The name is absent

51

those patients who withdraw are the sicker in Group A and the healthier in Group
B. However, such phenomenon is unlikely, especially in a blinded randomized trial.

Consistency

Note that the estimators β, β_c, Â(-) and Φ(∙) satisfy the definition of “self-
consistent”, which was first introduced by Efron (1967). Based upon such def-
inition, many research projects were conducted, among which Tsai and Crowley
(1985) discussed the theoretical properties of self-consistent estimators in general
non-regression settings. They showed (1) the guaranteed convergence of the above
iteration algorithm and its connection with the Expectation-Maximization (EM) al-
gorithm (Dempster et al., 1977); (2) such a self-consistent estimator is actually a gen-
eralized maximum-likelihood estimator in the sense of Kiefer and Wolfowitz (1956);
(3) the strong consistency of the self-consistent estimators; and (4) its weak conver-
gence to a Gaussian process. Zheng and Klein (1994) also shows their S(t) and R(t)
are self-consistent estimators (see Section 2.5 for details).

These results and the simulation studies in the next section indicate potentially
good large sample properties of our estimators in the regression setting. However,
further theoretical investigation will be helpful.

Covariance

The covariance matrices of the above estimators can be obtained by the bootstrap

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