleague Craig Boutilier, who has done similar things, which resulted in him writing the following paper that attempts to solve the problem:: On the foundations of expectedexpected utility. I believe that, unfortunately, this paper does not actually solve the problem, which is essentially the same as the problem of interpersonal utility comparisons.

    • 12. Adriana  |  2010-05-11 at 3:58 am

      Why do you think it is a problem the fact that utility functions are defined only up to an arbitrary affine transformation? Because, when working with utilities, one is not interested about their value per se, but about the ratio between the values. Specifically, one is not interested in computing max{util(item_1),…,util(item_n)} but argmax{util(item_1),…,util(item_n)}.

      • 13. Radford Neal  |  2010-05-12 at 1:42 am

        There is no problem with utilities being defined only up to an arbitrary rescaling and shift, as long as you don’t start taking expectations or other sorts of averages of them. Taking an average of x, y, and z is meaningless if x, y, and z can equally well be changed to x+10, 2y-88, and 5z. In particular, which option has the highest average utility before such (different) affine transformations needn’t be the same as the option with highest average utility after such transformations.

  • 14. Ali  |  2010-01-18 at 4:57 am

    Here is a site with huge Information On Pregnancy Diseases And Genetic Testing. You can find information regarding Down Syndrome in the family in:

  • 15. Radford Neal  |  2010-01-20 at 2:18 am

    Thanks for the link. It seems to be about risk of Down Syndrome when someone related to the parents has Down Syndrome (eg, a previous child). That’s an interesting question, but not one that most people face for their own personal decision.

  • 16. MarkB  |  2010-04-22 at 10:39 pm

    Hey Rad,

    If you want to apply decision theory to this subject matter, which is completely inappropriate, get your facts straight! I couldn’t care less about which side of the moral fence you stand on, but it’s embarassing to read your arguments predicated on outright bad data. If you did take the time to research the numbers, you would see how ludicrous this post is. Frankly, this was just a deperate attempt to apply the theory.

    I have to tell you Rad, as a U of T Math grad myself, bad decision.


  • 17. Radford Neal  |  2010-04-23 at 9:33 am

    Hey Mark,

    Would you like to give us all SOME hint as to what it is you think is wrong in the post?

    As it is, your comment reads like it’s meant as a parody of a ridiculous blog comment. I’d suspect it was some sort of automaticly generated spam (with the spammer’s motive hard to discern) if it weren’t that it seems to contain slightly too specific references for a bot.


  • 18. Dr. Harris Meyer  |  2010-05-10 at 5:55 pm

    Like some posts, this one is interesting to begin with but reading thru the comments is amazingly juicy. Who knew decision theory would attracting on going attention a year and a half after the original post.

  • 19. Lion McLean  |  2010-06-23 at 1:18 pm

    Someone pointed out the utility of peace of mind. This is absolutely the case.
    To take another example there is no reason to subject your child to ultrasound. It is harmful, but people do it anyways, just so they will know.
    Are they going to terminate the pregnancy if it is a boy or a girl, or twins? Not likely. But do they still want to know? Sure do.

  • 20. Warren Dew  |  2010-10-20 at 9:14 pm

    It seems to me you’re not thinking this through.

    A pregnancy with a 1 in 6 chance of Down Syndrome has a 5x higher chance of a bad result than a 1 in 30 chance of congenital defects, even ignoring the fact that Down is much more severe than most of the other possibilities. The 1 in 30 chance is irrelevant.

    The extra cost of raising a Down child is much higher than having an additional pregnancy for most people. Aborting a pregnancy with a 1 in 6 chance of Down is something that a lot of couples would consider.

    For older women, the comparison changes in the opposite direction from what you seem to believe. For example, for a 40 year old with the average 1% chance of Down, the decision to have amnio is equivalent to aborting a pregnancy that has a 2/3 chance of being a Down embryo, and only 1/3 chance of being free of Down syndrome. Most women – even 40 year old women – would abort such a pregnancy.

    I have two children, we did amnio on one of them, and the decision in both cases was completely consistent with what we would have done in the decision theory equivalent case. You seem to think you are making a point, but I have a hard time seeing what it is.

    • 21. Radford Neal  |  2010-10-20 at 10:22 pm

      I mention the general 1 in 30 chance of congenital defects as a point of reference. Of course a 1 in 6 chance of Down Syndrome is five times higher. Factors of five are small enough that one can think about them intuitively. If you thought 1 in 30 was acceptable, is a five times higher risk also acceptable? I’m not saying what your answer to this question should be, just that it may be easier to think about than questions with bigger numbers like 1 in 1000.

      Regarding 40-year-olds, my comment assumed the same 1 in 1000 chance of Down Syndrome based on non-invasive tests and age. Of course 40-year-olds overall have a higher chance of having a Down Syndrom baby, but after accounting for the non-invasive blood and ultrasound tests, it’s quite possible for the probability to be 1 in 1000. The difference then is that a 40-year-old woman has a lower chance of getting pregnant again than a younger woman, which may for some people affect their decision.

      What point am I making? I’m definitely NOT trying to tell people what they should do. I’m just showing that there’s an equivalent decision problem that may help people clarify what they want to do. In your case, it seems your initial inclinations for the equivalent decisions are the same, so it wouldn’t help clarify anything for you. For other people, it may.


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