Biomedical Engineering Reference
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ratio by age is displayed in Figure 1 for the hospitalization model. The
smooth line represents the RR for the gender covariate estimated by a
model that contained a MALE(t2:5 yrs) interaction term, which as-
sumes an exponential trend in the RR across the 0-4 age interval. The step
function pertains to a model which contained MALEI(0t1 year),
: : :, MALEI(4 years < t5 years), assuming a constant RR within each
one-year age interval. As Figure 1 indicates, the decrease in the RR for
MALE is consistent with an exponential decrease; hence, the continuous
form of the time interaction was retained for the remainder of the analysis
in the interests of parsimony and eciency. As implied by Tables 5 and
6, the interaction term was centered at the mid-point of the observation
period (i.e., 2.5 years). Hence, the rate ratio parameter for MALE (main
eect) refers to the RR for male gender at age 2.5 years.
Table 5
Risk factors for pre-school asthma: Hospitalizations
naive
robust
b
d
b
d
b
b
k
Covariate
k
SE(
k
)
SE(
k
)
expf
k
g (95% CI)
1
LBW
0.708
0.192
0.257
2.03
(1.23, 3.36)
2
RDS
1.295
0.226
0.313
3.65
(1.98, 6.75)
3
TTN
0.469
0.269
0.339
1.60
(0.82, 3.10)
4
ASPH.mod
0.517
0.181
0.319
1.68
(0.90, 3.14)
5
ASPH.sev
1.227
0.201
0.471
3.41
(1.36, 8.58)
6
MALE
0.598
0.110
0.202
1.89
(1.22, 2.70)
(t = 2:5 yrs)
7
MALEt
-0.001
0.0003
0.0004
0.9989
(0.9981, 0.9998)
The lack of proportionality with respect to the gender eect was also
suggested by the gender-specic residual plots in Figure 2, where the
residuals were computed as
P
n
i=1
MALE
i
fN
i
P
b
n
i=1
(1
i
(C
i
;
b
)gand
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