For example, when dealing with dichotomous data the number "1" might conveniently indicate that the characteristic is present instead of "yes" or "true," and the number "0" conveniently indicates "no" or "false". When analyzing data, it is always easier to deal with numeric data instead of text. The true relationship was confounded by these other factors. In other words, it is only after "taking into account" these two confounding variables that we can see that there really is a relationship between diet score and BMI. We can also see (in this very hypothetical example) that there is a striking linear relationship between "diet score" and BMI within each of the four age and gender groups. In other words, both age and gender meet the criteria to be confounders.
In addition, age and gender are also associated with "diet score," which is the "exposure" of interest, because diet scores are not equally distributed by gender or by age. These findings indicate that both age and gender have an impact on BMI, because the older group has higher BMIs than the younger group, while males consistently have higher BMIs than the females. The investigator suspected that gender might also be a confounding factor, and when she identified males and females, the graph looked like this: She first identifies which subjects who are older than 20 years old, and it turns out that the younger subjects and older subjects are clustered in the scatter plot, as shown in the figure below. While this is discouraging, the investigator considers that it is possible that confounding by age and/or gender is masking the true relationship between "diet score" and BMI. The graph below shows the relationship between the new "diet score" and BMI, and it suggests that the "diet score" is not a very good predictor, (i.e., there is little if any association between the two. Information is collected from a small sample of subjects in order to compute their "diet score," and the weight and height of each subject is measured in order to compute their BMI. The investigator wanted to test this new "diet score" to determine how closely it was associated with actual measurements of BMI. Suppose an investigator had developed a scoring system that enabled her to predict an individual's body mass index (BMI) based on information about what they ate and how much. To provide an intuitive understanding of how multiple linear regression does this, consider the following hypothetical example. This is a very useful procedure for identifying and adjusting for confounding. However, if there were other factors (independent variables) that influenced body weight besides height (e.g., age, calorie intake, and exercise level), we might expect that the points for individual subjects would be more loosely scattered around the line, since we are only taking height into account. If height were the only determinant of body weight, we would expect that the points for individual subjects would lie close to the line. In this simple linear regression, we are examining the impact of one independent variable on the outcome.
In this example, if an individual was 70 inches tall, we would predict his weight to be:
We could use the equation to predict weight if we knew an individual's height. We could also describe this relationship with the equation for a line, Y = a + b(x), where 'a' is the Y-intercept and 'b' is the slope of the line. If we were to plot height (the independent or 'predictor' variable) as a function of body weight (the dependent or 'outcome' variable), we might see a very linear relationship, as illustrated below. For example, suppose that height was the only determinant of body weight. Regression analysis makes use of mathematical models to describe relationships. LaMorte, MD, PhD, MPH, Professor of Epidemiologyīoston University School of Public Health Lisa Sullivan, Professor of Biostatistics
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