Biomedical Engineering Reference
In-Depth Information
The parameter
0
reects the degree of non-proportionality. In our set-
up, the eect of Z
i
increases with increasing follow-up time, ranging from
0
0:51:25 = 0:068 at t = 0 to 1.318 at t = 2:5. The mean number
of observed events was 0.625 for the Z
i
= 0 subjects and 1.06 for subjects
with Z
i
= 1. The number of observed events ranged from 0 to 25.
A total of 5,000 replications per data conguration were generated. Bias
was estimated by comparing the mean parameter estimate (across the 5,000
replicates) with its true value. The accuracy of the asymptotic robust stan-
dard error estimators were assessed by comparing their average values (de-
noted ASE) with the empirical standard deviation (ESD) and through com-
paring the empirical coverage probability (ECP) with its nominal value of
0.95.
Simulation results are presented in Table 1. For all data congurations,
b
b
and
were approximately unbiased, even for n=30. Generally, the accu-
racy of asymptotic standard errors increased as the intra-subject event time
correlation decreased. Coverage probabilities for the asymptotic condence
intervals for
0
and
0
were approximately equal across all parameter com-
binations, and increased as intra-subject event time correlation decreased.
For uncorrelated intra-subject event times, n=50 was required to obtain
ECP of at least 0.92; for moderate to high event time correlations (
2
=0.5,
1.0), n=100 was required. A sample size of n=100 failed to yield ECP> 0.92
in the case of extremely high event-time correlation (
2
=2.0), although this
was achieved with n=200.
5. Analysis of Preschool Asthma Data
We tted separate rate models for asthma-attributable hospitalizations and
days hospitalized. Time, t, was measured in days; since t = 0 corresponded
to the child's date of birth, the times axis was also the age axis. The selected
set of covariates included binary indicators of low birth weight (LBW),
respiratory distress syndrome (RDS), transient tachypnea of the newborn
(TTN), birth asphyxia, and gender, with each coded as 1 for `present' and
0 for `absent'. Gender was coded as 0 for females and 1 for males. Initially,
rate models were tted, with the degree of departure from proportionality
examined separately for each covariate by sequentially tting models with
Z
ij
t interactions, and examining the corresponding Wald statistic (using
a robust SE estimate) and degree of improvement in t as depicted by plots
of the residual, N
i
b
), suggested by Lawless
12
. The nal model is
b
i
(C
i
;
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