Prostate Cancer StudyIt is believed that menâ??s prostate glands grow with age. Therefore, prostate-

Prostate Cancer StudyIt is believed that men’s prostate glands grow with age. Therefore, prostate-specific antigen (PSA), asubstance made in the prostate, increases slightly as men become older. Oncologists have established thatprostate cancer cells are more permeable than normal prostate cells, causing the PSA level to rise in mostcases of prostate cancer. When prostate cancer is not detected early enough the tumor can develop andpenetrate the prostatic capsule.Dr. Donn Young, at the The Ohio State University Comprehensive Cancer Center, collected data, includingdemographic variables, and various test results on a cohort of men with prostate cancer. The interest is inhow to use various test results among patients, and in particular, whether variables measured at the baselineexam 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 ofProstatic Capsule 0 = No Penetration,1 = Penetration Age Age Years Drexam Results of the DigitalRectal Exam 0 = No Nodule1 = Unilobar or Bilobar Nodule PSA Prostatic SpecificAntigen 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 andDrexam as the covariate. Does Drexam have any association with capsule penetration? Use the odds ratio andinterpret the results.4. Run a logistic regression model with capsule (penetration = 1) as the response variable andPSA as the covariate. Does PSA have any association with capsule penetration? Use the odds ratio and interpretthe results.5. What is the multiplicative effect of a unit increase in PSA level? Explain what this means.