The log-odds ratio, lor sub s, is defined as the natural logarithm of the ratio of two quantities. The numerator of the ratio is pi 2 sub s divided by 1 minus pi 2 sub s. The denominator of the ratio is pi 1 sub s divided by 1 minus pi 1 sub s, where pi 1 sub s is the 2006-2008 prevalence rate and pi 2 sub s is the 2008-2010 prevalence rate for substate area s.

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The estimate of the log-odds ratio, lor hat sub s, is defined as the natural logarithm of the ratio of two quantities. The numerator of the ratio is p 2 sub s divided by 1 minus p 2 sub s. The denominator of the ratio is p 1 sub s divided by 1 minus p 1 sub s, where p 1 sub s is the 2006-2008 small area estimate and p 2 sub s is the 2008-2010 small area estimate for substate area s.

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The covariance between the natural logarithm of Theta 1 hat and the natural logarithm of Theta 2 hat is equal to the correlation between the natural logarithm of Theta 1 hat and the natural logarithm of Theta 2 hat multiplied by the square root of the product of the variances of the natural logarithm of Theta 1 hat and the natural logarithm of Theta 2 hat.

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