Abstract
This study considered the problem of predicting survival, based on three alternative models: a single Weibull, a mixture of Weibulls and a cure model. Instead of the common procedure of choosing a single “best” model, where “best” is defined in terms of goodness of fit to the data, a Bayesian model averaging (BMA) approach was adopted to account for model uncertainty. This was illustrated using a case study in which the aim was the description of lymphoma cancer survival with covariates given by phenotypes and gene expression. The results of this study indicate that if the sample size is sufficiently large, one of the three models emerge as having highest probability given the data, as indicated by the goodness of fit measure; the Bayesian information criterion (BIC). However, when the sample size was reduced, no single model was revealed as “best”, suggesting that a BMA approach would be appropriate. Although a BMA approach can compromise on goodness of fit to the data (when compared to the true model), it can provide robust predictions and facilitate more detailed investigation of the relationships between gene expression and patient survival.
Highlights
Modelling survival data plays an important role in the application of statistics in medicine and health science
In addition to a nonparametric formulation, there are many parametric models available for describing survival, including models based on a single distribution such as the Exponential and Weibull, mixture models based for example on mixtures of distributions and a mixture of susceptible and insusceptible individuals or so-called cure models which account for a fraction of the patients being cured from the disease
We calculated the Kaplan-Meier estimates of overall survival according to the gene expression and the relation between the gene expression score and the subgroups phenotype of Diffuse Large B-cell Lymphoma (DLBCL)
Summary
Modelling survival data plays an important role in the application of statistics in medicine and health science. In addition to a nonparametric formulation, there are many parametric models available for describing survival, including models based on a single distribution such as the Exponential and Weibull, mixture models based for example on mixtures of distributions and a mixture of susceptible and insusceptible individuals or so-called cure models which account for a fraction of the patients being cured from the disease. Given the wealth of models, the dilemma that is faced by many practitioners is the choice of a survival model. The problem of model selection is abundant throughout the literature. This includes both covariate selection and choice of the model itself.
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