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Incorrect metrics

As indicated by the well known aphorism, "It is not the heat, it’s the humidity," choosing the right metric is very important. Bayesians like to clobber the incorrect metric known as p-value, as can be seen by the following table due to Freeman (Freeman PR. The role of p-values in analysing trial results. Statistics in Medicine. 1993 Aug; 12(15-16): 1443-52).

Number of Patients Receiving A and B	Numbers Preferring A:B	Percent Preferring A	two-sided p-value
20	15: 5	75.00	0.04
200	115: 86	57.50	0.04
2000	1046: 954	52.30	0.04
2000000	1001445: 998555	50.07	0.04

The same “statistically significant .04” appears in each row yet the practical significance is wildly different as the sample size varies, indicating that p-value as a metric is deficient.

The choice of an appropriate metric in health care is exceedingly important. An illustration from the Wall Street Journal of March 31, 2010 shows how misleading the five-year survival rate metric can be. A letter writer defending the U.S. against the evils of socialized medicine here replies to someone who was critical of the U.S. health care system compared to other countries:

For prostate cancer specifically, the rather astounding numbers are 92% in the U.S. versus 51% in the U.K. I am sure that the additional four out of 10 men in the U.K. who will die of prostate cancer find that to be significant, even if Dr. Krock does not.

Those “astounding numbers” refer to five-year survival rates. From Gigerenzer we learn of the misinterpretation common to patients and physicians: reliance on survival rates rather than mortality rates. The paper begins with former New York City mayor Rudy Giuliani thanking God for being treated for prostate cancer in the capitalist U.S. where his five-year survival chances were 82% as compared to “only 44% under socialized medicine.” Turns out that “Giuliani’s numbers, however, are meaningless” because in the U.S. prostate cancer is being diagnosed earlier, a lead-time bias, and the cancer is being over diagnosed, that is, a pseudodisease is detected,--“screening-detected abnormalities that meet the pathologic definition of cancer but will never progress to cause symptoms in the patient’s lifetime.” When it comes to mortality rates, there are “About 26 prostate cancer deaths per 100,000 American men versus 27 per 100,000 in Britain.” The data “suggests that many American men have been unnecessarily diagnosed (i.e., overdiagnosed) with prostate cancer during the PSA era and have undergone unnecessary surgery and radiation treatment, which often leads to impotence and/or incontinence.” In a nutshell, “The problem is that there is no relationship between 5-year survival and mortality.”

Discussion

1. The "lead-time bias" is due to screening, i.e., mass testing, which is much more common in the U.S. than in other countries. Google the recent discussions regarding the efficacy of breast cancer screening in woman below the age of 50.

2. Gigarenzer’s article contains other interesting observations regarding relative risk vs. absolute risk. It also discusses the need to present Bayes theorem in a non-confusing way so that a patient and a doctor can understand the often remarkable numerical difference between Prob(test+|diseased) and Prob(diseased|test+).

Census errors

Can you trust Census data?
by Justin Wolfers, New York Times, Freakonomics blog, 2 February 2010

Census Bureau obscured personal data—Too well, some say
by Carl Bialik, Numbers Guy column, Wall Street Journal, 6 February 2010

These stories describe problems with the Census Bureau' IPUMS (Integrated Public Use Mircodata Series) data, which provides subsamples of Census data to outside researchers. In order to protect the privacy of citizens, the records are altered slightly. For example, incomes may be rounded and ages may be tweaked by a small amount. Ideally this would make it impossible to identify any particular individual, while at the same time not introducing any important distortion into the overall demographic profile.

Unfortunately, it appears that serious distortions have resulted. A recent NBER working paper details the problems, which seem to be especially pronounced in data for ages 65 above. The Freakonomics post reproduces the following graph from the paper

http://graphics8.nytimes.com/images/2010/02/02/opinion/Census-Chart/blogSpan.jpg

showing how total population estimates based on the microdata diverge from the actual Census counts for older Americans. Breakdowns within particular age groups are also distorted. For example, The Wall Street Journal article has an interactive graphic, revealing how data released in 2006 showed inexplicable fluctuations from one age year to the next in the percentage of women who were married (those errors were corrected in 2007).

As Bialik notes, "The anomalies highlight how vulnerable research is to potential problems with underlying numbers supplied by other sources, even when the source is the government. And they illustrate how tricky it can be to balance privacy with accuracy."

Submitted by Bill Peterson