4. Consider data from 14 trials into breast cancer recurrence under tamoxifen, with y denoting numbers with recurrence after a year’s treatment (EBCTCG, 1998). Compare inferences about the drug effect under a log odds ratio comparison using a normal-normal model and using a binomial sampling model. Under the normal approximation the empirical log odds ratio may be obtained as

with variances s2 i = 1/(yiT + 0.5) + 1/(yiC + 0.5) + 1/(NiC − yiC + 0.5) + 1/(NiT − yiT + 0.5).

r = = log ([yir +0.5][Nic - Yic +0.5]\ [yic +0.5][NiTyiT +0.5], Trial Control Study y N Y N 122 55 97 67 101 137 282 187 306 3 505 927 590 915 4 62 123 74 140 5 99 239 118 236 6 50 130 49 107 7 185 311 200 319 8 186 303 187 307 9 148 325 178 325 10 25 79 38 86 11 223 344 224 350 12 183 937 185 936 13 2 12 0 8 14 129 434 159 449