Volume 90, Issue 6, December (2003), pp. 1087-1095 © The Author 2003
doi:10.1079/BJN2003989

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

Gary K. Grunwald^1,2, Debra K. Sullivan⁴, Mary Hise⁴, Joseph E. Donnelly³, Dennis J. Jacobsen³, Susan L. Johnson¹, James O. Hill^1
1Center for Human Nutrition, Box C-263, University of Colorado Health Sciences Center, , Denver, CO, 80262, , USA
²Department of Preventive Medicine and Biometrics, University of Colorado Health Sciences Center, Denver, CO, , USA
³Energy Balance Laboratory, Department of Health, Sport and Exercise Sciences, The University of Kansas, Lawrence, KS, , USA
⁴Department of Dietetics and Nutrition, University of Kansas Medical Center, Kansas City, KS, , USA

 (Received 2 May 2002–Revised 7 July 2003–Accepted 28 July 2003)

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.

Keywords:
Dietary assessment, Dietary intake, Dietary variability, Within-subject variation, Between-subject variation

Abbreviations:
D, number of days/subject per period, N, number of subjects/group, R_P=σ_P/σ_E, period variation as a fraction of daily variation, σ_E, day-to-day standard deviation, σ_P, period-to-period standard deviation, σ_S, between-subject standard deviation