Seriously, someone at the Trib smack Dold over the head for allowing this crap in his paper.
The problem with dismissing the Carroll study because it is epidemiological is that you’ll also have to dismiss a multitude of public health studies, including ones claiming a link between radon and lung cancer. These are the same epidemiological studies that alarmed millions of Americans, frightening them into buying radon detectors and creating a huge radon mitigation business. No study is perfect, and Carroll’s shortcoming is that his data do not allow comparisons of individual women over time. But other major studies have, and according to one unchallenged compressive analysis of those studies, they show that a pregnant woman who has never had a child before and aborts in the first term increased her chance of breast cancer by 50 percent.
Let me offer up the model from the paper
Two explanatory variables are selected for modeling: (abortion)and (fertility).The trends for abortion and fertility are shown in Figures 8 and 9 for countries considered. The Mathematical Model is then:
Yi = a + b1x1i + b2x2i + ei
where Y represents cumulated cohort incidence of breast cancer within a particular age group; a is intercept, b1 and b2 are coefficients, and e is random error.
That creates a guffaw from those who know statistics at all.
He has a correlation Coefficient of .98.
Those who understand correlation coefficients are shooting liquid through their nose if they were drinking anything right now. I had to look at it about 20 minutes to understand this moron was trying to sell a .98 correlation coefficient.
What he has done is take mass data that shows one factor increasing (abortion) and another decreasing (fertility) and then regresses it upon a variable that is increasing-incidence of breast cancer.
So if I were to regress the number of abortions and the fertility rate on the number of televisions sold per person, I’d get about the same result over this period of time. So I can, according to this dumbass, claim credibly that television leads to breat cancer. Or, as the Orac points out, the reduction in the number of pirates has led to global warming.
There’s a variety of problems in this study starting with he throws out independent variables well established by other studies. In the case of linear regression, the problem is that if you do not include other variables, you cannot control for those variables and so not are just theoretical variables excluded, but well established variables demonstrated over and over are excluded from the analysis. To say the least, this is an underspecified
A regression model is underspecified if the regression equation is missing one or more important predictor variables. This situation is perhaps the worst-case scenario, because an underspecified model yields biased regression coefficients and biased predictions of the response. That is, in using the model, we would consistently underestimate or overestimate the population slopes and the population means. To make already bad matters even worse, the mean square error MSE tends to overestimate ?2, thereby yielding wider confidence intervals than it should.
No one accepts a .98 coefficient. No one. That is essentially regressing one variable on itself and in this case, it’s the regressing less restrictive abortion laws with a number of factors that have led to an increase in breast cancer.
Ecological inference is not an acceptable means of imputing causation on individuals from macro level data and this study violates the principle. One might use it to explore potential causes and whether there is a gross correlation, but not to determine causality. For that one requires cohort information or some other way to address individual observations.
It’s junk science. Yet the Chicago Tribune keeps publishing a clown who insists there is a link, but is wholly unqualified to judge that and uses crappy studies to do it. Why?