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University of Chicago Writing Program

Sentence of the Week: Who should get a mammogram?

This week's sentence:

The proportion of biopsies that occur because of these false-positive results that are retrospectively deemed unnecessary (that is, the woman did not have cancer) is about 7%; therefore, many more women will undergo unnecessary biopsies under annual screening than biennial screening.

The authors of this week's sentence face a real rhetorical challenge. They're trying to recommend a change in a common medical practice (annual mammograms for women over forty), and they're making this recommendation to an extremely large and diverse audience. How can they do a better job of making their case?

What went right: the clear conclusion

This week's sentence is divided by its semicolon into two parts: evidence first, conclusion last. Kudos to the authors for presenting the conclusion in such a reader-friendly way.

The conclusion has a clear, easy-to-understand subject -- women. Readers anxious to discover what's happening to the women are relieved by the prompt appearance of the verb -- "will undergo" -- and an object -- "unnecessary biopsies." Right away, readers know the conclusion's basic story. So they're ready for the mildly complex modifiers at the end: "under annual screening than biennial screening."

More good news: the conclusion also links back to data about annual and biennial mammograms that appeared a sentence earlier in the authors' report. The authors point out that women who receive annual mammograms end up getting "almost twice" as many false positives as women who receive biennial mammograms.

We'll return to this part of the argument later. But first, let's take a look at the beginning of this week's sentence. This bit intervenes between the data about women who get annual mammograms and the conclusion about women who get biopsies. Readers must understand it if they're to follow the authors' logic.

What went wrong, part 1: the belated verb

Unfortunately, this first part of the sentence is not quite as easy as the conclusion. Like the sentence we featured last week on this site, this one gets cumbersome because its verb is delayed for so long. Readers must struggle with an extremely complicated subject before the verb -- "is" -- makes its appearance.

The proportion of biopsies that occur because of these false-positive results that are retrospectively deemed unnecessary (that is, the woman did not have cancer) is about 7% . . .

The sentence would be much easier if the simpler information at the end appeared at the beginning. Such a revision would be tricky, however, because if all we do is say "seven per cent of biopsies," we won't make much progress in shortening the wait for the verb. We might get stuck squeezing in the long list of modifiers attached to "biopsies."

We need, therefore, a new subject for the sentence. Fortunately one lies near at hand -- women. That's the subject the authors use in their conclusion, and they also use it in an explanatory parenthesis. Since the authors felt the explanatory parenthesis was necessary, why not mention the women a little sooner?

About seven per cent of women will prove cancer-free when they receive biopsies that occur because of these false-positive results; therefore, many more women will undergo unnecessary biopsies under annual screening than biennial screening.

This version has some advantages and one towering problem. The advantages: it will be easier for many readers. It will also allow them to track the character -- women -- that's important in the conclusion.

The problem: Readers acquainted with probability theory will know that this is not at all what the authors meant.

What went wrong, part 2: the chain of "that" modifiers

So we're not done. The revision is much easier, but it doesn't reflect the meaning of the original. There are a couple reasons for this. One is the inherent weirdness of the math of false positives, which we'll put to one side until part III. The second: the original sentence linked so many modifiers to "biopsies" that it's even harder than it should be to come up with the answer to the question: "seven per cent of what?"

Let's go back to the original sentence's long subject and try to figure out what it means.

The proportion of biopsies that occur because of these false-positive results that are retrospectively deemed unnecessary . . .

Okay, let's unpack the logic here. We're talking about a group of biopsies. What qualifies a biopsy to be part of this group? The group's qualities are listed in the two "that" clauses:

1. biopsies that occur because of these false-positive results AND

2. biopsies that are retrospectively deemed unnecessary

But wait! Did we get that right? Two questions spring to mind. First, does the second "that" clause really describe "biopsies" or "false positive results?"

1. biopsies that occur because of these false-positive results

2. false-positive results that are retrospectively deemed unnecessary

I'm afraid there's no way to determine the answer to this question. The sentence doesn't make clear how readers are supposed to connect the chain of "that" modifiers.

It's tempting to presume that the second quality (deemed unnecessary) is meant to describe biopsies, because if it does, it seems relevant as a reasonable bit of evidence for the sentence's conclusion. If some of these of biopsies are deemed unnecessary, then maybe fewer of them should be performed. How do you do that? You give fewer mammograms that suggest -- in some cases falsely -- that a biopsy is necessary. Okay, that sounds clear: readers may debate it, but it's understandable enough to debate.

But this is not what the sentence unambiguously says, leaving readers to guess about a crucial point in the argument. How can the sentence be made more clear?

We'll start by untangling the "that" modifiers, both to make the sentence more readable and to highlight a key point in the argument. It's crucial to the author's conclusion to help readers make the connection between a false positive result and an unnecessary biopsy. A better way to do so might be to extract this point from the nest of "thats" and give it a sentence of its own.

These false-positive results on mammograms can lead to unnecessary biopsies. When women between the ages of forty and sixty-nine receive annual mammograms and then get a biopsy, X% of them will prove cancer-free. . .

The math remains to be tackled, but readers will now not be battling a convoluted opening when they confront it.

What went wrong, part 3: a missing statistic

We're still left with one final question: do we really have the right subject for our most crucial verb? To write our first revision, we used the original sentence's figure of seven per cent, and applied this figure to the character named in the parenthetical explanation (women). But given the sentence's convoluted opening, can we really trust those parentheses and be sure that the seven per cent applies to women? What part of the opening tangle of clauses is the parenthetical explanation meant to translate? All of it? Some of it?

Readers are thus left alone with a number -- seven per cent -- and no clear idea of what that seven per cent represents: something about patients, something about biopsies, or something about false positives. The ambiguity is fatal, because the rate of false positives and the rate of cancer among patients are two different things. The mathematical relationship between them is simple, but counter-intuitive: for a useful primer, go here. One brain-teasing sample: if mammograms are ninety per cent accurate, less than one per cent of the women who test positive will prove to have cancer. (Confused? So are we! The first time we tried to work out the math in the sentence, we got it entirely wrong.)

Unfortunately, so did many other readers, which did not help the writers make their case. We can't help the authors with their math -- we probably would lead them astray even if we tried to help them balance their checkbooks -- but we can suggest ways that expert writers can make an effective mathematical argument to a diverse audience.

We'll tackle this question from two perspectives: persuasiveness and clarity. Persuasiveness first. As far as persuasion is concerned, not all numbers are created equal. Two statements that are mathematically equivalent -- and both true -- can have radically different persuasive effects. Let's say, for example, that you want to argue that depression is a serious problem among plumbers. Let's assume further -- and purely hypothetically, since as far as we know plumbers are perfectly cheerful -- that you have evidence for two statistics:

  • a) that fifteen per cent of plumbers are experiencing depression at any one moment, and
  • b) that sixty per cent of plumbers will experience depression at some point in their careers.

What headline would you want for your article on the subject? Ten per cent or sixty per cent? In this (again, hypothetical) scenario, both figures are true. But the second would do considerably more work for the argument.

In the case of this week's passage, the authors wanted to emphasize that the number of unnecessary biopsies is large enough to worry about. There are several numbers they might have used to support their argument in the sentence, all equally true. The number that actually appears, seven per cent, is by no means the largest of the candidates. Logically this is unobjectionable. But rhetorically, it's a missed opportunity to persuade. For the sake of persuasiveness, the authors would have been better served by trotting the highest number they could find that was both true and relevant to the point about too many unnecessary biopsies.

But if that way of thinking seems a bit too Machiavellian, consider the case for clarity. To make any argument clear, writers need to supply evidence for all the parts of their point. The point the authors are making, in this case, concerns both the benefits and harms of mammography. It would help if the authors included statistics about both benefits and harms. And if, in this side-by-side comparison, it turns out that the benefits are much smaller than the harms, then the same handy comparison would serve the purposes of both clarity and persuasiveness.

To give some idea of what this might look like, our revision could be rewritten one more time. Again, we'll leave the math itself to the authors, but the argument readers need to see would look something like this:

When women between the ages of forty and sixty-nine receive annual mammograms, they get almost twice as many false-positive results as they would if they received mammograms biennially. These false-positive results can lead to unnecessary biopsies. When women in this age group get a positive result on an annual mammogram and then get a biopsy, only X% of them prove to have cancer. But the other Y% prove to be cancer free. Therefore, many more women will undergo unnecessary biopsies under annual screening than biennial screening.

Armed by the authors with the actual values for both X (women who benefit) and Y (women who are harmed), readers will be able to make more informed decisions about whether a mammogram is worth the time, the money, the inconvenience, the (occasional) pain -- and the risk of unnecessary treatment.

Like many medical experts who face similar rhetorical challenges, the authors are writing about a subject of deep concern to millions of patients. These patients are entirely dependent upon experts to provide them with a complete and accurate report of the medical evidence. Unless the report is clear, that won't happen, and patients will be left in the dark.

Do you have a candidate for sentence of the week?

If so, submit it to Sentences must be from published, professional prose (sorry, no poetry). You must include a complete citation with your entry. If we use a sentence, we will thank you publicly (if you wish) or privately (if that's what you'd prefer), and we will also reward you with gratitude, kind thoughts, and good karma. If a sentence is good, we will reveal the name of the author on the site; if a sentence is bad, we will gracefully conceal the author's identity, telling only a few dozen of our closest friends and relations, as well as anyone else who asks nicely. All others are encouraged to try googling the sentence, which usually returns an answer faster than we do.

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