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wei_gau_joint.stan
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wei_gau_joint.stan
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/* Variable naming:
obs = observed
cen = (right) censored
N = number of samples
M = number of covariates
bg = established risk (or protective) factors
biom = candidate biomarkers (candidate risk factors)
tau = scale parameter
NM = non-diabetic men
NW = non-diabetic women
DM = diabetic men
DW = diabetic women
(or any other four groups induced by two binary variables)
*/
// Tomi Peltola, tomi.peltola@aalto.fi
functions {
vector sqrt_vec(vector x) {
vector[dims(x)[1]] res;
for (m in 1:dims(x)[1]){
res[m] <- sqrt(x[m]);
}
return res;
}
matrix joint_prior_lp(
matrix beta_raw, // raw beta parameters
vector csprime, // cp and sp
vector cs_params,
vector r, // scales of beta
matrix V // eigenvectors of the correlation matrix
) {
matrix[dims(r)[1], 4] beta;
csprime[1] ~ beta(cs_params[1], cs_params[2]);
csprime[2] ~ beta(cs_params[3], cs_params[4]);
col(beta_raw, 1) ~ normal(0.0, 1.0);
col(beta_raw, 2) ~ normal(0.0, 1.0);
col(beta_raw, 3) ~ normal(0.0, 1.0);
col(beta_raw, 4) ~ normal(0.0, 1.0);
{
real c;
real s;
real lambda;
vector[4] eigvals;
c <- 1.0 - 1.0/(1.0 - csprime[1]);
s <- 1.0 - 1.0/(1.0 - csprime[2]);
lambda <- sqrt((2.0 * c - 1.0) * (2.0 * s - 1.0) * (2.0 * (c + s) - 1.0) / ((1.0 - 2.0 * (c + s - c * s)) * (c + s - 1.0)));
eigvals[1] <- 1.0;
eigvals[2] <- 1.0/sqrt(1.0 - 2.0 * c);
eigvals[3] <- 1.0/sqrt(1.0 - 2.0 * s);
eigvals[4] <- 1.0/sqrt(1.0 - 2.0 * (c + s));
for (m in 1:dims(r)[1]) {
beta[m] <- (r[m] * lambda) * (V * (eigvals .* (V' * beta_raw[m]')))';
}
}
return beta;
}
vector gau_prior_lp(real r1_global, real r2_global, vector ones_biom) {
r1_global ~ normal(0.0, 1.0);
r2_global ~ inv_gamma(0.5, 0.5);
return (r1_global * sqrt(r2_global)) * ones_biom;
}
vector bg_prior_lp(real r_global, vector r_local) {
r_global ~ normal(0.0, 10.0);
r_local ~ inv_chi_square(1.0);
return r_global * sqrt_vec(r_local);
}
}
data {
int<lower=0> NobsNM;
int<lower=0> NobsNW;
int<lower=0> NobsDM;
int<lower=0> NobsDW;
int<lower=0> NcenNM;
int<lower=0> NcenNW;
int<lower=0> NcenDM;
int<lower=0> NcenDW;
int<lower=0> M_bg;
int<lower=0> M_biom;
vector[NobsNM] yobsNM;
vector[NcenNM] ycenNM;
matrix[NobsNM, M_bg] Xobs_bgNM;
matrix[NcenNM, M_bg] Xcen_bgNM;
matrix[NobsNM, M_biom] Xobs_biomNM;
matrix[NcenNM, M_biom] Xcen_biomNM;
vector[NobsNW] yobsNW;
vector[NcenNW] ycenNW;
matrix[NobsNW, M_bg] Xobs_bgNW;
matrix[NcenNW, M_bg] Xcen_bgNW;
matrix[NobsNW, M_biom] Xobs_biomNW;
matrix[NcenNW, M_biom] Xcen_biomNW;
vector[NobsDM] yobsDM;
vector[NcenDM] ycenDM;
matrix[NobsDM, M_bg] Xobs_bgDM;
matrix[NcenDM, M_bg] Xcen_bgDM;
matrix[NobsDM, M_biom] Xobs_biomDM;
matrix[NcenDM, M_biom] Xcen_biomDM;
vector[NobsDW] yobsDW;
vector[NcenDW] ycenDW;
matrix[NobsDW, M_bg] Xobs_bgDW;
matrix[NcenDW, M_bg] Xcen_bgDW;
matrix[NobsDW, M_biom] Xobs_biomDW;
matrix[NcenDW, M_biom] Xcen_biomDW;
}
transformed data {
real<lower=0> tau_mu;
vector<lower=0>[1] tau_al;
matrix[4,4] V; // eigenvectors of the correlation matrix
vector[M_biom] ones_biom;
tau_mu <- 10.0;
tau_al[1] <- 10.0;
V[1,1] <- 0.5; V[2,1] <- 0.5; V[3,1] <- 0.5; V[4,1] <- 0.5;
V[1,2] <- -0.5; V[2,2] <- 0.5; V[3,2] <- -0.5; V[4,2] <- 0.5;
V[1,3] <- -0.5; V[2,3] <- -0.5; V[3,3] <- 0.5; V[4,3] <- 0.5;
V[1,4] <- 0.5; V[2,4] <- -0.5; V[3,4] <- -0.5; V[4,4] <- 0.5;
for (m in 1:M_biom) {
ones_biom[m] <- 1.0;
}
}
parameters {
vector<lower=0,upper=1>[2] csprime_biom;
vector<lower=0,upper=1>[2] csprime_bg;
vector<lower=0,upper=1>[2] csprime_al;
vector<lower=0>[4] cs_params; // a_c & b_c, and a_s & b_s
real<lower=0> tau_s_bg_raw;
vector<lower=0>[M_bg] tau_bg_raw;
real<lower=0> tau_s1_biom_raw;
real<lower=0> tau_s2_biom_raw;
matrix[1, 4] alpha_raw;
matrix[M_bg, 4] beta_bg_raw;
matrix[M_biom,4] beta_biom_raw;
vector[4] mu;
}
transformed parameters {
matrix[M_biom,4] beta_biom;
matrix[M_bg,4] beta_bg;
matrix[1,4] alpha;
beta_biom <- joint_prior_lp(beta_biom_raw, csprime_biom, cs_params,
gau_prior_lp(tau_s1_biom_raw, tau_s2_biom_raw, ones_biom), V);
beta_bg <- joint_prior_lp(beta_bg_raw, csprime_bg, cs_params,
bg_prior_lp(tau_s_bg_raw, tau_bg_raw), V);
alpha <- exp(joint_prior_lp(alpha_raw, csprime_al, cs_params, tau_al, V));
}
model {
yobsNM ~ weibull(alpha[1,1], exp(-(mu[1] + Xobs_bgNM * col(beta_bg, 1) + Xobs_biomNM * col(beta_biom, 1))/alpha[1,1]));
yobsNW ~ weibull(alpha[1,2], exp(-(mu[2] + Xobs_bgNW * col(beta_bg, 2) + Xobs_biomNW * col(beta_biom, 2))/alpha[1,2]));
yobsDM ~ weibull(alpha[1,3], exp(-(mu[3] + Xobs_bgDM * col(beta_bg, 3) + Xobs_biomDM * col(beta_biom, 3))/alpha[1,3]));
yobsDW ~ weibull(alpha[1,4], exp(-(mu[4] + Xobs_bgDW * col(beta_bg, 4) + Xobs_biomDW * col(beta_biom, 4))/alpha[1,4]));
increment_log_prob(weibull_ccdf_log(ycenNM, alpha[1,1], exp(-(mu[1] + Xcen_bgNM * col(beta_bg, 1) + Xcen_biomNM * col(beta_biom, 1))/alpha[1,1])));
increment_log_prob(weibull_ccdf_log(ycenNW, alpha[1,2], exp(-(mu[2] + Xcen_bgNW * col(beta_bg, 2) + Xcen_biomNW * col(beta_biom, 2))/alpha[1,2])));
increment_log_prob(weibull_ccdf_log(ycenDM, alpha[1,3], exp(-(mu[3] + Xcen_bgDM * col(beta_bg, 3) + Xcen_biomDM * col(beta_biom, 3))/alpha[1,3])));
increment_log_prob(weibull_ccdf_log(ycenDW, alpha[1,4], exp(-(mu[4] + Xcen_bgDW * col(beta_bg, 4) + Xcen_biomDW * col(beta_biom, 4))/alpha[1,4])));
// cs_params ~ gamma(0.5, 0.25);
// changed to half-normal
cs_params ~ normal(0.0, 10.0);
mu ~ normal(0.0, tau_mu);
}