CoDMod 2 - Modeling Cause-Specific Death Rates

Y_c,t,a ~ NegativeBinomial(mu_c,t,a, alpha)

    where   s: super-region
            r: region
            c: country
            t: year
            a: age

    Y_c,t,a     ~ observed deaths due to a cause in a country/year/age/sex

    mu_c,t,a    ~ exp(beta*X_c,t,a + ln(E) + pi_s + pi_r + pi_c + e_c,t,a)

                beta    ~ fixed effects (coefficients on covariates)
                          Laplace with Mean = 0
                X_c,t,a ~ covariates (by country/year/age)

                E       ~ exposure (total number of all-cause deaths observed)
                          Binomial(n = total deaths in country, p = proportion recorded in study)
                
                pi_s    ~ 'random effect' by super-region
                          year*age grid of offsets
                          sampled from MVN with matern covariance then interpolated via cubic spline
                pi_r    ~ 'random effect' by region
                          year*age grid of offsets
                          sampled from MVN with matern covariance then interpolated via cubic spline
                pi_c    ~ 'random effect' by country
                          year*age grid of offsets
                          sampled from MVN with matern covariance then interpolated via cubic spline

                e_c,t,a ~ error

    alpha       ~ overdispersion parameter