  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.
