Until recently, PSA was commonly recommended as a screening mechanism for detecting prostate cancer.




1.      Build the model (Prostate-specific antigen study)

A university medical center urology group (Stamey, et al., 1989) was interested in the association between a prostate-specific antigen (PSA) and a number of prognostic clinical measurements in men with advanced prostate cancer. Data were collected on 97 men who were about to undergo radical prostectomies. (download the data, “PSA.txt” from CANVAS).


Variable name



Identification number



PSA level

Serum prostate-specific antigen level (mg/ml)


Cancer volume

Estimate of prostate cancer volume (cc)



Prostate weight (gm)



Age of patient (years)


Benign prostatic

Amount of benign prostatic hyperplasia (cm2) hyperplasia


Seminal vesicle invasion

Presence or absence of seminal vesicle invasion: 1 if yes; 0 if no


Capsular penetration

Degree of capsular penetration (cm)


Gleason score

Pathologically determined grade of disease (6,7,8), higher indicates worse prognosis

Background: Until recently, PSA was commonly recommended as a screening mechanism for detecting prostate cancer. To be an efficient screening tool it is important that we understand how PSA levels relate to factors that may determine prognosis and outcome. The PSA test measures the blood level of prostate-specific antigen, an enzyme produced by the prostate. PSA levels under 4 ng/mL (nanograms per milliliter) are generally considered normal, while levels over 4 ng/mL are considered abnormal (although in men over 65 levels up to 6.5 ng/mL may be acceptable, depending upon each laboratorys reference ranges). PSA levels between 4 and 10 ng/mL indicate a risk of prostate cancer higher than normal, but the risk does not seem to rise within this six-point range. When the PSA level is above 10 ng/mL, the association with cancer becomes stronger. However, PSA is not a perfect test. Some men with prostate cancer do not have an elevated PSA, and most men with an elevated PSA do not have prostate cancer. PSA levels can change for many reasons other than cancer. Two common causes of high PSA levels are enlargement of the prostate (benign prostatic hypertrophy (BPH)) and infection in the prostate (prostatitis).


Use the data to build a multiple regression model to predict PSA level from the cancer volume, Prostate weight, and Age. A reasonable strategy would be to:

1)      Examine the relationship between the response and the potential predictors.

2)      Decide whether any of the variables should be transformed.

3)      Perform a model selection using the desired response and predictors.

4)      Given the selected model, examine the residuals and check for influential cases.

5)      Repeat the process, if necessary.

6)      Interpret the model and discuss any model limitations.


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