Prostate Cancer Study It is believed that men's prostate glands grow with age. Therefore, prostate-specific antigen (PSA), a substance made in the prostate, increases slightly as men become older. Oncologists have established that prostate cancer cells are more permeable than normal prostate cells, causing the PSA level to rise in most cases of prostate cancer. When prostate cancer is not detected early enough the tumor can develop and penetrate the prostatic capsule. Dr. Donn Young, at the The Ohio State University Comprehensive Cancer Center, collected data, including demographic variables, and various test results on a cohort of men with prostate cancer. The interest is in how to use various test results among patients, and in particular, whether variables measured at the baseline exam can be used to predict whether or not the tumor has penetrated the prostatic capsule. The following is a description of the variables in the data file: Variable Description Codes/Values ID Identification Code 1 - 380 Capsule Tumor Penetration of Prostatic Capsule 0 = No Penetration, 1 = Penetration Age Age Years Drexam Results of the Digital Rectal Exam 0 = No Nodule 1 = Unilobar or Bilobar Nodule PSA Prostatic Specific Antigen Value mg/ml 1. Is there any association between PSA and age. In particular, does the data suggest that PSA increases with age? Describe any observed pattern in the data other than relationship between PSA and age. 2. Create a cross-tabulation of capsule (column) versus Drexam (row) into your report. Is there any association between Drexam and capsule penetration? Explain. 3. Run a logistic regression model with capsule (penetration = 1) as the response variable and Drexam as the covariate. Does Drexam have any association with capsule penetration? Use the odds ratio and interpret the results. 4. Run a logistic regression model with capsule (penetration = 1) as the response variable and PSA as the covariate. Does PSA have any association with capsule penetration? Use the odds ratio and interpret the results. 5. What is the multiplicative effect of a unit increase in PSA level? Explain what this means