Resumen de Survival data analysis with heavy-censoring and long-term survivors
Lucas López Segovia
The research developed in this thesis has been motivated by two datasets, which are introduced in Chapter 2, one concerning the mortality of calves from birth to weaning while the other refers to survival of patients diagnosed with melanoma. In both cases the percentage of censoring is high, it is very likely to have immune individuals and proper analysis accounting for the possibility of a not negligible proportion of cured individuals has to be performed. Cure models are introduced in Chapter 3 together with the available software to perform the analysis, such as SAS, R and STATA, among others. We investigate the effect that heavy censoring could have on the estimation of the regression coefficients in the Cox model via a simulation study which considers several scenarios given by different sample sizes and censoring levels, results presented in Chapter 4. An application of a mixture cure model, which includes a Cox model for the survival part and a logistic model for the cure part of patients with melanoma, is described in Chapter 5. In addition, discussions about test for sufficient follow-up and censoring levels are also presented for this data. The data analysis is carried out using the macro in SAS: PSPMCM. The results show that patients with Sentinel Lymph Node (SLN): negative status to biopsy, Clark's level of invasion I-III, Histopathological of Malignant Melanoma subtype: Superficial Spreading Melanoma (SSM), younger than 46 years, and female, are more likely to be cured, whereas patients with melanoma in head and neck, Breslow's micrometric depth = 4mm and ulceration presents, are patients with increased risk of relapse. In particular, patients with Breslow's micrometric depth = 4mm are at higher risk for death. Furthermore, since mixture cure models do not have the property of proportional hazards for the entire population, they can be extended to non-mixture cure models by means of nonlinear transformation models as defined in Tsodikov (2003). An application of the extended hazard models is presented for the mortality of calves in Chapter 6. The methodology allows to get estimates for the cure rate as well as for genetic and environmental effects for each herd. A relevant feature of the non-mixture cure models is that they model, separately, factors which could affect survival from those affecting the cure model, making the interpretation of these models relatively easy. Results are shown in section 6.3.1, and were obtained using the library NLTM of the statistical package R. The short (mortality) and long term (survivors) effects are determined for each factors, as well as its statistical significance in each herd. For example in the herd 1, we find that calving month and difficulty at birth is the set of statistically significant factors for the nonsusceptible (long-term survivors) proportion. Calves born in the period march-august have lower probability of survive than those born in September-February; and the probability of survive is much lower for those that have difficulties at calving for herd 1. For herd 7 the effect of difficulty at calving is different as for herd 1, here only is significative the category strongly assisted. Calves that born from strongly assisted calving have lower probability of survive that calves from without assistance calving. Regarding short-term (mortality) effects, we only find statistically significant predictors in herd 7 where the risk of death of calves born from older mothers, hence with a longer reproductive life, is twice the risk of death of calves born from younger mothers. The obtained results have been compared with those coming from standard survival models. It is also included, a discussion about the likely erroneous conclusions that may yield from standard models, without taking into account the cure.
