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Reducing Suicide: A National Imperative
TABLE A-1 Comparison of Maximum Marginal Likeihood (MMLE) and Generalized Estimating Equations (GEE) for the Clustered Poisson Regression Model
MMLE
GEE
Effect
Estimate
SE
Prob
Estimate
SE
Prob
Intercept
–4.331
0.040
<0.0001
–4.408000
0.048000
<0.0001
Female
–1.009
0.076
<0.0001
–1.009000
0.073000
<0.0001
Black vs Other
–0.292
0.103
0.0046
–0.279000
0.112000
0.0127
15–24 vs 05–14
2.788
0.041
<0.0001
2.787000
0.043000
<0.0001
25–44 vs 05–14
3.030
0.040
<0.0001
3.021000
0.043000
<0.0001
45–64 vs 05–14
2.971
0.041
<0.0001
2.975000
0.046000
<0.0001
65+ vs 05–14
3.371
0.041
<0.0001
3.390000
0.047000
<0.0001
Female x Black
–0.345
0.036
<0.0001
–0.345000
0.041000
<0.0001
Female x 15–24
–0.664
0.080
<0.0001
–0.663000
0.077000
<0.0001
Female x 25–44
–0.355
0.077
<0.0001
–0.357000
0.074000
<0.0001
Female x 45–64
–0.223
0.077
0.0038
–0.223000
0.075000
0.0029
Female x 65+
–0.938
0.078
<0.0001
–0.945000
0.078000
<0.0001
Black x 15–24
0.065
0.106
0.5434
0.068000
0.107000
0.5297
Black x 25–44
–0.139
0.105
0.1829
–0.141000
0.107000
0.1877
Black x 45–64
–0.473
0.107
<0.0001
–0.486000
0.111000
<0.0001
Black x 65+
–0.740
0.112
<0.0001
–0.748000
0.117000
<0.0001
County Variance
0.280
0.003
<0.0001
displays observed and expected annual suicide rates for both methods of estimation, broken down by age, sex, and race. Inspection of Table A-2 reveals several interesting results. In general, suicide increases with age, is higher in males, and is lower in African Americans. Black females have the lowest suicide rates across the age range. In white males, the suicide rate is increasing with age whereas in all other groups, the suicide rate either is constant or decreases after age 65. Comparison of the expected frequencies for the GEE and mixed-effects models reveal that they are quite similar and the GEE does a slightly better job of recovering the observed marginal rates.
A special feature of the mixed-effects model is the ability of estimating county-specific rates using empirical Bayes estimates of the random effects as described in the previous section. Using these estimates, we can accomplish two goals. First, we can estimate county-specific expected suicide rates, which directly incorporate the effects race, sex, and age of that county. Table A-3 provides a comparison of observed and expected numbers of suicides (1996-1998) for 100 randomly selected counties. In-
