A NEW MODEL FOR ANALYZING THE SURVIVAL OF HETEROGENEOUS DATA

A model was proposed for analyzing the survival of heterogeneous populations. The model is a mixture of classes, where each class is modeled by a compound distribution. These conditional distributions can have an increasing, constant and decreasing hazard function, respectively. One of the parameters of that distribution can be compounded using a continuous distribution. Different values of that parameter reflect different levels of frailty. The theory behind the formulation of the model is that the total variability in survival can be regarded as coming from two sources: between classes and within classes.;Some new properties of the compound Weibull distribution are derived. Its hazard function takes the inverse bathtub shape, if its conditional hazard is increasing. The characteristics of the hazard function of the model as a mixture of either compound Weibull or Gompertz are studied.;Properties of the hazard function in general were studied. For example, it was found that a decreasing hazard implies a decreasing density function but the converse is not true; and an increasing density implies an increasing hazard function but the converse is not true. A relation between the proportion of cases at risk at time t belonging to a certain subpopulation, the first derivative of the density function, the overall hazard function, and, its derivative has been derived. This relation is useful in determining the time where the overall hazard is minimized or maximized.;Lifetimes following a mixture of compound Weibull distribution are generated. A reparameterization of the distribution was found to be useful in accurately estimating parameters. When data are less heterogeneous, estimates are less accurate. The model was used to analyse the disease-free survival of patients with breast cancer.;The Weibull and the Gompertz distributions are considered to model conditional survival. A new distribution, the compound Gompertz, has been developed by assuming a conditional random variable following the Gompertz distribution, whose scale parameter obeys a gamma distribution. The properties of that distribution are derived. Its hazard function has the interesting property that it can be decreasing, constant or increasing, when its conditional hazard is increasing.