Progressive disease 12 6271 2288 alternating female

progressive disease 12 6.271 2.288
alternating female no change 7 10.767 – 1.148
alternating female partial remission 3 3.433 – 0.234
alternating female complete remission 1 2.529 – 0.962
(c) For the model in (a) the Wald statistic for alternating compared to sequential
treatment is 0.1473/0.2094 = 0.70 (p-value = 0.482) which provides no
support 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 the
2
(1)  distribution) – the same result as (c).
(e) Adjacent category and continuation ratio models can be fitted using SAS. A
continuation ratio model does not describe the data any better than a
proportional odds model. However, the adjacent categories model is better
able to describe the treatment difference in the ‘progressive disease’ category.
The choice of link function makes little difference to the results.

12
8.4 If the probability density function in Figure 8.2 is the Normal distribution then
( ) T
i i
 =  x β from Section 7.3 so the probit model 1 ( ) T
i i
 −  = x β is appropriate.
CHAPTER 9
9.2 (a) Claim rates appear to increase with CAR , decrease with AGE and are higher
for DIST = 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 X
2
= 17.65, d.f. = 2, p-value < 0.001. The same
goodness of fit statistic is obtained for the log-linear model with terms for
treatment and response categories.
(a) Fitted values are the ‘expected frequencies’ for a conventional chi -squared
test. X
2
= 17.65, D = 18.64 with the largest residuals for ‘small’ response.
(b) For the placebo group the estimated probabilities for the ‘small’, ‘moderate’
and ‘large’ responses are
11 12 13
ˆ ˆ ˆ 0.638, 0.282 and 0.080,    = = =
respectively. For the vaccine group there is a shift of – 1.8373 in the values of
( )
21 22 23
ˆ ˆ ˆ
log /   
 
+
 
and
 
21 22 23
ˆ ˆ ˆ
log ( )/    + to give
21 22 23
ˆ ˆ ˆ
0.220, 0.426 and 0.354.    = = =
9.5 The log-linear model with all 3 two-way interaction terms produces the same
results 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 response
and ulcer type and aspirin use as the predictor variables produces the same
results as the log-linear model with terms GD + CC + AP + GD  CC + GD  AP
+ CC  AP ( see Tables 9.11 and 9.12).

13
CHAPTER 10
10.1(b) Plots suggest that either the Weibull or exponential distributions with the
proportional hazards model may be appropriate, except for a small number of
possible outliers.
(c) The estimated shape parameter for the Weibull distribution is
ˆ
0.961  = (95%
CI: 0.731, 1.262) suggesting that the simpler exponential distribution could be
used.
(d) Two subjects with AG positive, white blood cell count = 100 and survival
time = 1 have large residuals, but otherwise the Cox-Snell residuals are
consistent with the exponential distribution with a parameter of one. These
two points also have the largest deviance residuals.