Lead Time, or How to Live Longer but Die at the Same Time

Andrew J. Vickers, PhD

Disclosures

January 07, 2009

Rock and roll fans know that a "lead" is when a guitarist cranks up the amplifier, plugs in the fuzzbox, and spends the next couple of minutes rolling around the stage making a lot of noise. As you may guess then, the first time I heard "lead time" during a statistics seminar I got quite excited and started limbering up for some extended facial grimacing. There then followed a discussion about prostate cancer, during which time no one even mentioned Frank Zappa, and my professor kept on saying that lead time was a good thing — but had to be avoided at all costs.

When statisticians discuss lead time, they are more likely to be referring to disease screening than Deep Purple. Lead time is the period between when you can catch a disease early with a screening test and diagnosing it later because the patient has symptoms. This sounds like a good idea because diseases are generally easier to treat if they are found early. Certainly this is the case in prostate cancer: An early-stage cancer can be cured by surgical removal of the prostate; once the cancer has grown large enough to cause symptoms, it has often spread to other organs and the patient will likely die of his disease.

However, here's a quick cautionary note before you sign up for prostate screening: Having your prostate removed is no picnic, and you can be left incontinent and impotent. A long lead time may well mean "lots of time to catch the prostate cancer early," but it also means "lots of time to die before you realize you have cancer." This means that you could go for surgery, miss the opportunity to spend your sunset years enjoying sex and dry underpants, and then die of a heart attack well before the cancer would have caused any problems.

The statistician's equivalent of wet underpants is "lead-time bias." A few years back, a group of researchers reported excellent survival rates in patients who had lung cancer discovered by a screening computed tomographic (CT) scan, and were then treated surgically. Because survival in lung cancer is generally dismal, the researchers concluded that screening was effective. The problem is that they may well have concluded the same thing had the patients not been treated at all, and screening can't help you if a positive test doesn't lead to an effective treatment. The Figure shows progression of cancer from the first few tumor cells to death from disease. Even if no treatment is given, or if treatment is totally ineffective, there is a longer period of time between diagnosis and death if the cancer is screen-detected. The difference is equivalent to the lead time, and biases the comparison between survival rates.

Figure.

Progression of cancer from the first few tumor cells to death from disease.

Another cancer researcher, who happens to be a colleague of mine, later showed that lung cancer screening probably doesn't affect how long anyone actually lived. (It also turned out that the lung screening advocates had unreported conflicts of interest, used tobacco industry money, and hadn't been entirely candid when reporting the results of their study, but that is another matter.) My colleague's theory is that different lung tumors grow at different rates. Some tumors grow so slowly that they are only likely to cause symptoms if the patient lives to, say, 157; other tumors double in size so rapidly that a patient could have a completely clean CT scan and then be dead 9 months later from widespread disease. Guess which ones you'd pick up on a screening CT scan? Statisticians call this problem "length-biased sampling." Then again, they also use the term "lead-time bias" to refer to a statistical artifact of disease screening, when it really means that the other guitarist is stealing my solo.

Note: This article is for teaching about statistics. Please don't use this article for information about any of the following: (1) the value of cancer screening, (2) my opinions about the value of cancer screening, (3) the artistic merits of Deep Purple, and (4) artistic tensions in my band.

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