Table 10.10 shows results of a teratology experiment, available in the Teratology data file at the text website. Female rats on iron-deficient diets were assigned to four groups. Group 1 received only placebo injections. The other groups received injections of an iron supplement according to various schedules. The rats were made pregnant and then sacrificed after three weeks. For each fetus in each rat’s litter, the response was whether the fetus was dead.

a. Let yi denote the number of dead fetuses for the Ti fetuses in litter i. Let πit denote the probability of death for fetus t in litter i. Let zig = 1 if litter i is in group g and 0 otherwise. Ignoring the clustering and treating yi as a binomial variate, fit the model logit(πit) = α + β2zi2 + β3zi3 + β4zi4.
Allowing observations within each litter to be correlated, use the GEE approach to fit the model. Compare parameter estimates and standard errors. Interpret.

b. Specify the corresponding GLMM. Fit it and compare results to those in (a).
Table 10.10 Response counts of (litter size, number dead) for 58 litters of rats in low-iron teratology study.

Group 1: Untreated (Low Iron)

(10, 1) (11, 4) (12, 9) (4, 4) (10, 10) (11, 9) (9, 9) (11, 11) (10, 10) (10, 7) (12, 12)

(10, 9) (8, 8) (11, 9) (6, 4) (9, 7) (14, 14) (12, 7) (11, 9) (13, 8) (14, 5) (10, 10)

(12, 10) (13, 8) (10, 10) (14, 3) (13, 13) (4, 3) (8, 8) (13, 5) (12, 12)

Group 2: Injections Days 7 and 10

(10, 1) (3, 1) (13, 1) (12, 0) (14, 4) (9, 2) (13, 2) (16, 1) (11, 0) (4, 0) (1, 0) (12, 0)

Group 3: Injections Days 0 and 7

(8, 0) (11, 1) (14, 0) (14, 1) (11, 0)

Group 4: Injections Weekly

(3, 0) (13, 0) (9, 2) (17, 2) (15, 0) (2, 0) (14, 1) (8, 0) (6, 0) (17, 0)

Source: D.F. Moore and A. Tsiatis, Biometrics 47: 383–401 (1991).