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.
Highlights
In clinical practice, disease diagnosis and subsequent treatment are often guided by a strict threshold of a biomarker
In the case of diabetes diagnosis, the diagnostic threshold was at fasting plasma glucose (FPG) >140 mg/dl before 1997
We demonstrated how reduced isotonic regression can be implemented in parametric time-to-event data analysis with survival time following an exponential or Weibull distribution
Summary
Disease diagnosis and subsequent treatment are often guided by a strict threshold (i.e. change point) of a biomarker. Fasting plasma glucose (FPG) at 126 mg/dl is the cutoff to diagnose type II diabetes, and more intensive treatment is used when FPG reaches 140 mg/dl Such change points are often identified through a large scale health study where disease risk. In 1997, increased cardiovascular and micro-vascular disease risk at lower values prompted the American Diabetes Association to recommend lowering the diagnostic threshold to 126 mg/dl. Changes like this have huge effects on medical practice, especially the initiation of a treatment, a systematic approach to identify change points in a covariate is well worth the effort
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