Poisson Variance

With Provided Count

This selection assumes the dependent variable is y = c, where c is the adjusted count, which equals either:

• The count, if the count is greater than zero.
• The count plus one half, if the count is equal to zero.

Assume the random errors are Poisson, and estimate the regression coefficients by weighted least squares, where weights at each point are:

• For model y = xb
  w = 1/c, where c is the adjusted count for that point.

• For model ln(y) = xb
  w = c, where c is the adjusted count for that point. (Motivated by delta method.)

With Calculated Crude Rate

This selection assumes the dependent variable is y = c/p, where c is the adjusted count and p is the population.   The adjusted count will be equal to either:

• The count, if the count is greater than zero.
• The count plus one half, if the count is equal to zero.

Assume the random errors are Poisson, and estimate the regression coefficients by weighted least squares, where weights at each point are:

• For model y = xb
  w = p2/c, where c is the adjusted count and p2 is the square of the population for that point..

• For model ln(y) = xb
  w = c, where c is the adjusted count for that point. (Motivated by delta method.)

Adding 0.5 to Zero Counts

When analyzing counts or computing crude rates, Joinpoint will add 0.5 to any zero count under the circumstances listed here.