Abstract
Progress in immunotherapy revolutionized the treatment landscape for advanced
lung cancer, raising survival expectations beyond those that were historically
anticipated with this disease. In the present study, we describe the methods
for the adjustment of mixture parametric models of two populations for survival
analysis in the presence of long survivors. A methodology is proposed in
several five steps: first, it is proposed to use the multimodality test to
decide the number of subpopulations to be considered in the model, second to
adjust simple parametric survival models and mixture distribution models, to
estimate the parameters and to select the best model fitted the data, finally,
to test the hypotheses to compare the effectiveness of immunotherapies in the
context of randomized clinical trials. The methodology is illustrated with data
from a clinical trial that evaluates the effectiveness of the therapeutic
vaccine CIMAvaxEGF vs the best supportive care for the treatment of advanced
lung cancer. The mixture survival model allows estimating the presence of a
subpopulation of long survivors that is 44% for vaccinated patients. The
differences between the treated and control group were significant in both
subpopulations (population of short-term survival: p = 0.001, the population of
long-term survival: p = 0.0002). For cancer therapies, where a proportion of
patients achieves long-term control of the disease, the heterogeneity of the
population must be taken into account. Mixture parametric models may be more
suitable to detect the effectiveness of immunotherapies compared to standard
models.