A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

Modelling basin level allocation of water in the Murray-Darling Basin in a world of uncertainty, Murray-Darling Program Working Papers WPM05-1, Risk and Sustainable Management Group, 8 February 2005

Abstract: The Murray-Darling Basin comprises over 1 million km2; it lies within four states and one territory; and over 12, 800 GL of irrigation water is used to produce over 40% of the nation's gross value of agricultural production. This production is used by a diverse collection of some-times mutually exclusive commodities (e.g. pasture; stone fruit; grapes; cotton and field crops). The supply of water for irrigation is subject to climatic and policy uncertainty. Variable inflows mean that water property rights do not provide a guaranteed supply. With increasing public scrutiny and environmental issues facing irrigators, greater pressure is being placed on this finite resource. The uncertainty of the water supply, water quality (salinity), combined with where water is utilised, while attempting to maximising return for investment makes for an interesting research field. The utilisation and comparison of a GAMS and Excel based modelling approach has been used to ask: where should we allocate water?; amongst what commodities?; and how does this affect both the quantity of water and the quality of water along the Murray-Darling river system?