Local linear estimation and plug-in bandwidth selection for the ratio of two hazard rate functions

An estimator of the ratio of two hazard rate functions is derived, based on the local linear smoothing of a piecewise constant empirical estimator of the ratio. The asymptotic properties of the estimator are studied analytically and employed in developing a plug-in bandwidth selector which facilitates its optimal implementation. The asymptotic consistency and distribution of the practically useful (data-driven) version of the bandwidth rule are also studied herein. The potential of the method as a data-analytic tool is illustrated by its application in evaluating the effect on survival of a treatment response for primary biliary cirrhosis patients.