The name is absent

52

method (Efron, 1979). By the algorithm in Section 3.3, it can be seen that the final
survival estimator <S₀(∙) has jumps at event time points only. And R(β) has jumps at
informative censored time points only.

Ties

When there are tied failure events, the proposed method (Equation of likelihood
function 3.10 and 3.11) can handle them as in the Breslow’s (1974) method. Actually,
if we view the pieces of mass D_i(xβ, i = 1,..., j, as ties at time x_j, then the formation
of the lβ^τ∖β) and L^f'^c∖ββ (in Equations 3.10 and 3.11) are obtained from Breslow’s
method. In the simulation process, ties can be avoided easily. In the application case,
for simplicity, we trimmed the data before fitting the model to eliminate ties, which
has no impact to the conclusion. See details in Chapter 4.

Values of the a

In this research, the parameter a was not estimated. Instead, it was assumed to
be known. In reality, it is unknown. But when knowledge is available from experts
or literature about the degree and direction of the association between events and
informative censoring, our approach can be used to obtain less biased parameter es-
timates. If not much knowledge is available, the proposed method can be used to do
a sensitivity analysis in a very conservative way, just as was done by Park, Tian and
Wei (2006). That is, letting the Kendall’s τ change from near -1 to near 1 to perform

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