Introduction to Categorical Data Analysis

112 LOGISTIC REGRESSION
Table 4.4. Development of AIDS Symptoms by AZT
Use and Race
Symptoms
Race AZT Use Yes No
White Yes 14 93
No 32 81
Black Yes 11 52
No 12 43
odds ratio between immediate AZT use and development of AIDS symptoms equals
exp(−0.720) = 0.49. For each race, the estimated odds of developing symptoms are
half as high for those who took AZT immediately.
The hypothesis of conditional independence of AZT treatment and the development
of AIDS symptoms, controlling for race, is H0: β1 = 0. The likelihood-ratio
(LR) statistic −2(L0 − L1) comparing models (4.6) and (4.5) equals 6.87, with
df = 1, showing evidence of association (P = 0.009). The Wald statistic ( ˆβ1/SE) 2 =
(−0.720/0.279) 2 = 6.65 provides similar results (P = 0.010). The effect of race is
not significant (Table 4.5 reports LR statistic = 0.04 and P -value = 0.85).
Table 4.5. Computer Output for Logit Model with AIDS Symptoms Data
Log Likelihood −167.5756
Analysis of Maximum Likelihood Estimates
Parameter Estimate Std Error Wald Chi-Square Pr > ChiSq
Intercept −1.0736 0.2629 16.6705 ChiSq
azt 1 6.87 0.0088
race 1 0.04 0.8473
Obs race azt y n pi_hat lower upper
1 1 1 14 107 0.14962 0.09897 0.21987
2 1 0 32 113 0.26540 0.19668 0.34774
3 0 1 11 63 0.14270 0.08704 0.22519
4 0 0 12 55 0.25472 0.16953 0.36396