Screening Trade-Offs

• “Screening detects disease, therefore screening must be good.” Health care policy makers are now starting to question this simple mantra.What they are worried about are screening errors.

• They are faced with the following dilemma: As one makes a test more sensitive, thus decreasing the rate of false negatives, one usually has to increase the rate of false positives! So just calling for more accurate screening tests doesn’t solve everything!

A Parallel Case from Physics

• Suppose one is trying to detect a new particle. How should one set the threshold on the detector? If one makes the detector too sensitive, one will pick up lots of noise and thus may misinterpret a noise spike as a particle (false positive).

• But if one sets it too high one may miss a little peak that actually represents the sort of particle or event that one is looking for (false negative).

• In the physics case one may be able to reanalyze the raw data using different thresholds of significance. And one can certainly report which sensitivity setting was chosen.

Disclosure of Error in Medical Context

• When human beings are involved, handling screening errors is not so simple. Disseminating information about error rates seems to be the obvious first step.

• But it is hard to convey information about error rates to the public. And it is often difficult to get research money to collect the sort of data that is needed to give an accurate measurement of error rates.

• Furthermore, insurance companies are very nervous about law suits. From a legal point of view one does not automatically decrease one’s liability when one informs the patient the test is imperfect!

Medical Screening: Cervical Smears

• An example: Kent Hospital in GB conducted a huge study in which they rechecked the records of 91,000 cervical smears collected in a 5 year period. 333 women had erroneously been told their smears were normal and hence received no further medical attention.

• Of the 333, eight have since died of cervical cancer and 30 have undergone hysterectomies. Some are “seeking legal advice with a view to compensation”. Shouldn’t the test be made more accurate?

• Yet, 333 out of 91,000 represents a false-negative error rate of only 0.37%! A test that is successful in identifying cervical anomalies 99.63% of the time isn’t that bad!

Cervical Smear Example,Cont.: Data about False Positives

• More sensitivity might also increase the rate of false positives. According to the Lancet editorial, UK screens 4 million smears a year. Of these, 9% (or 14,400) come back as positive.

• It is not reported how many of these positive identifications turn out to be false positives. However, we are told that screening for cervical cancer is estimated to prevent from 1000 to 4000 cases a year.

• This seems to imply that the rate of false positives on the original test is very high. In this case, false positives lead to less harm than do false negatives, but following up on them can be quite expensive.

Morals of the Story

• For an individual, there is no dilemma when one is given the rates of error. A cervical smear test is a good way to detect cancer - a negative result is very trustworthy though not infallible.

• A positive result is much more likely to be wrong and one shouldn’t panic before following up with a repeat test or other diagnostic procedure. It is false negatives that are a cause for worry.

• However, as we will see, there are examples where a false positive can lead to more harm than a false negative.

False Positives and Incest Accusations

• A controversial example concerns the reliability of so-called Recovered Memories - cases where an adult patient develops memories of previously forgotten childhood incest and identifies the abuser who may then be charged.

• If the memory is not accurate (a false positive), a relative of the patient will be falsely accused and their reputation ruined even if they are eventually acquitted.

• But what about false negatives? This would be the case where the patient mistakenly believes that s/he was not abused, thus allowing the perpetrator to go unscathed.

When Not to Seek More Information - #1: Small Stuff

• We saw in the buying stock example that if there is not much difference among the options before us and they are all fairly satisfactory, there is no big reason to spend a lot of effort refining our matrix.

• One good role for habits is to help us quickly act on trivial matters. If I always have a small regular coffee in the AM and a decaffeinated latte in the PM that’s two decisions during the day I don’t need to worry about!

• However, this also indicates that at some point early on one needs to evaluate such habits pretty critically.

When Not to Seek…#2:
Huge Life Choices!?

• Samuel Johnson said: “Life is not long, and too much of it must not pass in idle deliberation how it shall be spent: deliberation which those who begin it by prudence, and continue it with subtlety, must, after long expence of thought, conclude by chance. To prefer one future mode of life to another, upon just reasons, requires faculties which it has not pleased our Creator to give to us.”

• What Johnson writes seems to go against the present ethos in which students are constantly exhorted to look ahead and put a great deal of thought into their career choices!

Elster on Life Choices

• “Suppose I am about to choose between going to law school or to a school of forestry - a choice not simply of career but of lifestyle. I am attracted to both professions, but I cannot rank and compare them. If I had tried both for a lifetime, I might be able to make an informed choice between them. As it is I know too little to make a rational decision.

• What often happens in such cases is that peripheral considerations move to the center…Perhaps I opt for law school because that will make it easier for me to visit my parents on weekends. This way of deciding is as good as any - but it is not one that can be underwritten by rational choice as superior to, say, just tossing a coin.”

Cases Where It’s Better to Toss a Coin than to Seek More Information

• Elster lists several:

– If you’re lost in the woods, it is better to toss a coin at each fork than to try to make a rational choice between them.

– Some gamblers use chance to determine when to bluff in order that their opponents not detect a pattern.

– It might be better to choose a soldier for a dangerous mission by a lottery than by a decision from the commanding officer that would supposedly be based on an estimate of who would do the best job but might be perceived as punitive.

Solomon and the Child with Two Mothers

• Then came there two women, that were harlots, unto the king, and stood before him. And the one woman said, O my lord, I and this woman dwell in one house; and I was delivered of a child with her in the house .And it came to pass the third day after that I was delivered, that this woman was delivered also: and we were together; there was no stranger with us in the house, save we two in the house.

• And this woman's child died in the night; because she overlaid it. And she arose at midnight, and took my son from beside me, while thine handmaid slept, and laid it in her bosom, and laid her dead child in my bosom. And when I rose in the morning to give my child suck, behold, it was dead: but when I had considered it in the morning, behold, it was not my son, which I did bear.

• And the other woman said, Nay; but the living is my son, and the dead is thy son. And this said, No; but the dead is thy son, and the living is my son. Thus they spake before the king.

From the Book of Kings

How Solomon Got More Information

• And the king said, Bring me a sword. And they brought a sword before the king. And the king said, Divide the living child in two, and give half to the one, and half to the other.

• Then spake the woman whose the living child was unto the king, for her bowels yearned upon her son, and she said, O my lord, give her the living child, and in no wise slay it. But the other said, Let it be neither mine nor thine, but divide it.

• Then the king answered and said, Give her the living child, and in no wise slay it: she is the mother thereof. And all Israel heard of the judgment which the king had judged; and they feared the king: for they saw that the wisdom of God was in him, to do judgment.

Elster on the Solomon Story

• Elster asks what Solomon should have done if neither woman had given in. His answer is “Toss a coin.” As the story is set up it appears that there was really no way to gather more evidence about who the true mother was and so it would be hypocritical to pretend that a rational choice could be made.

• Elster also points out the bind the true mother is put in. The more she presses the case that the child is really hers, the more she appears to be undermining her concern for the child’s welfare as opposed to her own. (Cf. Pascal’s Wager)

Elster on Child Custody Disputes Today

• Elster criticizes current policy of having the court trying to collect information in order to try to make a rational choice of the parent who is best suited to take primary responsibility for the child.

• We are participating in an exercise of what he calls “hyper-rationality”.

• Except for a few cases where one parent is obviously unsuitable (and hence no further info would be required) Elster says it is not only useless, but harmful to collect such information.

The Harm Caused By Collecting More Information

• It is useless for reasons given by Samuel Johnson. Who can foretell what will happen with either parent and how it will affect the child?

• It is harmful because:

– it takes time when the child needs to have a secure plan for the future as soon as possible;

– it encourages parents to dig up dirt on each other and air it in front of the child;

– it thus discourages arriving at a possible compromise arrangement

– it suggests that the person who eventually loses is definitely a second class parent.