Statistica Sinica 18(2008), 235-253

UNIFORMLY BALANCED REPEATED MEASUREMENTS

DESIGNS IN THE PRESENCE OF SUBJECT DROPOUT

Dibyen Majumdar, Angela M. Dean and Susan M. Lewis

University of Illinois at Chicago, The Ohio State University

and University of Southampton

Abstract: Low, Lewis and Prescott (1999) showed that a crossover design based on a Williams Latin square of order $4$ can suffer substantial loss of efficiency if some observations in the final period are unavailable. Indeed, if all observations are missing, the design becomes disconnected. We derive the information matrix for the direct effects of a Uniformly Balanced Repeated Measurements Design (UBRMD) in $t$ periods when subjects may drop out before the end of the study, and examine the maximum loss of information. The special case of loss of observations in the final period only is examined in detail. In particular we show that a UBRMD in $t\geq 5$ periods remains connected when some or all observations in the final period are unavailable.

Key words and phrases: Crossover designs, efficiency, missing observations, Williams Latin Squares.