The Scalpel Weekly News for November 24, 2014, includes a CDC report that states that the costs of treating skin cancer are skyrocketing. While that is interesting in its own right, the report’s presentation of statistics is noteworthy as well. Lawyers are often called upon to present statistics. This CDC report offers an opportunity to analyze how statistics may be presented strategically, learn that statistics can reflect what the numbers mean in different ways, and how to critically review the use of statistics in the public media. Lawyers presenting statistical summaries and lawyers defending statistical data need to be able to understand what this type of statistical summary may obscure and what further questions to ask to determine whether the conclusions the statistics present are borne out by the underlying data.
The assertion that the costs of treating skin cancer are skyrocketing was based on a study of adult skin cancer data between 2002 and 2011. The researchers created two five-year periods of data from 2002-2006 and 2007-2011 to allow for a comparison over time and to improve the precision of the estimates. The average annual number of adults treated for skin cancer increased from 3.4 million in 2002-2006 to 4.9 million in 2007-2011. The average annual cost for skin cancer treatment increased from $3.6 billion during 2002-2006, to $8.1 billion during 2007-2011, an increase in costs of 126 percent.
Statistical summaries such as this necessarily simplify the amount of data presented. This simplification may not be intended to hide salient facts. However, careful analysis of the statistics is needed to fully understand the study results and the implications. A reader interested in the results would want to see the original data, at least for each year. Without that data, it’s hard to assess whether important details are minimized or omitted. The researcher’s choice of two five-year windows is not unreasonable, but could, theoretically, obscure trends that may contradict the statements that the incidence of skin cancer is increasing and “the costs of treating skin cancer are skyrocketing.” Thus, counsel will want to carefully consider the basis of the statistics.
Consider Scenarios A and B pictured in the bar charts, which were developed by the author of this post and Dr. Robert Wieman, associate professor of mathematics at Virginia State University. In the first scenario, the incidence of skin cancer is rising at a steady rate, and the average for the first five years is 3.4 million, while the average for the last five years is 4.9 million, just as the CDC study reports. The second scenario also has the average for the first five years of 3.4 million, and the average for the last five years is 4.9 million, but the year-by-year data tells a much different story. In this scenario, the incidence in the sixth year is much higher (12.1 million), and since that time, the incidence has actually decreased below the 3.4 million of the first five years. This second scenario may not be wholly realistic for skin cancer incidence increase, but it does demonstrate how the same statistical summary may reflect more than one trend in underlying data.
Gathering data into five-year clumps this way can be useful when the year-by-year data has wide fluctuations, to make it easier to see trends over time. However, if the fluctuations from year to year are so large, then that variance is also noteworthy, and a reader would have more confidence in a trend that held over several five-year periods, rather than just two. A statistician would want to know the variance of the year-to-year data, so they could compare the magnitude of the perceived trend with the magnitude of the variance. There are other statistical methods for summarizing ten years of data, such as linear regression, which would distinguish Scenario A from Scenario B.
There are other reasons a reader could question whether the trend appears more significant than the statistics indicate. First, the data of incidence is not normalized by population. As population increases, one expects the number of cases of skin cancer to increase; the more relevant question is how much the rate of skin cancer (that is, the percentage of the population that is treated for skin cancer) has increased. Based on US Census data for population and the averages reported in the CDC study, on average 1.16% of the population was treated for skin cancer each year in the years 2002-2006, while 1.60% of the population was treated for skin cancer each year in the years 2007-2011. This is just restating the reported increase from 3.4 million to 4.9 million, but has less impact as a change in percentage.
Second, the CDC study states that the costs of treating skin cancer are skyrocketing based on the change in average annual cost, from $3.6 billion to $8.1 billion. The same concerns about the incidence data being aggregated in five-year groups apply to the costs data: without year-by-year data, or a linear regression of the data, very different scenarios could yield these same two averages. It is also notable that part of this increase in cost is just a restatement of the increase in incidence: if there are more people being treated for skin cancer, the overall cost increases. Even with no increase in average cost per person treated ($3.6 bn/3.4 million is approximately $1,060 per person), the reader would expect the cost to rise, to $5.2 billion ($1,060 times 4.9 million).
Furthermore, any increase in cost over time should take inflation into account, specifically inflation in the health sector. Because inflation is an increase in cost over time, without the year-by-year data a reader cannot determine how the increase in skin cancer treatment cost compares to the health sector in general. As an extreme example, consider Scenario C: if there were 17 million skin cancer patients in the first five years in 2002, none in the years 2003-2010, and then 24.5 million patients in 2011, the average incidence over the first five years would still be 3.4 million, and the average over the last five years would still be 4.9 million. Based on publicly accessible data on the increase in health care costs from 2002 to 2011, the cost would rise by 137%, even more than was reported, simply because of the larger number of patients in 2011 and the increase of health care costs generally. On the other hand, if the year to year data is more like Scenario A, then the increase in cost of all skin cancer treatment would be large even compared to the average increase in health care costs. Without more specific data, there is no way to determine how much of the increase would be expected of any health care treatment, as opposed to skin cancer particularly.
Note that the publicly available data on health care costs referred to above is total US health care costs as a percentage of GDP, as stated by the Centers for Medicare and Medicaid Services, combined with annual GDP from the Bureau of Economic Analysis. According to these, health care costs in aggregate increased by 64.3% from 2002 to 2011, and (considering the centers of the two five-year windows, which is appropriate for Scenario A) is 31.4% from 2004 to 2009.
By Sarah Kelman, J.D., Dr. Robert Wieman, associate professor of mathematics at Virginia State University, and the experts and editors at Medical Law Perspectives.
For more details, see the Scalpel Weekly News for November 24, 2014.
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For more information on cancer diagnosis error, see the Medical Law Perspectives, October 2012 Report: Mistakes in Diagnosing Cancer: Liability Concerns for Misdiagnosis, Failure to Diagnose, and Delayed Diagnosis