Abstract
Proportional hazard regression models are widely used in survival analysis to understand and exploit the relationship between survival time and covariates. For left censored survival times, reversed hazard rate functions are more appropriate. In this paper, we develop a parametric proportional hazard rates model using an inverted Weibull distribution. The estimation and construction of confidence intervals for the parameters are discussed. We assess the performance of the proposed procedure based on a large number of Monte Carlo simulations. We illustrate the proposed method using a real case example.
Highlights
In survival studies, covariates or explanatory variables are usually employed to represent heterogeneity in a population
The most commonly used parametric model is the Weibull regression model, which satisfies the proportional relationship between hazard rate functions of the lifetimes of two subjects
For more properties and applications of parametric regression models, one should refer to Lawless [1]
Summary
Covariates or explanatory variables are usually employed to represent heterogeneity in a population. The most commonly used parametric model is the Weibull regression model, which satisfies the proportional relationship between hazard rate functions of the lifetimes of two subjects. Introduced by Barlow et al [3], the function λ(t) has been used in various contexts such as the estimation of distribution function under left censoring [1], defining a new stochastic order [4], characterization of lifetime distributions [5,6,7], studying ageing behavior [8, 9], evolving new repair and maintenance strategies [10, 11], the mixed proportional hazards model [12], and stress hybrid hazards model [13]. We introduce a fully parametric regression model that satisfies the proportional reversed hazards property.
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