Highly Stratified Model in Biostatistics (Cont'd)

improve the MPLE's performance, and it indicates the use of the
simple MPLE in situations where a
practical or approximate ``best" estimator cannot be constructed.
In this part, we want to generalize the result from Goldstein and Zhang (2009). Note that Goldstein and Zhang (2009) gives the efficiency result of NCCS for the case of under highly stratified models. Naturally, it would be very interesting to see if the same result holds when
. In general, the calculation would be very complicated and difficult if the baseline function is unspecified. Hence, we will exploit the efficiency calculation by assuming a known baseline hazard to be a parametric function but with unknown parameters under a highly stratified model. The model now reduces to a parametric model with an unknown parameter of interest along with other nuisance parameters. Hence, the information bound and the efficiency result
could be obtained. Furthermore, since the censoring mechanism plays a key role in biostatistics, we will extend the result in
Goldstein and Zhang (2009) to incorporate the censoring mechanisms into our project, and exploit the same questions as
specified above.
The analysis in Goldstein and Zhang (2009) will be extended from the Cox model to an additive model, where
the conditional
hazard at time is assumed to be
given a time-independent covariate . The performance of the MPLE from the NCCS design will be explored under a highly stratified model. The same questions
as proposed above will be answered accordingly as well.

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