In this edition of the Archives, Evans et al1 examine whether prehospital intubation results in higher rates of ventilator-associated pneumonia (VAP). They use logistic regression to study the impact of their main exposure variable (prehospital intubation) on their primary outcome (VAP). To adjust for other potentially confounding variables, they add multiple other independent variables to their logistic regression model. Evans et al find that prehospital intubation does not confer an increased risk of VAP. This analysis is a nice example of using multiple regression to study the relationship of an exposure and an outcome after adjusting for potentially confounding variables.
Venn diagram of explained variation in multiple regression equation Y = b0 + b1X1 + b2X2 + e. Y represents the total variance of the dependent variable. X1 and X2 are the variances associated with these independent variables. The amount of the Y variance explained by X1 is p and q. Where both variables X1 and X2 overlap (q), the Y variance is explained by both of these independent variables. Thus, the segment p is that part of the Y variance explained only by X1. The error term, e, is that amount of the Y variance not explained by X1 or X2 (the area outside of p, q, and r).
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