Multiple Regression and Partial Effects

EXAMPLE: BERYLLIUM EXPOSURE

Rom (et al 1983) (abstract) examined beryllium exposure in a prospective study of workers in a Utah mine. Beryllium exposure, in even small amounts, can lead to chronic beryllium disease (CBD) in a small percentage of workers who become sensitized to beryllium. See Beryllium Med Facts for lots more information). Berylllium is a suspected carcinogen, and beryllium workers have an increased rate of lung cancer. The latency period from first exposure to onset of CBD symptoms may be as long as 10 years. Research efforts have been to develop a screening test to identify workers who are sensitive to beryllium, before they develop symptoms and to relocate them to limit additional exposure. The article by Rom et al. suggests that sensitization to beryllium is related to exposure and is reversible. The blastogenic lymphocyte transformation ratio is used as a measure of sensitization, and the researchers expected that higher exposure levels would be associated with higher LT ratios.

Let's see...

SAS commands and data

Variables:

• Worker
• AGE
• YREMP = Years of Employment
• EXPLEV = exposure level in 1979; 1 (low) to 4 (high) as estimated by the company for each job category
• LTratio = Lymphocyte Transformation Ratio; values > 2 considered "positive", a 2 fold increase in Lymphocyte Transformation over control values.

Scatter Plot Matrix of all variables.

Simple Linear Regression of LT Ratio on Exposure

Multiple Linear Regression of LT Ratio on Exposure, Age, and Years of Employment

Scatter Plot Matrix with log(LT Ratio) and other variables.

Multiple Linear Regression of log(LT Ratio) on Exposure, Age, and Years of Employment

Multiple Linear Regression of log(LT Ratio) on Exposure, Age, and Years of Employment (without case 14)

Multiple Linear Regression of log(LT Ratio) on Exposure and Years of Employment (without case 14)