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Table 1:
Estimates of a Gompertz model without frailty and modified DeMoivre hazard models with Gamma-distributed frailty (Dfemale denotes a dummy variable for females)
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| Data |
Male and Female Mortality in Bulgaria, 1992–93 |
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Age 40–95 |
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| Method |
Gompertz
hazard,
no frailty |
Modified DeMoivre hazard function
with Gamma-distributed relative frailty |
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Model 0 |
Model 1 |
Model 2 |
Model 3 |
Model 4 |
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| Specification for a = exp(a0 + a1Dfemale) |
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| a0 (Constant) |
-5.5713 |
-5.6350 |
-5.5686 |
-5.4365 |
-5.5249 |
| |
(0.0117)* |
(0.0110)* |
(0.0114)* |
(0.0129)* |
(0.0116)* |
| a1 (Female) |
-1.3205 |
-0.7302 |
-0.8385 |
-1.1086 |
-0.9163 |
| |
(0.0198)* |
(0.0100)* |
(0.0117)* |
(0.0182)* |
(0.0139)* |
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| Specification for b = b0 + b1Dfemale |
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| b0 (Constant) |
0.0825 |
0.0755 |
0.0749 |
0.0687 |
0.0740 |
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(0.0004)* |
(0.0004)* |
(0.0004)* |
(0.0005)* |
(0.0005)* |
| b1 (Female) |
0.0254 |
– |
– |
0.0103 |
– |
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(0.0006)* |
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(0.0004)* |
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| Specification for s2 = exp(g0 + g1Dfemale) |
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| g0 (Constant) |
– |
-0.6186 |
-0.4876 |
-0.7411 |
0.0960 |
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|
(0.0239)* |
(0.0234)* |
(0.0263)* |
(0.0281)* |
| g1 (Female) |
– |
– |
-0.4285 |
– |
– |
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(0.0255)* |
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| Specification for w |
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| w |
– |
set to
122.45 |
set to
122.45 |
set to
122.45 |
104.2420
(0.3475)* |
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Notes:
Standard errors in parentheses. p-values: + p < 0.01; * p < 0.001.
Age has been rescaled in the estimation so that the parameter a reflects the mortality level of
the population at age 40, and s2 indicates the variance
of unobserved frailty at this age.
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