survival-modelslisted

# Survival Models ## Data Structure ```stan data { int<lower=0> N; vector<lower=0>[N] time; // Observed/censored time array[N] int<lower=0,upper=1> event; // 1=event, 0=censored matrix[N, K] X; // Covariates } ``` ## Exponential Model ### Stan ```stan parameters { real alpha; // Log baseline hazard vector[K] beta; } model { alpha ~ normal(0, 2); beta ~ normal(0, 1); for (n in 1:N) { real lambda = exp(alpha + X[n] * beta); if (event[n] == 1) target += exponential_lpdf(time[n] | lambda); else target += exponential_lccdf(time[n] | lambda); // Survival } } ``` ### JAGS (with censoring) ``` model { for (i in 1:N) { is.censored[i] ~ dinterval(t[i], t.cen[i]) t[i] ~ dexp(lambda[i]) log(lambda[i]) <- alpha + inprod(X[i,], beta[]) } alpha ~ dnorm(0, 0.25) for (k in 1:K) { beta[k] ~ dnorm(0, 1) } } ``` ## Weibull Model ### Stan (AFT Parameterization) ```stan parameters { real alpha; // Intercept (log scale) vector[K] beta; real<lower=0> shape; // Weibull shape } model { alpha ~ normal(0, 5); beta ~ normal(0, 2); shape ~ exponential(1); for (n in 1:N) { real mu = alpha + X[n] * beta; if (event[n] == 1) target += weibull_lpdf(time[n] | shape, exp(mu)); else target += weibull_lccdf(time[n] | shape, exp(mu)); } } ``` ### JAGS ``` model { for (i in 1:N) { is.censored[i] ~ dinterval(t[i], t.cen[i]) t[i] ~ dweib