Analysis of competing risks by using Bayesian smoothing (Q2711678)

An i.i.d. right censored sample \((T_i,\delta_i)\) is observed, where \( T_j\) is the censored failure time \(U_j\), \(\delta_j=0\) if the \(j\)-th individual was censored and otherwise \(\delta_j=\zeta_j\in\{1,\dots,d\}\) is the number of specific failure cause. The data distribution is described by the common failure hazard function \(h(t)=F'(t)/(1-F(t-))\), \(F(t)=\;Pr\{U<t\}\) and NEWLINE\[NEWLINE\pi_i(t)=\Pr\{\zeta=i |U=t\}\quad\text{for}\quad i=1,\dots, d.NEWLINE\]NEWLINE The nonparametric Bayesian technique is used to estimate \(h(t)\) and \(\pi_i(t)\) by the sample. Priors for \(\pi_i\) and \(h\) are defined as kernel smoothed picewise constant random processes. These processes have Poisson jump points and Dirichlet distributed values. For such models a likelihood is described and a Markov chain Monte-Carlo sampler for the posterior distribution is constructed. NEWLINENEWLINENEWLINEThe work of the sampler is described by a contraceptive failure data analysis. The results of ``smoothed priors'' are compared to smoothing of posterior means derived from non-smooth priors.