Selecting a sample size for studies with repeated measures

Guo et al. BMC Medical Research Methodology 2013, 13:100 http://www.biomedcentral.com/1471-2288/13/100 CORRESPONDENCE Open Access Selecting a sample size for studies with repeated measures Yi Guo1,2*, Henrietta L Logan2,3, Deborah H Glueck4 and Keith E Muller1,2 Abstract Many researchers favor repeated measures designs because they allow the detection of within-person change over time and typically have higher statistical power than cross-sectional designs. However, the plethora of inputs needed for repeated measures designs can make sample size selection, a critical step in designing a successful study, difficult. Using a dental pain study as a driving example, we provide guidance for selecting an appropriate sample size for testing a time by treatment interaction for studies with repeated measures. We describe how to (1) gather the required inputs for the sample size calculation, (2) choose appropriate software to perform the calculation, and (3) address practical considerations such as missing data, multiple aims, and continuous covariates. Keywords: Sample size selection, Repeated measures, Interaction Correspondence Selecting an appropriate sample size is a crucial step in designing a successful study. A study with an insufficient sample size may not have sufficient statistical power to detect meaningful effects and may produce unreliable answers to important research questions. On the other hand, a study with an excessive sample size wastes resources and may unnecessarily expose study participants to potential harm. Choosing the right sample size increases the chance of detecting an effect, and ensures that the study is both ethical and cost-effective. Repeated measures designs are widely used because they have advantages over cross-sectional designs. For instance, collecting repeated measurements of key variables can provide a more definitive evaluation of within-person change across time. Moreover, collecting repeated measurements can simultaneously increase statistical power for detecting changes while reducing the costs of conducting a study. In spite of the advantages over cross-sectional designs, repeated measures designs complicate the crucial process of selecting a sample size. Unlike studies with independent observations, repeated measurements taken from the same participant * Correspondence: 1 Department of Health Outcomes and Policy, College of Medicine, University of Florida, Gainesville, FL, USA 2 Southeast Center for Research to Reduce Disparities in Oral Health, University of Florida, Gainesville, FL, USA Full list of author information is available at the end of the article are correlated, and the correlations must be accounted for in calculating the appropriate sample size. Some current software packages used for sample size calculations are based on oversimplified assumptions about correlation patterns. As discussed later in the paper, oversimplified assumptions can give investigators false confidence in the chosen sample size. In addition, some current software may require programming skills that are beyond the resources available to many researchers. In the present article, we describe methods for gathering the information required for selecting a sample size for studies with repeated measurements of normally distributed continuous responses. We also illustrate the process of sample size selection by working through an example with repeated measurements of pain memory, using the web-based power and sample size program GLIMMPSE. Tasks for selecting a sample size Select a data analysis method For the sake of brevity, we will not elaborate on the fundamental question of choosing a data analysis method. Although statistical consulting will have value at any stage of research, the earlier stages of planning a study profit most from consulting. We assume the iterative process of choosing and refining the research goals, the primary outcomes, and the sampling plan has succeeded. In turn, we also assume that an appropriate analysis plan © 2013 Guo et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Guo et al. BMC Medical Research Methodology 2013, 13:100 http://www.biomedcentral.com/1471-2288/13/100 has been selected, which sets the stage for sample size selection. Select a power analysis method One of the first steps in computing a sample size is to select a power analysis method that adequately aligns with the data analysis method [1]. As an example, consider a study in which a researcher plans to test whether veterans and non-veterans respond similarly to a drug. The researcher plans to control for both gender and age. The planned data analysis is an analysis of covariance (ANCOVA), with age as the covariate. In this case, a sample size calculation based on a two-group t-test would be inappropriate, since the planned data analysis is not a t-test. Misalignment between the design used for sample size calculations and the design used for data analysis can lead to a sample size that is either too large or too small [1], contributing to inconclusive findings. In practice, mixed models have become the most popular method for analyzing repeated measures and longitudinal data. However, validated power and sample size methods exist only for a limited class of mixed models [2]. In addition, most of these methods are based on approximations, and make simple assumptions about the study design. In some cases, the planned data analysis has no published power analysis methods aligned with the data analysis. One possible method for finding reliable power or sample size when no power formulas are available is to conduct a computer simulation study. We recommend using appropriate software that has been tested and validated whenever it is available. Packaged software has the advantages of requiring less programming and less statistical sophistication. Based on the current state of knowledge, we recommend using power methods developed for multivariate models to calculate sample size for studies using common mixed models for data analysis. For carefully built mixed models [3,4], power methods developed for multivariate models provide the best available power analysis. Technical background can be found in Muller et al. [1], Muller et al. [5], and Johnson et al. [6]. Another option is to use the large sample approximation for power described by Liu and Liang. They proposed a method to compute sample sizes for studies with correlated observations based on the generalized estimating equation (GEE1) approach [7]. Model complex variance and correlation patterns When planning a study with repeated measures, scientists must specify variance and correlation patterns among the repeated measurements. Failing t (...truncated)