Ashok Krishnaswami1, Thomas Alloggiamento2, Daniel E Forman3, Thomas K Leong4, Alan S Go5, Charles E Mcculloch6. 1. Cardiologist at the San Jose Medical Center in CA. ashok.krishnaswami@kp.org. 2. Cardiologist at the San Jose Medical Center in CA. thomas.alloggiamento@kp.org. 3. Cardiologist at the Division of Geriatric Cardiology, University of Pittsburgh and the Geriatric Research, Education and Clinical Center at the Veterans Administration Pittsburgh Healthcare System in PA. formand@pitt.edu. 4. Consulting Data Analyst at the Division of Research in Oakland, CA. thomas.k.leong@kp.org. 5. Chair of the Cardiovascular and Metabolic Conditions Section and Director of the Comprehensive Clinical Research Unit at the Division of Research in Oakland, CA. alan.s.go@kp.org. 6. Professor and Chair of the Division of Biostatistics and the Vice Chair of the Department of Epidemiology and Biostatistics in the School of Medicine at the University of California, San Francisco. charles.mcculloch@ucsf.edu.
Abstract
BACKGROUND: The clinical effects of age occur over an age continuum, yet age as a primary predictor is often analyzed using arbitrary age cut-points. OBJECTIVE: To assess whether transformation of a continuous variable such as age using a spline function can uncover nonlinear associations between age and cardiovascular outcomes. DESIGN: Observational retrospective cohort study in 1015 Kaiser Permanente Northern California patients with end-stage renal disease after index coronary revascularization. Age, the primary predictor, was modeled by 5 different techniques: 1) dichotomized at 65 years or older; 2) at 80 years or older (as a sensitivity analysis); 3) categorized as younger than 55 years (reference), 55 to 64, 65 to 74, and 75 years or older; 4) linear (every 5 years) variable; and 5) nonlinear by transformation into a cubic spline. Age categories were changed in a sensitivity analysis. MAIN OUTCOME MEASURES: Primary and secondary outcomes were all-cause mortality and repeat revascularization, respectively. RESULTS: Graphical assessment demonstrated that age dichotomized at either 65 years and older or 80 years and older led to loss of information. Categorized age underestimated or overestimated risk at the extremes of age. A sensitivity analysis demonstrated that an arbitrary change in the age category led to a different conclusion. Age modeled linearly adequately represented mortality risk but was suboptimal with repeat revascularization. Only the cubic spline demonstrated the nonlinear association between age and repeat revascularization. CONCLUSION: Employing the continuous variable age as a case study, we have demonstrated that the use of flexible transformations, such as spline functions, can unearth clinically meaningful associations that would not have been possible otherwise. Future research should determine whether incorporation of these methods can improve decision making at a population level.
BACKGROUND: The clinical effects of age occur over an age continuum, yet age as a primary predictor is often analyzed using arbitrary age cut-points. OBJECTIVE: To assess whether transformation of a continuous variable such as age using a spline function can uncover nonlinear associations between age and cardiovascular outcomes. DESIGN: Observational retrospective cohort study in 1015 Kaiser Permanente Northern Californiapatients with end-stage renal disease after index coronary revascularization. Age, the primary predictor, was modeled by 5 different techniques: 1) dichotomized at 65 years or older; 2) at 80 years or older (as a sensitivity analysis); 3) categorized as younger than 55 years (reference), 55 to 64, 65 to 74, and 75 years or older; 4) linear (every 5 years) variable; and 5) nonlinear by transformation into a cubic spline. Age categories were changed in a sensitivity analysis. MAIN OUTCOME MEASURES: Primary and secondary outcomes were all-cause mortality and repeat revascularization, respectively. RESULTS: Graphical assessment demonstrated that age dichotomized at either 65 years and older or 80 years and older led to loss of information. Categorized age underestimated or overestimated risk at the extremes of age. A sensitivity analysis demonstrated that an arbitrary change in the age category led to a different conclusion. Age modeled linearly adequately represented mortality risk but was suboptimal with repeat revascularization. Only the cubic spline demonstrated the nonlinear association between age and repeat revascularization. CONCLUSION: Employing the continuous variable age as a case study, we have demonstrated that the use of flexible transformations, such as spline functions, can unearth clinically meaningful associations that would not have been possible otherwise. Future research should determine whether incorporation of these methods can improve decision making at a population level.
Authors: L David Hillis; Peter K Smith; Jeffrey L Anderson; John A Bittl; Charles R Bridges; John G Byrne; Joaquin E Cigarroa; Verdi J Disesa; Loren F Hiratzka; Adolph M Hutter; Michael E Jessen; Ellen C Keeley; Stephen J Lahey; Richard A Lange; Martin J London; Michael J Mack; Manesh R Patel; John D Puskas; Joseph F Sabik; Ola Selnes; David M Shahian; Jeffrey C Trost; Michael D Winniford Journal: Circulation Date: 2011-11-07 Impact factor: 29.690
Authors: Mark J Pletcher; Eric Vittinghoff; Ravi Kalhan; Joshua Richman; Monika Safford; Stephen Sidney; Feng Lin; Stefan Kertesz Journal: JAMA Date: 2012-01-11 Impact factor: 56.272
Authors: Ka He; Eric B Rimm; Anwar Merchant; Bernard A Rosner; Meir J Stampfer; Walter C Willett; Alberto Ascherio Journal: JAMA Date: 2002-12-25 Impact factor: 56.272
Authors: Karen P Alexander; L Kristin Newby; Christopher P Cannon; Paul W Armstrong; W Brian Gibler; Michael W Rich; Frans Van de Werf; Harvey D White; W Douglas Weaver; Mary D Naylor; Joel M Gore; Harlan M Krumholz; E Magnus Ohman Journal: Circulation Date: 2007-05-15 Impact factor: 29.690
Authors: Karen P Alexander; L Kristin Newby; Paul W Armstrong; Christopher P Cannon; W Brian Gibler; Michael W Rich; Frans Van de Werf; Harvey D White; W Douglas Weaver; Mary D Naylor; Joel M Gore; Harlan M Krumholz; E Magnus Ohman Journal: Circulation Date: 2007-05-15 Impact factor: 29.690