Use the data from the Prostatic Cancer Study described in Section 1.6.3 to answer the following questions:

(a) By fitting a series of logistic regression models show that RACE is not a confounder of the PSA CAPSULE odds ratio but is an effect modifier (at the 10 percent level).

(b) Graph the estimated logits from the interactions model versus PSA and interpret the two lines that appear on the graph. Use the graph to illustrate the log-odds of Black versus White for a subject with PSA = 7.

Use the graph to illustrate the log-odds for a 5-unit increase in PSA for Whites and for Blacks.

(c) Estimate the point and 95 percent confidence interval estimates of the odds ratios corresponding to each of the log-odds illustrated in problem 2(b). Add the 95 percent confidence bands to the graph of the estimated logits from the interactions model in Exercise 2(b).

Transform the lines and bands in this plot to obtain a plot of the estimated probability with its 95 percent confidence bands. Use the graph to estimate, point and interval, the probability of penetration for both a White and Black with PSA = 7.

Interpret the two point and interval estimates.