Consider Table 6.19, from a study of nonmetastatic osteosarcoma. The response is whether the subject achieved a three-year disease-free interval.

a. Show that each predictor has a significant effect when used individually without the others.

b. Try to fit a main-effects logistic regression model containing all three predictors. Explain why the ML estimate for the effect of lymphocytic infiltration is infinite.

c. Using conditional logistic regression, (I) conduct an exact test for the effect of lymphocytic infiltration, controlling for the other variables; and (ii) find a 95% confidence interval for the effect. Interpret results.

Table 6.19:

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Disease-Free Lymphocytic Infiltration Osteoblastic Yes Gender Pathology No High Female No 3 Yes Male No 4 Yes No Female Low Yes 2 Male No 4 Yes 11