SURVIVAL ANALYSIS AND REGRESSION MODELS IN THE PRESENCE OF COMPETING AND SEMI-COMPETING RISKS

Evaluation of a therapeutic strategy is complex when the course of a disease is characterized by the occurrence of different kinds of events. Competing risks arise when the occurrence of specific events prevents the observation of other events. Different survival or incidence functions can be defined in the presence of competing risks and a relevant issue is an adequate knowledge of the methodological background in order to apply a suitable statistical analysis for the study aims. This work aims at presenting different estimates of survival or incidence probabilities used in this framework. From clinical application, it emerges that crude cumulative incidence is widely diffuses both to estimate incidence probabilities and to evaluate covariate effects. On the contrary net survival functions, although of clinical interest, are not diffused because of more difficult model structure and lack of software availability. If the independence assumption between different events is tenable, Kaplan-Meier method can be used to estimate net survival. Otherwise multivariate distribution of times based on Copulas can be adopted. In the case of different causes of death, relative survival can be interpreted as net survival only under specific assumptions on the mortality pattern. A particular case on competing risks arises when only fatal events can prevent the observation of the non fatal ones, but not vice versa (semi-competing risks). The estimate of an interpretable measure of association between times to non fatal and fatal event is often of biological interest, in order to understand the disease progression. In the statistical literature some approaches have been proposed to estimate the association between two independently doubly censored failure times, but more specific approach have to be applied in the presence of semi-competing risks. After estimating the association parameter, the survival function of a non terminal event can be estimated after fixing a copula structure by means of the semi parametric methods proposed by Fine, Jiang and Chappell or the copula graphic estimator. Furthermore when the interest is to evaluate the effect of different therapeutic strategies or covariates on the occurrence of a non terminal event in a semi-competing risks setting, specific regression model have to be adopted. I propose here to adopt the methodology based on pseudo-observations, having the advantage to be implemented by generalized linear models approaches. Simulation studies are performed to compare the performances of methods to estimate the association between events, of methods based on Copulas models to estimate net survival and of regression method for net survival in the presence of semi-competing risks. A case series of breast cancer patients is used to illustrate different methods of estimating net survival functions on the causes of deaths and on the severe non fatal events in the presence of competing and semi-competing risks framework.