British Journal of Nutrition

Research Article

Number of days, number of subjects, and sources of variation in longitudinal intervention or crossover feeding trials with multiple days of measurement

Gary K. Grunwalda1a2 c1, Debra K. Sullivana4, Mary Hisea4, Joseph E. Donnellya3, Dennis J. Jacobsena3, Susan L. Johnsona1 and James O. Hilla1

a1 Center for Human Nutrition, Box C-263, University of Colorado Health Sciences Center, Denver CO 80262, USA

a2 Department of Preventive Medicine and Biometrics, University of Colorado Health Sciences Center, Denver CO, USA

a3 Energy Balance Laboratory, Department of Health, Sport and Exercise Sciences, The University of Kansas, Lawrence KS, USA

a4 Department of Dietetics and Nutrition, University of Kansas Medical Center, Kansas City KS, USA


Dietary studies are often conducted as longitudinal intervention or crossover trials using multiple days of measurement on each subject during each of several measurement periods, and determining the required numbers of days and subjects is important in designing these studies. Linear mixed statistical models were used to derive equations for precision, statistical power and sample size (number of days and number of subjects) and to obtain estimates of between-subject, period-to-period, and day-to-day variation needed to apply the equations. Two cohorts of an on-going exercise intervention study, and a crossover study of Olestra, each with 14 d of measurement/subject per period, were used to obtain estimates of variability for energy and macronutrient intake. Numerical examples illustrate how the equations for calculating the number of days or number of subjects are applied in typical situations, and sample SAS code is given. It was found that between-subject, period-to-period, and day-to-day variation all contributed significantly to the variation in energy and macronutrient intake. The ratio of period-to-period and day-to-day standard deviations controls the trade-off between the number of days and the number of subjects, and this remained relatively stable across studies and energy and macronutrient intake variables. The greatest gains in precision were seen over the first few measurement days. Greater precision and fewer required days were noted in the study (Olestra) that exerted greater control over the subjects and diets during the feeding protocol.

(Received May 02 2002)

(Revised July 07 2003)

(Accepted July 28 2003)


c1 *Corresponding author: Dr Gary K. Grunwald, fax +1 303 315 9976, email