The multivariate L1-median and associated data depth

This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in ℝd, a problem that can be traced to Fermat and has fascinated applied mathematicians for over three centuries; (ii) a new general definition for depth functions, as functions of multivariate medians, so that different definitions of medians will, correspondingly, give rise to different dept functions; and (iii) a simple closed-form formula of the L1-depth function for a given data cloud in ℝd.

Number needed to screen: development of a statistic for disease screening

Objectives: To develop the number needed to screen, a new statistic to overcome inappropriate national strategies for disease screening. Number needed to screen is defined as the number of people that need to be screened for a given duration to prevent one death or adverse event.