Isotonic regression or monotonic regression (also called order restricted hypothesis testing) has been developed for a long time and it provides a simple, yet useful way to investigate the relationship between a general response variable and an ordinal predictor variable with an order constraint. The resulting model is usually a monotonic step function, which can be further simplified by combining those steps which do not differ greatly. Such an analog of isotonic regression is referred to as the reduced isotonic regression. The reduced isotonic regression model has the advantage of categorizing a continuous variable with less over-fitting and it can be viewed as a change-point model with unknown number of monotonic shifts. Only recently, isotonic regression has been applied in survival data analysis by Ancukiewicz, Finkel-stein and Schoenfeld (2003). However, reduced isotonic regression has not been studied in survival data analysis.
In this dissertation, we explore the use of reduced isotonic regression in survival data analysis. Differently from the two step procedure, we integrate the second step (the 'reducing' step) into the first step through a dynamic programming (DP) algorithm. We term this approach 'flexible isotonic regression' because by pre-specifying the testing significance, we can have a full model or more parsimonious model, hence flexible. We start with the exponential distribution and then move on to the more general Weibull distribution. Finally, a piecewise proportional hazard (PPH) model with isotonic regression is described, which has a more non-parametric flavored estimate for the baseline hazard. Parameters are estimated with the maximum likelihood method.
We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set. All three approaches, exponential, Weibull and PPH are used and the results compared. Models generated from the three approaches are very similar. All suggest a non-linear negative association between HbA1C and risk of severe hypoglycemia. With mild testing added, HbA1C values at 6.2, 7.3 and 9.6 are identified as potential change points in its association with severe hypoglycemia.
|Advisor:||Lai, Yinglei, Lachin, John M.|
|Commitee:||Follmann, Dean A., Larsen, Michael D., Modarres, Reza, Pan, Qing|
|School:||The George Washington University|
|School Location:||United States -- District of Columbia|
|Source:||DAI-B 71/09, Dissertation Abstracts International|
|Keywords:||Dynamic programming, Exponential distribution, Isotonic regression, Piecewise exponential distribution, Survival analysis, Weibull distribution|
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