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 2002-2004 prevalence rate and Pi 2 sub s is the 2004-2006 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 2002-2004 SAE and p 2 sub s is the 2004-2006 SAE for substate area s.

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Variance v of the estimate of the log-odds ratio, lor hat sub s, is a function of three quantities: q1, q2, and q3. It is expressed as the sum of q1 and q2 minus q3, where q1 is the variance of the natural logarithm of Theta 1 hat, q2 is the variance of the natural logarithm of Theta 2 hat, and q3 is 2 times the covariance between the natural logarithm of Theta 1 hat and the natural logarithm of Theta 2 hat.

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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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