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 193

Rate Ratio: M/F, Asthma hospitalizations

0 1 2 3 4 5

t (years)

b

Fig. 1. Mean ratio (expf k g), male:female, for asthma hospitalizations. The curve

b b

equals expf 7 (t2:5yrs)gfrom model (14), while the step function corresponds to

a model with separate year-specic MALE coecients.

6 +

tom). The baseline rates were smoothed using local regression via the
loess() function in R. For both hospitalizations and days hospitalized, the
baseline rate tends to increase with age.
Estimated cumulative mean numbers of asthma-attributable hospital-
izations and days hospitalized are depicted in Figure 4. For children with
no neonatal risk factors (i.e., LBW i + RDS i + : : : + ASP H:sev i = 0), the
model predicts a mean (and 95% CI) of 13.9 (8.7, 19.0) hospitalizations per
1,000 females (top left panel) and 24.9 (18.7, 31.1) per 1,000 males (top
right panel) during the rst 5 years of life. For days hospitalized, the corre-
sponding model predicted means (95% CIs) are 43.8 (24.4, 63.1) per 1,000
females (bottom left panel) and 89.5 (54.2, 124.8) per 1,000 males (bottom
right panel) during the same period.
As a check of the adequacy of the nal models, the tted cumula-
tive mean number of asthma events is plotted against time, and com-
pared with the observed counts in Figure 5. These two quantities are the
components of the residuals discussed previously. Several covariate pat-
terns were examined; two are presented for illustration, and labelled `un-
exposed' (LBW+RDS+... +ASPH.sev=0) and exposed (LBW+RDS+...