Number of words: 750<\/p>\n\n\n\n
To understand the Bailar-Smith analysis, we need to begin by understanding what it was not. Right from the outset, Bailar rejected the metric most familiar to patients: changes in survival rates over time. A five-year survival rate is a measure of the fraction of patients diagnosed with a particular kind of cancer who are alive at five years after diagnosis. But a crucial pitfall of survival-rate analysis is that it can be sensitive to biases.<\/p>\n\n\n\n
To understand these biases, imagine two neighboring villages that have identical populations and identical death rates from cancer. On average, cancer is diagnosed at age seventy in both villages. Patients survive for ten years after diagnosis and die at age eighty.<\/p>\n\n\n\n
Imagine now that in one of those villages, a new, highly specific test for cancer is introduced\u2014say the level of a protein Preventin in the blood as a marker for cancer. Suppose Preventin is a perfect detection test. Preventin \u201cpositive\u201d men and women are thus immediately counted among those who have cancer.<\/p>\n\n\n\n
Preventin, let us further suppose, is an exquisitely sensitive test and reveals very early cancer. Soon after its introduction, the average age of cancer diagnosis in village 1 thus shifts from seventy years to sixty years, because earlier and earlier cancer is being caught by this incredible new test. However, since no therapeutic intervention is available even after the introduction of Preventin tests, the average age of death remains identical in both villages.<\/p>\n\n\n\n
To a naive observer, the scenario might produce a strange effect. In village 1, where Preventin screening is active, cancer is now detected at age sixty and patients die at age eighty\u2014i.e., there is a twenty-year survival. In village 2, without Preventin screening, cancer is detected at age seventy and patients die at age eighty\u2014i.e., a ten-year survival. Yet the \u201cincreased\u201d survival cannot be real. How can Preventin, by its mere existence, have increased survival without any therapeutic intervention?<\/p>\n\n\n\n
The answer is immediately obvious: the increase in survival is, of course, an artifact. Survival rates seem to increase, although what has really increased is the time from diagnosis to death because of a screening test.<\/p>\n\n\n\n
A simple way to avoid this bias is to not measure survival rates, but overall mortality. (In the example above, mortality remains unchanged, even after the introduction of the test for earlier diagnosis.)<\/p>\n\n\n\n
But here, too, there are profound methodological glitches. \u201cCancer-related death\u201d is a raw number in a cancer registry, a statistic that arises from the diagnosis entered by a physician when pronouncing a patient dead. The problem with comparing that raw number over long stretches of time is that the American population (like any) is gradually aging overall, and the rate of cancer-related mortality naturally increases with it. Old age inevitably drags cancer with it, like flotsam on a tide. A nation with a larger fraction of older citizens will seem more cancer-ridden than a nation with younger citizens, even if actual cancer mortality has not changed.<\/p>\n\n\n\n
To compare samples over time, some means is needed to normalize two populations to the same standard\u2014in effect, by statistically \u201cshrinking\u201d one into another. This brings us to the crux of the innovation in Bailar\u2019s analysis: to achieve this scaling, he used a particularly effective form of normalization called age-adjustment.<\/p>\n\n\n\n
To understand age-adjustment, imagine two very different populations. One population is markedly skewed toward young men and women. The second population is skewed toward older men and women. If one measures the \u201craw\u201d cancer deaths, the older-skewed population obviously has more cancer deaths.<\/p>\n\n\n\n
Now imagine normalizing the second population such that this age skew is eliminated. The first population is kept as a reference. The second population is adjusted: the age-skew is eliminated and the death rate shrunk proportionally as well. Both populations now contain identical age-adjusted populations of older and younger men, and the death rate, adjusted accordingly, yields identical cancer-specific death rates. Bailar performed this exercise repeatedly over dozens of years: he divided the population for every year into age cohorts\u201420\u201329 years, 30\u201339 years, 40\u201349, and so forth\u2014then used the population distribution from 1980 (chosen arbitrarily as a standard) to convert the population distributions for all other years into the same distribution. Cancer rates were adjusted accordingly. Once all the distributions were fitted into the same standard demographic, the populations could be studied and compared over time.<\/p>\n\n\n\n