on semi-parametric survival analysis using SAS a Bayesian Piecewise Exponential Model for assessing risk in subjects affected by sarcoma

In bio-statistical applications non-parametric and semi-parametric methods have been preferred over parametric ones for assessing the prognostic role of clinical/biological variables: in fact parametric distributional models for times to event are usually restrictive. In particular Proportional Hazard Models are widely adopted due to their simplicity and flexibility. In PH models the effect of prognostic variables is represented as a multiplier of a baseline hazard function h0(t) : so that the relative hazard of any two subject profiles does not vary with time. The most frequently used model is the Cox Model, in which no assumption of the functional form of h0(t) is made. However, such characteristic becomes a drawback if the interest lies on the hazard function or in predictive modeling. In the Piecewise Exponential Model (PE) the baseline hazard h0(t) is piecewise constant on a partition of the time axis: this specification preserves flexibility without requiring restrictive distributional assumptions. Time intervals are included as predictors in the regression model through dummy variables. Furthermore, the PE model can be estimated by GLM techniques, so that it can be easily implemented with standard statistical software. The above mentioned properties have made the PE model an appealing approach for the analysis of continuous time-to-event data. The comparison of results among different case series are generally provided in terms of regression coefficients and/or survival function S(t) with respective interval estimates. In the classical GLM framework, interval estimates of regression coefficients are directly provided, but those of S(t) are not easy to obtain. When prior information derived from different studies is available, Bayesian methodology allow to evaluate how the information provided by the new study modifies such prior belief. Interval estimates of S(t) are derived from its posterior density. The posterior density is a by-product of the MCMC estimation method, since S(t), being a function of Markov Chains (corresponding to regression coefficients), can be treated itself as a Markov Chain. When different priors have to be evaluated a model with non informative priors could be considered as reference. The aim is to show how the Piecewise Exponential Model can be implemented using SAS both in frequentist and Bayesian framework. Frequentist estimates were obtaines by proc GENMOD after having replicated the dataset. Bayesian estimates were obtained with PROC PHREG. The SAS code is shown in the boxes below. Survival Analysis