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.
Reference Type
Journal Article
Periodical Full
PloS one
Publication Year
2014
Volume
9
Issue
12
Other Pages
e113948
Publisher
Public Library of Science
Place of Publication
United States
ISSN/ISBN
1932-6203
Document Object Index
10.1371/journal.pone.0113948
URL
https://www.ncbi.nlm.nih.gov/pubmed/25473827
PMID
25473827