title: Identifying change points in a covariate effect on time-to-event analysis with reduced isotonic regression.
abstract: Isotonic regression is a useful tool to investigate the relationship between a quantitative covariate and a time-to-event outcome. The resulting non-parametric model is a monotonic step function of a covariate X and the steps can be viewed as change points in the underlying hazard function. However, when there are too many steps, over-fitting can occur and further reduction is desirable. We propose a reduced isotonic regression approach to allow combination of small neighboring steps that are not statistically significantly different. In this approach, a second stage, the reduction stage, is integrated into the usual monotonic step building algorithm by comparing the adjacent steps using appropriate statistical testing. This is achieved through a modified dynamic programming algorithm. We implemented the approach with the simple exponential distribution and then its extension, the Weibull distribution. Simulation studies are used to investigate the properties of the resulting isotonic functions. We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set to identify potential change points in the association between HbA1c and the risk of severe hypoglycemia.
authors.affiliation: The Biostatistics Center, George Washington University, Rockville, MD, United States of America; Department of Epidemiology and Biostatistics, Milken Institute School of Public Health, George Washington University, Washington, DC, United States of America.
authors.forename: Yong
authors.initials: Y
authors.lastname: Ma
authors.affiliation: The Biostatistics Center, George Washington University, Rockville, MD, United States of America; Department of Statistics, George Washington University, Washington, DC, United States of America.
authors.forename: Yinglei
authors.initials: Y
authors.lastname: Lai
authors.affiliation: The Biostatistics Center, George Washington University, Rockville, MD, United States of America; Department of Epidemiology and Biostatistics, Milken Institute School of Public Health, George Washington University, Washington, DC, United States of America.
authors.forename: John M
authors.initials: JM
authors.lastname: Lachin
mesh_terms: D000465:Algorithms; D006442:Glycated Hemoglobin / Q000032:analysis; D006801:Humans; D007003:Hypoglycemia / Q000473:pathology; D008962:Models, Theoretical; D012307:Risk Factors; D012720:Severity of Illness Index
chemical_list: D006442:Glycated Hemoglobin; C517652:hemoglobin A1c protein, human