An Unified Semiparametric Approach to Model Lifetime Data with Crossing Survival Curves
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The proportional hazards (PH), proportional odds (PO) and accelerated failure time (AFT) models have been widely used in different applications of survival analysis. Despite their popularity, these models are not suitable to handle lifetime data with crossing survival curves. In 2005, Yang and Prentice proposed a semiparametric two-sample strategy (YP model), including the PH and PO frameworks as particular cases, to deal with this type of data. Assuming a general regression setting, the present paper proposes an unified approach to fit the YP model by employing Bernstein polynomials to manage the baseline hazard and odds under both the frequentist and Bayesian frameworks. The use of the Bernstein polynomials has some advantages: it allows for uniform approximation of the baseline distribution, it leads to closed-form expressions for all baseline functions, it simplifies the inference procedure, and the presence of a continuous survival function allows a more accurate estimation of the crossing survival time. Extensive simulation studies are carried out to evaluate the behavior of the models. The analysis of a clinical trial data set, related to non-small-cell lung cancer, is also developed as an illustration. Our findings indicate that assuming the usual PH model, ignoring the existing crossing survival feature in the real data, is a serious mistake with implications for those patients in the initial stage of treatment.
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