Graduate Thesis Or Dissertation
 

A distribution-free approach for grouped survival data : analysis and calculation of efficiency

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  • A distribution-free analysis is proposed for inference concerning treatment effects in factorial survival experiments in which the recorded data are grouped by time intervals. A grouped data model is built by applying the continuous-time Cox regression and life model. This models the treatments to have multiplicative effects, possibly time dependent, on some unrestricted, hence distribution-free, underlying hazard function. By making certain good approximations a likelihood expression is obtained which depends only on parameters associated with the treatment effects. This allows large sample maximum likelihood inference about the treatment effects to proceed unburdened by nuisance parameters associated with the underlying hazard function. It is shown that, despite the approximation, the estimators obtained are consistent. The main error caused by the approximation concerns variance estimates, but this error will be small for most practical problems. When the underlying hazard function can be smoothly modeled by some parametric form, the efficiency of the distribution -free analysis is found to be very high. This efficiency is investigated by considering smoothing restrictions on the previously unrestricted parameters associated with the underlying hazard function of the grouped data model. It is shown that the distribution-free analysis is geared to give high efficiency for local alternatives to the hypothesis of no treatment effect and for smooth modeling allowing monotone decreasing hazard functions.
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