Microsoft Word - liw_06_adjusted_rates-ejs.doc

• Main Authors: Wenjun Li, Edward J Stanek Iii, Jenny Kelsey, ?, Liz Bertone, Wenyun
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Greenland
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1069.5012; http://www.umass.edu/cluster/ed/publication/yr2006/wenjun/liw_06_adjusted_rates-ejs.pdf

The usual goal of adjustment was never variance reduction, but rather to get an unbiased estimate or prediction of what the crude rate in some population (which supplies the "standard" distribution) would be (or would have been) if the covariate-specific rates were different than what they actually were. The goal is to allow comparisons unconfounded by the adjustment covariates. The final sections of Ch. 3 and Ch. 4 of Rothman and Greenland (ME2) talks about this (they should read those) and there is an enormous literature on the topic going back a century at least. I think that there are several issues here that need to be clearly articulated so that the problem addressed is clear. In the BRFSS, there is a sample of a population. The statistical context is sampling, and there is a target parameter (the crude rate in population). (Note that for example, if smoking rates vary by gender, the crude rate is an weighted average of the gender specific rates. Some may argue that the crude rate isn't interesting here, since the gender specific rates differ. This is another issue.). I would disagree with Sandra that the goal is 'to allow comparisons unconfounded by the adjustment covariates'. I would say the goal is to develop the most accurate estimate of the crude rate. Yates (JRSS 1934) is a classic and had it right (he even pointed out how two SMRs were not comparably standardized). There was a very nice article on standardization and its relation regression and prediction by Lane and Nelder in Biometrics 1982, which they should download from JSTOR and read. I didn't go back and look at Yates paper, but the focus of comparing populations is different from the focus of estimating a parameter in a population. This is the problem that we are addressing here. The paper by Lane and Nelder seems like a similar context to the one we consider-where we want to estimate what would happen if we knew the entire population. In section 2, they describe a problem in terms of a randomized block experiment. This is a more complicated ...