Adjustment for continuous confounders: an example of how to prevent residual confounding

For all analyses, we used R for Windows, version 2.13.1.16 In the cohort studies described above, the outcome was binary, and we used logistic regression to analyze the association between exposure and outcome. We estimated a crude (unadjusted) association between exposure and outcome. We adjusted for confounding by including the confounder age in the regression model in the following ways. First, we dichotomized age at the median value of the continuous confounder and included age as a dichotomous variable in the adjustment model. Second, we categorized age in 5 categories (based on quintiles of the continuous confounder) and included it in the regression model as a categorical variable.17 Third, we included age as a continuous covariate in the regression model. Fourth, we applied fractional polynomials and restricted cubic splines, which are both methods that more flexibly model the relation between continuous variables and an outcome. In both methods, a smooth nonlinear relation between the continuous confounder and outcome is modelled by including not only the linear form of the continuous confounder, but also other powers (e.g., square root or quadratic terms).3,11,12 In the case of fractional polynomials, the relation between the continuous confounder and the outcome is modelled for the whole range of values of the confounder.11,12 When applying restricted cubic splines, the range of the confounder values is first split up in parts, based on the number of so-called knots (typically 5).3 Then, for each part, the relation between the confounder and the outcome is modelled using the linear form of the continuous confounder as well as other powers. We used the functions mfp() and fp() from the library mfp18 to fit the fractional polynomials and the function rcspline.eval() from the library Hmisc19 to fit restricted cubic splines. To visually evaluate the functional form of the relation between age and the outcomes, we used the function rcspline.plot() from the library Hmisc.19 This graphically shows the relation between the continuous confounder and the log(odds) of the outcome. Confounding can be controlled for in the design or analysis of an observational study.20 When confounding is controlled for in the analysis, this is typically done by including confounders as covariates in, for example, a multivariable regression model. One key problem is confounders that are unobserved, which makes adjustment impossible. A much more subtle problem is confounders