Table 5.8 is from a study of nonmetastatic osteosarcoma described in the LogXact 7 manual (Cytel Software, 2005, p. 171). The response is whether the subject achieved a three-year disease-free interval.

a. Show that each explanatory variable has a significant effect when it is used as the sole predictor in logistic regression. Try to fit a main-effects model containing all three predictors. Explain why the ML estimate for the effect of lymphocytic infiltration is actually infinite.

b. Report and interpret results from fitting the main-effects model using either Firth’s penalized logistic regression or Bayesian inference.