Bone marrow transplants are a standard treatment for acute leukemia. Recovery following bone marrow transplantation is a multi-state process. This article examines predictions of probabilities at some points in multi-state survival models. Cox's proportional hazards model has been widely used for the analysis of treatment and prognostic effects with censored survival data. The model was developed based on the relation between survival and the patient characteristic observed when the patient entered the study. When the covariates values change for the duration of the study, however, some theoretical problems to be solved with respect to baseline survival function and baseline cumulative hazard function are involved. Several prognostic models have become widespread using the Cox's proportional hazards modes for the analysis of survival data having time-dependent covariates. In the present study, we propose nonlinear analysis based on generalized additive models with
B-spline to predict the survival for the following short-term (say, 1 year) at any time during the course of the disease, and select the optimum smoothing parameters based on a valiant multifold cross-validation method. In order to summarize the measure of goodness-of-fit, the deviance on fitting a generalized additive model can be bootstrapped.
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