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Assuming a is known, we get the time of event Ti and dependent censoring Ci. In
addition, we generated another random time variable Si from a Uniform distribution,
which is independent of everything else. This was the independent censoring time.
Then, the obtained observations are Xi = min(Ti,Ci, Si). We also had indicators
<5ι = ʃ(ɪ = T) and ¾ = I(X = C). After putting all the data in ascending order
by the time of observations, we used the proposed method in Section 3.3 to get the
estimators of β and βc and their standard errors.
Test 1
In Test 1, a Uniform (2,12) is used to generate Si. The percentage of events is 47%;
the percentage of dependent censoring is 48.5%; and the percentage of independent
censoring is 4.5%. The results by the proposed method are summarized in Table
3.1. In contrast, the results from falsely assumed independent censoring are shown
in Table 3.2. Please note that in the proposed method, the parameter a was not
estimated. Instead, it was assumed to be known as 0.00000001258, corresponding to
τ = 0.8.
From Tables 3.1 and 3.2, it can be seen that the proposed method outperforms
the traditional Coxph method. The parameter estimates from the proposed method
are closer to the true value than the ones from the Coxph method. The Standard
Deviation (SD) and the Standard Error (SE) of estimators from the proposed method
are close to the ones from the Coxph method. Similarly, the survival curves obtained