lognormalEB             package:DCluster             R Documentation

_E_m_p_i_r_i_c_a_l _B_a_y_e_s _S_m_o_o_t_h_i_n_g _u_s_i_n_g _a _l_o_g-_n_o_r_m_a_l _m_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     Smooth  relative risks from a set of expected and observed number
     of cases using a log-Normal model as proposed by _Clayton and
     Kaldor_ (1987). There are estimated by  betatilde_i
     =log((O_i+1/2)/E_i) in order to prevent taking the logarithm of
     zero.

     If this case, the log-relative risks are assumed be independant
     and to have a normal distribution with mean varphi and variance
     sigma2.  Clayton y Kaldor (1987) use the EM algorithm to develop
     estimates of these two parameters which are used to compute the
     Empirical Bayes estimate of b_i. The formula is not listed here,
     but it can be consulted in Clayton and Kaldor (1987).

_U_s_a_g_e:

     lognormalEB(Observed, Expected, maxiter = 20, tol = 1e-05)

_A_r_g_u_m_e_n_t_s:

Observed: Vector of observed cases.

Expected: Vector of expected cases.

 maxiter: Maximum number of iterations allowed.

     tol: Tolerance used to stop the iterative procedure.

_V_a_l_u_e:

     A list of four elements: 

       n: Number of regions.

     phi: Estimate of phi.

  sigma2: Estimate of sigma2.

  smthrr: Vector of smoothed relative risks.

_R_e_f_e_r_e_n_c_e_s:

     Clayton, David and Kaldor, John (1987). Empirical Bayes Estimates
     of Age-standardized Relative Risks for Use in Disease Mapping.
     Biometrics 43, 671-681.

_E_x_a_m_p_l_e_s:

     library(spdep)

     data(nc.sids)

     sids<-data.frame(Observed=nc.sids$SID74)
     sids<-cbind(sids, Expected=nc.sids$BIR74*sum(nc.sids$SID74)/sum(nc.sids$BIR74))

     smth<-lognormalEB(sids$Observed, sids$Expected)

