Biostatistics

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 $\theta_0 = 0$ under highly stratified models. Naturally, it would be very interesting to see if the same result holds when $\theta_0 \ne 0$. In general, the calculation would be very complicated and difficult if the baseline function $\lambda_0(t)$ 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 $\theta_0$ 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 $t$ is assumed to be $\lambda(t\vert z) = \lambda_0(t) + \theta_0 z,$ given a time-independent covariate $z$. 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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