Estimates of relative risk
For the two-sample model with proportional hazard, i.e., for \(\bar G(x)=1-G(x)=[\bar F(x)]^{\theta}=[1-F(x)]^{\theta}\), \(x\in R\), \(\theta >0\), the problem of estimating the relative risk \((\theta)\) is considered for the conventional uncensored data model. This model corresponds to the classical Cox regression model [\textit{D. R. Cox}, J. R. Stat. Soc., Ser. B 34, 187-220 (1972; Zbl 0243.62041)] when the concomitant variate can assume only two values, 0 and 1. A two-step estimator of \(\theta\) is considered. \({\tilde \theta}\), an initial estimator of \(\theta\) is based on the identity \(\bar FdG=\bar GdF\), and this is incorporated in the formulation of the final step estimator. This two-step estimator and the Cox partial maximum likelihood estimator of \(\theta\) share the minimum asymptotic variance property within the class of all rank based regular estimators of the relative risk.
estimation of the constant of proportionality
Cox partial maximum likelihood estimator
scientific article; zbMATH DE number 4107946