progressive disease126.2712.288alternatingfemaleno change710.767–1.148alternatingfemalepartial remission33.433–0.234alternatingfemalecomplete remission12.529–0.962(c)For the model in (a) the Wald statistic for alternating compared to sequentialtreatment is 0.1473/0.2094 = 0.70 (p-value = 0.482) which provides nosupport for a treatment difference.(d)Proportional odds models with and without terms for treatment give deviance= 2(–398.4509 + 398.6975) = 0.493, p-value = 0.482 (compared with the2(1)distribution)–the same result as (c).(e)Adjacent category and continuation ratio models can be fitted using SAS. Acontinuation ratio model does not describe the data any better than aproportional odds model. However, the adjacent categories model is betterable to describe the treatment difference in the ‘progressive disease’ category.The choice of link function makes little difference to the results.

128.4If the probability density function in Figure 8.2 is the Normal distribution then()Tii= xβfrom Section 7.3 so the probit model1()Tii−=xβis appropriate.CHAPTER 99.2 (a) Claim rates appear to increase withCAR, decrease withAGEand are higherforDIST= 1.(c)This model is simpler than (b), fits well (deviance = 53.11, d.f. = 60, p-value =0.72) and gives coefficients (standard errors):AGE,–0.177 (0.018);CAR,0.198 (0.021);DIST, 0.210 (0.059), consistent with (a).9.3 (a) Usual chi-squared test gives X2= 17.65, d.f. = 2, p-value < 0.001. The samegoodness of fit statistic is obtained for the log-linear model with terms fortreatment and response categories.(a)Fitted values are the ‘expected frequencies’ for a conventional chi-squaredtest. X2= 17.65, D = 18.64 with the largest residuals for ‘small’ response.(b)Forthe placebo group the estimated probabilities for the ‘small’, ‘moderate’and ‘large’ responses are111213ˆˆˆ0.638,0.282 and0.080,===respectively. For the vaccine group there is a shift of–1.8373 in the values of()212223ˆˆˆlog/+and212223ˆˆˆlog ()/+to give212223ˆˆˆ0.220,0.426 and0.354.===9.5The log-linear model with all 3 two-way interaction terms produces the sameresults as the nominal regression model–see solutions for Exercise 8.2 (d).9.6(c) The binary logistic regression model with case or control status as the responseand ulcer type and aspirin use as the predictor variables produces the sameresults as the log-linear model with termsGD+CC+AP+GDCC+GDAP+CCAP( see Tables 9.11 and 9.12).

13CHAPTER 1010.1(b) Plots suggest that either the Weibull or exponential distributions with theproportional hazards model may be appropriate, except for a small number ofpossible outliers.(c)The estimated shape parameter for the Weibull distribution isˆ0.961=(95%CI: 0.731, 1.262) suggesting that the simpler exponential distribution could beused.(d)Two subjects with AG positive, white blood cell count = 100 and survivaltime = 1 have large residuals, but otherwise the Cox-Snell residuals areconsistent with the exponential distribution with a parameter of one. Thesetwo points also have the largest deviance residuals.

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