Sample Size Determination for Hierarchical Longitudinal Designs with Differential Attrition Rates

Authors

  • Anindya Roy,

    1. Center for Health Statistics, University of Illinois at Chicago, 1601 W. Taylor St., Chicago, Illinois 60612, U.S.A.
    2. Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, U.S.A.
    Search for more papers by this author
  • Dulal K. Bhaumik,

    1. Center for Health Statistics, University of Illinois at Chicago, 1601 W. Taylor St., Chicago, Illinois 60612, U.S.A.
    2. Department of Psychiatry, University of Illinois at Chicago, 1601 W. Taylor St., Chicago, Illinois 60612, U.S.A.
    3. Division of Epidemiology and Biostatistics, University of Illinois at Chicago, 1601 W. Taylor St. Chicago, Illinois 60612, U.S.A.
    Search for more papers by this author
  • Subhash Aryal,

    1. Center for Health Statistics, University of Illinois at Chicago, 1601 W. Taylor St., Chicago, Illinois 60612, U.S.A.
    2. Department of Psychiatry, University of Illinois at Chicago, 1601 W. Taylor St., Chicago, Illinois 60612, U.S.A.
    3. Division of Epidemiology and Biostatistics, University of Illinois at Chicago, 1601 W. Taylor St. Chicago, Illinois 60612, U.S.A.
    Search for more papers by this author
  • Robert D. Gibbons

    Corresponding author
    1. Center for Health Statistics, University of Illinois at Chicago, 1601 W. Taylor St., Chicago, Illinois 60612, U.S.A.
    2. Department of Psychiatry, University of Illinois at Chicago, 1601 W. Taylor St., Chicago, Illinois 60612, U.S.A.
    3. Division of Epidemiology and Biostatistics, University of Illinois at Chicago, 1601 W. Taylor St. Chicago, Illinois 60612, U.S.A.
    Search for more papers by this author

email:rdgib@uic.edu

Abstract

Summary We consider the problem of sample size determination for three-level mixed-effects linear regression models for the analysis of clustered longitudinal data. Three-level designs are used in many areas, but in particular, multicenter randomized longitudinal clinical trials in medical or health-related research. In this case, level 1 represents measurement occasion, level 2 represents subject, and level 3 represents center. The model we consider involves random effects of the time trends at both the subject level and the center level. In the most common case, we have two random effects (constant and a single trend), at both subject and center levels. The approach presented here is general with respect to sampling proportions, number of groups, and attrition rates over time. In addition, we also develop a cost model, as an aid in selecting the most parsimonious of several possible competing models (i.e., different combinations of centers, subjects within centers, and measurement occasions). We derive sample size requirements (i.e., power characteristics) for a test of treatment-by-time interaction(s) for designs based on either subject-level or cluster-level randomization. The general methodology is illustrated using two characteristic examples.

Ancillary