Longitudinal monitoring of amyotrophic lateral sclerosis by diffusion tensor imaging: Power calculations for group studies

Abstract

Introduction: Diffusion tensor imaging (DTI) can be used to map disease progression in amyotrophic lateral sclerosis (ALS) and therefore is a promising candidate for a biomarker in ALS. To this end, longitudinal study protocols need to be optimized and validated regarding group sizes and time intervals between visits. The objective of this study was to assess the influences of sample size, the schedule of follow-up measurements, and measurement uncertainties on the statistical power to optimize longitudinal DTI study protocols in ALS.

Patients and methods: To estimate the measurement uncertainty of a tract-of-interest-based DTI approach, longitudinal test-retest measurements were applied first to a normal data set. Then, DTI data sets of 80 patients with ALS and 50 healthy participants were analyzed in the simulation of longitudinal trajectories, that is, longitudinal fractional anisotropy (FA) values for follow-up sessions were simulated for synthetic patient and control groups with different rates of FA decrease in the corticospinal tract. Monte Carlo simulations of synthetic longitudinal study groups were used to estimate the statistical power and thus the potentially needed sample sizes for a various number of scans at one visit, different time intervals between baseline and follow-up measurements, and measurement uncertainties.

Results: From the simulation for different longitudinal FA decrease rates, it was found that two scans per session increased the statistical power in the investigated settings unless sample sizes were sufficiently large and time intervals were appropriately long. The positive effect of a second scan per session on the statistical power was particularly pronounced for FA values with high measurement uncertainty, for which the third scan per session increased the statistical power even further.

Conclusion: With more than one scan per session, the statistical power of longitudinal DTI studies can be increased in patients with ALS. Consequently, sufficient statistical power can be achieved even with limited sample sizes. An improved longitudinal DTI study protocol contributes to the detection of small changes in diffusion metrics and thereby supports DTI as an applicable and reliable non-invasive biomarker in ALS.

Keywords: Amyotrophic Lateral Sclerosis; Diffusion Tensor Imaging; longitudinal design; statistical power; study optimization.

FIGURE 1

Schematic workflow of statistical power calculations. In a first step, (A) subject-specific longitudinal fractional anisotropy (FA) values in the corticospinal tract (CST) were simulated. Therefore, synthetic baseline values for patients and healthy controls were generated from real subject data distributions. The calculation of synthetic “measured” follow-up FA values incorporated a predefined FA decrease and measurement uncertainty. In a second step, (B) longitudinal trajectories were generated for n subjects per group and the statistical power was calculated from 2,000 Monte Carlo resampled data sets. This procedure was performed for different time intervals between baseline and follow-up sessions, measurement uncertainties, longitudinal FA decrease rates, and sample sizes.

FIGURE 2

Statistical power for longitudinal diffusion tensor imaging studies in amyotrophic lateral sclerosis. Calculations were performed for (A) 0.5%, (B) 2.0%, and (C) 3.5% change per year of the fractional anisotropy in the corticospinal tract. Longitudinal simulations for a patient and a healthy control group were performed for different sample sizes per group, two magnitudes of measurement uncertainty, one to three scans per session, and time intervals t between baseline and the follow-up session.

FIGURE 3

Sample size per group to reach a statistical power of 0.8 with different decrease rates in fractional anisotropy (FA). FA values were either subject to (A) low or (B) high measurement uncertainty. Statistical power calculations were performed for 60, 90, and 120 days between baseline and follow-up sessions and one to three scans per session.