TITLE:
An Adaptive Approach for Hazard Regression Modeling
AUTHORS:
George J. Knafl
KEYWORDS:
Adaptive Regression, Fractional Polynomials, Hazard Rate, Likelihood Cross-Validation, Survival Times
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.3,
June
16,
2023
ABSTRACT: Regression models for survival time data involve estimation of the hazard
rate as a function of predictor variables and associated slope parameters. An
adaptive approach is formulated for such hazard regression modeling. The hazard
rate is modeled using fractional polynomials, that is, linear combinations of
products of power transforms of time together with other available predictors.
These fractional polynomial models are restricted to generating positive-valued
hazard rates and decreasing survival times. Exponentially distributed survival times are a special case. Parameters are estimated using maximum likelihood
estimation allowing for right censored survival times. Models are evaluated and
compared using likelihood cross-validation (LCV) scores. LCV scores and
tolerance parameters are used to control an adaptive search through alternative
fractional polynomial hazard rate models to identify effective models for the underlying survival time data. These methods are
demonstrated using two different survival time data sets including
survival times for lung cancer patients and
for multiple myeloma patients. For the lung cancer data, the hazard rate
depends distinctly on time. However, controlling for cell type provides a
distinct improvement while the hazard rate depends only on cell type and no
longer on time. Furthermore, Cox regression is unable to identify a cell type
effect. For the multiple myeloma data, the hazard rate also depends distinctly
on time. Moreover, consideration of hemoglobin at diagnosis provides a distinct
improvement, the hazard rate still depends distinctly on time, and hemoglobin
distinctly moderates the effect of time on the hazard rate. These results
indicate that adaptive hazard rate modeling can provide unique insights into
survival time data.