Test for linearity between continuous confounder and binary outcome first , run a multivariate regression analysis second

Previous statistical studies have indicated that dichotomizing a continuous confounding variable in multivariate regression analyses can lead to biased estimation of the effect of exposures, treatments, and risk factors on outcomes. We suggest that, prior to entry in the multivariate analysis, one should test whether or not the continuous confounding variable is linearly related to log-odds of the binary outcome or hazard ratios of the time-to-event binary outcome. If there is a linear relationship, we encourage that the variable not be dichotomized. We illustrate this issue using clinical data that we recently published in the New England Journal of Medicine (NEJM). The linearity assumption is tested by restricted cubic splines using SAS/Stat® procedures. INTRODUCTION In clinical studies, investigators are frequently interested in determining the association between risk factors and binary outcomes (e.g., dead or alive at discharge) or time-to-event binary outcomes (e.g., time to death, time to readmission) after adjusting for confounding variables. Continuous confounders (such as patient age, blood pressure, glucose, etc.) are often dichotomized prior to entry in the multivariate regression model (e.g., old vs. young, high vs. low blood pressure). Dichotomization is widespread in clinical studies (Del Priore 1997), as such simplicity simplifies the statistical analysis and leads to easy interpretation and presentation of the results. Dichotomization assumes that the relationship between the predictor and the outcome is flat within intervals, i.e., a discontinuity in outcome as interval boundaries are crossed, however, this assumption is far less reasonable than a linearity assumption in most cases. From a statistical point of view, dichotomization reduces statistical power, primarily due to the reduction in the inherent variability of the predictor variable. It is known that dichotomizing continuous predictor variables may result in biased estimation, either in ordinary linear regression (Cumsille et al. 2000), or in logistic regression (Becher 1992; Schulgen et al. 1994), or in Cox proportional hazards regression (Altman et al. 1994; Buettner et al. 1997; Royston et al. 2006). Furthermore, it may result in inflation of the type-I error of the risk factor (Altman et al. 1994; Austin and Brunner 2004). In this paper, we emphasize this issue based on a previous clinical study of time-to-event outcome of heart failure that we conducted (Bhatia et al. 2006). CASE STUDY: OUTCOME OF HEART FAILURE WITH PRESERVED EJECTION FRACTION We conducted a study to compare the features and outcomes of patients with heart failure with preserved ejection fraction (n=880) with those of patients with heart failure with reduced ejection fraction (n=1570). We used Cox proportional-hazards regression analysis to identify factors associated with an increased risk of death after hospitalization for heart failure. Backward variable elimination was used to create a parsimonious model for predicting mortality. Systolic blood pressure was one of the variables selected for inclusion in the final Cox model. By forcing the variable denoting ejection-fraction group into the final 1 Statistics and Data Analysis SAS Global Forum 2009