Consider Table 7.10, from a study of nonmetastatic osteosarcoma described in A. M. Goorin, J. Clinical Oncology, 5: 1178-1184 (1987) and the LogXact Turbo User Manual (1993, p. 5-22). The response is whether the subject achieved a three-year disease-free interval.

a. Show that each predictor has a significant effect when it is used individually without the other predictors.

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

c. Using conditional logistic regression, (i) conduct an exact test of the hy- pothesis of no effect of lymphocytic infiltration, controlling for the other variables; (ii) compute a 95% confidence interval for the effect. Interpret results.

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Table 7.10 Disease-Free Lymphocytic Infiltration Osteoblastic Sex Pathology Yes No High Female No 3 0 Yes 2 Male No 4 0 Yes 0 Low Female No Yes Male No Yes 5 6 1241 0 Source: LogXact-Turbo User Manual, Cambridge, MA: Cytel Software (1993), p. 5-23.