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RE: report find radium raises risk of bone cancer in men -- A lookat the raw data
I read the NJ Dept of Health and Senior Services radium/osteosarcoma report, available at <www.nj.gov/health/eoh/radium.pdf>, in hopes of understanding how they reached their conclusions.
They have 75 osteosarcomas in a population of 1.423 million over a period of 12 years. They conduct two separate analyses, one based on maximum contaminant levels for both combined radium and gross alpha, and the second based on a calculated Ra-228 equivalent. In the first analysis, they break the population down into eight groups and various aggregations of those groups. In the second, they break the population down into 16 groups and various aggregations.
An important question that they do not appear to have asked themselves and certainly have not answered in the report is: Does the overall data set allow us to reject the null hypothesis that variation among the 8 and 16 groups is just a reflection of random sampling within a population having an incidence of 3 osteosarcomas per million persons per year?
The report's Tables 3 and 4 allow that question to be asked and answered, since they provide the population associated with each of the 8 and 16 groups, respectively. First, we can use population and osteosarcoma incidence to compute the number of osteosarcomas expected in each of the 8 and 16 groups. Then, we can apply a Wilcoxon, two-sample test of the null hypothesis that the observed values were drawn from the same distribution as the expected values. The Wilcoxon test is almost as powerful as the two sample t test and doesn't require the strong assumptions on the nature of the underlying distribution that the t test does. In neither the 8 group nor the 16 group analysis do we get anywhere close to rejecting the null hypothesis.
Another analysis that is only approximately applicable, because of the small number of cases (i.e., less than 5) in several of the groups, is a Chi-square analysis of the goodness of fit of the observed data to the hypothesis that the data reflect only random variation in a 3 per million incidence population. In this case, Chi-square analysis appears to allow us to reject the null hypothesis at roughly the 0.001 level for the 8 group analysis and the 0.01 level for the 16 group analysis.
BUT, if you look at the contributions to the Chi-square statistic, only about a third of the value of the statistic is coming from groups with more cases observed than expected and about two-thirds is coming from groups with less osteosarcoma that would be predicted from the average incidence.
After this look at the standard null hypothesis, it is not too surprising that results of the data mining of the NJ epidemiologists are all over the map. In the eight group analysis, only one of the four groups shows a statistically significant increase in incidence and one appears to show a statistically significant decrease (3.27 cases expected and zero observed). [Note: the eight groups became four groups because the NJ epidemiologists compared each of its >MCL groups against the corresponding gender-age <MCL group] Similarly, in the 16 group analysis, two of the twelve groups show a statistically significant increase, and it appears that three of the twelve show a statistically significant decrease (expected values of 1.96, 1.47, and 3.08 versus observed values of zero, zero, and zero.
It doesn't appear to me that there is anything in this data set that provides useful information about the effect of radium in drinking water on osteosarcoma incidence.
I would be happy to provide my spreadsheet to anyone interested in checking my calculations.
Best regards,
Jim Dukelow
Pacific Northwest National Laboratory
Richland, WA
jim.dukelow@pnl.gov
These comments are mine and have not been reviewed and/or approved by my management or by the U.S. Department of Energy.
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