Biomedical Engineering Reference
In-Depth Information
11.3
Simulation Studies
Simulations are designed to illustrate the bias in parameter estimates using the
imputations from mid-point and right-endpoint in comparison with the \IntCox"
to mitigate the bias. The simulations are modied from the R library \IntCox" to
include the magnitude of censoring and/or observed time-to-event data.
11.3.1
Simulation Setup
For each trial, the simulation is described in the following steps:
1. 100 patients were randomly assigned to two treatment groups: x
1
= 1 for new
drug treatment and x
1
= 0 for placebo with probability of 0.5.
2. For each patient, we collect three sources of additional information (i.e., three
covariates of x
2
, x
3
, and x
4
) following normal distributions.
3. We assume that the clinical trial is conducted for 12 months and therefore if
a patient's survival time is greater than 12 months, it is considered censored.
4. For each patient, the survival times are simulated from a Weibull distri-
bution with shape parameter = 1 and scale parameter derived from
1
1=
with = exp(
0
+
1
x
1
+
2
x
2
+
3
x
3
+
4
x
4
), where
0
= 0:1
and = (
1
;
2
;
3
;
4
) = (0:5; 0:5; 0:5; 0:5). Each survival time is expanded
by 12 (months). Each survival time has probability p of being censored (i.e.,
the probability of observing a noncensored observation is 1 p). Further, an
interval was generated where its left endpoint is 1 month and its right end-
point is the end of clinical trial at 12 months. If the simulated survival time
is more than 12, the survival time is right-censored (left = t
1
= 12 and
right = t
2
= NA). Otherwise, the interval [1,12] is randomly divided into
sub-intervals in order to determine the corresponding interval endpoints for
the survival times that are not right-censored. Two cases are simulated to il-
lustrate bias. One is to simulate a more frequent observation time interval by
month as 1 to 12. Another is by 3 months for less frequent follow-up visits.
5. For the simulated interval-censored data, two data sets are generated for Cox
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