Estimate cause specific survival in soft tissue retroperitoneal sarcomas in the presence of competing risks : relative and net survival

Soft Tissue Sarcomas (STSs) are a rare and heterogeneous group of malignancies that originate from mesenchymal cells almost everywhere in the body. To evaluate therapy-related benefit, disease specific survival is surely of interest, being related to the mortality associated with the specific cancer diagnosis and disease evolution. Such a probability measure refers to the hypothetical situation of cause removal, i.e. only the cause of interest is acting. The naïve classical approach to estimate net/cause specific survival is based only on the events attributable to the disease, while times to other death causes are censored. This is appropriate only under independence among causes of death. However, from the statistical viewpoint, cause specific survival refers to the context of ‘competing risks’ and its estimation to a non identifiable problem, due to the interrelation among different causes of death. In population based cancer survival studies, relative survival methods were proposed for estimating the excess mortality with respect to that would be expected for the population to which patients belong, matched for sex, age, and year of birth. The observed excess mortality is assumed to be cancer related, capturing both directly and indirectly related death events. Although this approach does not provide a direct estimation of net survival, under specific assumptions can be interpreted as a net survival. However, this is not always holding and, in the presence of a reliable classification of the causes of death relative survival should be compared with a direst estimate of net survival. Several non parametric estimator based on copula functions have been proposed, but they are rarely used in clinical application, mainly because of the lack of dedicated software. The copula allow to specify the bivariate distribution among causes of death, leaving unspecified the marginal ones and several copula structures have been proposed so far. An advantage of these approaches is to provide an estimate of association among times to different causes of death, which could be itself of clinical interest. The choice of the appropriate copula structure is mainly based on clinical considerations since, in the presence of competing risks, it is not possible to assesse the goodness of fit. Nevertheless published simulation studies showed the robustness of Archimedean copulas. The aim of the present work is to compare relative and net sarcoma survival estimates in a clinical-epidemiology observational cohort setting in which the classification of causes of death is reliable, to have insights on other studies on the same pathology where the causes of death is not available. 192 adult patients with retroperitoneal STS admitted at the National Cancer Institute in Milan from January 1985 to September 2007 who underwent surgery on primary localized disease were included in the present analysis. The results highlighted that patients who underwent a diagnosis of retroperitoneal sarcoma had an excess mortality. The relative survival Poisson regression model showed that age, surgical margins, grading and tumour size are prognostic factors. These results were compared to the net survival curve estimated by Copula graphic estimator with pertinent confidence intervals.