CONFIDENCE LIMITS FOR DIRECTLY STANDARDIZED RATES

The Standard Error of the adjusted rate R ( seR ) is the square root of the variance of R ( see BDII eq 2.2 ) which is
      var(R)=  sum{ w(j)^2 *Var[ r(j) ] } 
		j
	    =  sum{ w(j)^2 * y(j) / n(j)^2 }
                j
This result is based on the assumption that y(j) can be treated as a Poisson variate* so that the variance of r(j) is estimated by
      var[ r(j) ] = y(j)/n(j)^2.

 METHOD  1.  If 95% CLS are obtained as
       CL.1 =  R - 1.96*seR
       CU.1 =  R + 1.96*seR
The lower CL may be negative if seR is large. This will happen when the component rates are based on sparse data.

METHOD 2. If the seR is not being used as a measure of statistical precision, but is being used to compute CLs then this should be done on the log scale as follows :

     CL.2 = R * exp( -1.96*selogR )
     CU.2 = R * exp(  1.96*selogR ),
where the standard error of log R is selogR = R / seR .

Method 2 is used to calculate CLs in ES Reports.This method should give reasonable approximate CLs as long as there is at least one event.

Also, note that to compare R1 and R2, the age-adjusted rates for groups 1 and 2 , then CLs for the rate ratio should also be computed on the log scale ( see BDII bottom p 64).