The name is absent

55

Assuming a is known, we get the time of event T_i and dependent censoring C_i. In
addition, we generated another random time variable S_i from a Uniform distribution,
which is independent of everything else. This was the independent censoring time.
Then, the obtained observations are X_i = min(T_i,C_i, S_i). 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 β_c and their standard errors.

Test 1

In Test 1, a Uniform (2,12) is used to generate S_i. 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

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