The empirical Bayes estimation is based on Bayes statistics.  It integrates a correlation method with statistical estimations to integrate prior knowledge or beliefs about the parameters of the dataset when estimating their values (Gatrell 1996, pp303.). The fundamental aspect of the Bayes estimation is

“prior belief  *  likelihood function =  posterior function.”

According to Langford (1994) joint probability is the culmination of two events as a product of a single event, and from the conditional probability of the second event.

In our study, the prior information is described by the gamma distribution (a, u), which represents the denominator populations required for the observed cases of the SMR. We incorporate a Poisson distribution as a Likelihood function to explain the number of observed counts occurring within the units (Langford, 1994).  The Empirical Bayes estimation of SMR is described as

(si + u) / (Ei + a)

Where si is the observed count and Ei is the expected count

The program to run the Bayes estimation was written in a MACRO environment and imported into MINITAB to run the analysis. The codes were obtained from Langford (1994) and modified slightly to iterate through them. The estimation of parameters were a= 37.4132 and n=37.8489. An in depth account of procedures for this method are explained in the references by Clayton and Kaldor (1987).