Monday, December 2, 2013

Regression Analysis

In a recent issue of the “Newsletter of the International Society for Evidence-Based Health Care,” (Newsletter 13, October 2013), Benkhadra et al (1) provide an interesting discussion of how to make sense of regression analysis. They position this as using an analogy from third-grade math. In their article, they note that for novices to evidence-based practice, the words “regression analysis” or “regression model” can put people off from reading further for simple fear they will not be able to understand what is being said. To help such readers, they provide an example based on simple math. I would like to use their example: they look at using results from a young middle-aged man looking to see if he qualifies for life insurance. In his case, he has elevated cholesterol. And he wonders if this might be due to his drinking alcohol. A study is found (2) that looks at the association between alcohol and cholesterol level, and this study is a regression analysis reporting results as regression coefficients. The value reported is 0.298, with p<0 .05="" confidence="" interval="" no="" o:p="" reported="">

To try to see what this means, the authors ask you to consider a simple “input/output” table, and they ask you to predict what values would come next:
Input=3, output=8
Input=4, output=10
Input=5, output=?
Input=6, output=?

 A moment’s thought shows you that the relation here is that output is equal to ( input x2)+2.  You could now develop a linear regression graph for several different people and show that (y=A*x+B) as the line best fitting this relationship. In the case of the paper we found, the actual measure is (cholesterol= 160+0.2998 x alcohol consumption per week).  This has some implications; for example, when alcohol consumption is 0, cholesterol would be 160, and as alcohol consumption increases, so does cholesterol levels at a predictable rate. This is a linear regression, and is a simple model. Of course, it gets more complex as we increase variables…

1.       Benkhadra K, Asi N, Haydour Q, Murad MH. Making sense of a study using regression analysis: analogy from third grade math. International Society of Health Care for Evidence-Based Health Care, October 2013: 4-6
2.       Porrini M, Simonettim P, Testolin G, Roggi C, Laddomada MS, Tencone MT. Relation between diet composition and coronary disease risk factors. J Epidemiol Community Health 1991;45:148-151

 Links for Further Explanation


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