A comparison of power analysis methods for evaluating effects of a predictor on slopes in longitudinal designs with missing data

Abstract

In many longitudinal studies, evaluating the effect of a binary or continuous predictor variable on the rate of change of the outcome, i.e. slope, is often of primary interest. Sample size determination of these studies, however, is complicated by the expectation that missing data will occur due to missed visits, early drop out, and staggered entry. Despite the availability of methods for assessing power in longitudinal studies with missing data, the impact on power of the magnitude and distribution of missing data in the study population remain poorly understood. As a result, simple but erroneous alterations of the sample size formulae for complete/balanced data are commonly applied. These 'naive' approaches include the average sum of squares and average number of subjects methods. The goal of this article is to explore in greater detail the effect of missing data on study power and compare the performance of naive sample size methods to a correct maximum likelihood-based method using both mathematical and simulation-based approaches. Two different longitudinal aging studies are used to illustrate the methods.

Keywords: compound symmetry; intraclass correlation; linear mixed effects model; monotone missing; sample size.

Figure 1

Ratio of sample size calculated using the average sum of squares (ASQ) method versus the MLE based method for n=2

Figure 2

Ratio of sample size calculated using the average sum of squares (ASQ) method versus the MLE based method for n=5

Figure 3

Ratio of sample size calculated using the average number of subjects (ANS) method versus the MLE based method for n=2

Figure 4

Ratio of sample size calculated using the average number of subjects (ANS) method versus the MLE based method for n=5