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6.14 Refer to Problem 5.1. Table 6.18 shows output for fitting a probit model. Interpret the parameter estimates (a) using characteristics of the normal cdf response curve, (b) finding the estimated rate of change in the probability of remission where it equals 0.5, and (c) finding the difference between the estimated probabilities of remission at the upper and lower quartiles of the labeling index, 14 and 28. TABLE 5.11 Computer Output for Problem 5.1 Intercept Intercept and Criterion Only Covariates -2 Log L 34.372 26.073 TABLE 6.18 Data for Problem 6.14 Testing Global Null Hypothesis: BETA = 0 Standard Likelihood Ratio 95% Chi - Test Chi - Square DF Pr > Chisq Parameter Estimate Error Confidence Limits Square Pr > Chisq Likelihood Ratio 8. 2988 0 . 0040 Score 7. 9311 0. 0049 Intercept -2. 3178 0 . 7795 - 4 . 0114 - 0 . 9084 8 . 84 0 . 0029 Wald 5.9594 0 . 0146 LI 0 . 0878 0 . 0328 0 . 0275 0 . 1575 7.19 0 . 0073 Parameter Estimate Standard Error Chi - Square Pr > Chisq 5.1 For a study using logistic regression to determine characteristics asso- Intercept -3. 7771 1. 3786 7. 5064 0. 0061 1i 0. 1449 0 . 0593 5. 9594 0. 0146 ciated with remission in cancer patients, Table 5.10 shows the most important explanatory variable, a labeling index (LI). This index mea- Odds Ratio Estimates sures proliferative activity of cells after a patient receives an injection Effect Point Estimate 954 Wald Confidence Limits of tritiated thymidine, representing the percentage of cells that are 1i 1. 156 1. 029 1.298 "labeled." The response Y measured whether the patient achieved remission (1 = yes). Software reports Table 5.11 for a logistic regres- Estimated Covariance Matrix sion model using LI to predict the probability of remission. Variable Intercept 1i Intercept 1. 900616 -0. 07653 1i 0. 07653 0 . 003521 TABLE 5.10 Data for Problem 5.1 Number Number of Number Number of Number Number of Obs li remiss pi-hat lower upper LI of Cases Remissions LI of Cases Remissions LI of Cases Remissions 1 8 0. 06797 0 . 01121 0. 31925 2 10 0. 08879 0 . 01809 0. 34010 8 18 28 C 10 20 32 12 W ww NI 14 24 38 16 26 Source: Data reprinted with permission from E. T. Lee, Comput. Prog. Biomed. 4: 80-92 (1974)