APPLICATION OF THE NON-PROPORTIONAL RATES MODEL TO RECURRENT EVENT DATA: ANALYSIS OF RISK FACTORS FOR PRE-SCHOOL ASTHMA - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 192

Table 6
Risk factors for pre-school asthma: Days hospitalized

naive robust

b b b b

d d

k Covariate k SE( k ) SE( k ) expf k g (95% CI)

1 LBW 0.863 0.095 0.353 2.37 (1.19, 4.74)

2 RDS 1.233 0.112 0.411 3.43 (1.53, 7.68)

3 TTN 0.400 0.139 0.460 1.49 (0.60, 3.68)

4 ASPH.mod 0.212 0.110 0.324 1.24 (0.65, 2.34)

5 ASPH.sev 1.745 0.085 0.590 5.73 (1.80, 18.21)

6 MALE 0.604 0.059 0.279 1.83 (1.06, 3.16)

(t = 2:5 yrs)

7 MALEt -0.002 0.0002 0.0005 0.9981 (0.9972, 0.9991)

b

MALE i )fN i )gfor males and females, respectively. Residuals for

the proportional rates model (denoted by `o') are of far greater magni-
tude than those for the time-dependent model (`t'). While residuals from
the proportional rates model display a distinct pattern (i.e., bow-shaped),
residuals for the time-dependent model display much little trend and ap-
pear to oscillate about 0. Careful examination of the `t's reveals that some
pattern in the residuals persists even for the non-proportional rates model;
it is possible that a more exible specication of the time-dependence (e.g.,
including a (t2:5 yrs) 2 term) may be warranted.
Results were quite similar for the days hospitalized model (data not
shown). Such plots were examined for several covariate combinations. Other
checks of proportionality included examining the Wald statistics of various
interaction terms with time. Evidence of non-proportionality was not found
for any covariate besides gender.
The baseline asthma rate per 1,000 children per day, is plotted against
age in Figure 3 for hospitalizations (top panel) and days hospitalized (bot-

b i (C i ;