Sample size considerations for paired experimental design with incomplete observations of continuous outcomes

Paired experimental design is widely used in clinical and health behavioral studies, where each study unit contributes a pair of observations. Investigators often encounter incomplete observations of paired outcomes in the data collected. Some study units contribute complete pairs of observations, while the others contribute either pre- or post-intervention observations. Statistical inference for paired experimental design with incomplete observations of continuous outcomes has been extensively studied in literature. However, sample size method for such study design is sparsely available. We derive a closed-form sample size formula based on the generalized estimating equation approach by treating the incomplete observations as missing data in a linear model. The proposed method properly accounts for the impact of mixed structure of observed data: a combination of paired and unpaired outcomes. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness, and correlation parameter values. We demonstrate that under complete observations, the proposed generalized estimating equation sample size estimate is the same as that based on the paired t-test. In the presence of missing data, the proposed method would lead to a more accurate sample size estimate comparing with the crude adjustment. Simulation studies are conducted to evaluate the finite-sample performance of the generalized estimating equation sample size formula. A real application example is presented for illustration.

Personalized, bilateral whole-body somatosensory cortex stimulation to relieve fatigue in multiple sclerosis

Background: The patients suffering from multiple sclerosis (MS) often consider fatigue the most debilitating symptom they experience, but conventional medicine currently offers poorly efficacious therapies. Objective: We executed a replication study of an innovative approach for relieving MS fatigue. Methods: According to the sample size estimate, we recruited 10 fatigued MS patients who received 5-day transcranial direct current stimulation (tDCS) in a randomized, double-blind, Sham-controlled, crossover study, with modified Fatigue Impact Scale (mFIS) score reduction at the end of the treatment as primary outcome. A personalized anodal electrode, shaped on the magnetic resonance imaging (MRI)-derived individual cortical folding, targeted the bilateral whole-body primary somatosensory cortex (S1) with an occipital cathode. Results: The amelioration of fatigue symptoms after Real stimulation (40% of baseline) was significantly larger than after Sham stimulation (14%, p = 0.012). Anodal whole body S1 induced a significant fatigue reduction in mildly disabled MS patients when the fatigue-related symptoms severely hampered their quality of life. Conclusion: This second result in an independent group of patients supports the idea that neuromodulation interventions that properly select a personalized target might be a suitable non-pharmacological treatment for MS fatigue.

Multigroup Moderation Test in Generalized Structured Component Analysis

Generalized Structured Component Analysis (GSCA) is an alternative method in structural modeling using alternating least squares. GSCA can be used for the complex analysis including multigroup. GSCA can be run with a free software called GeSCA, but in GeSCA there is no multigroup moderation test to compare the effect between groups. In this research we propose to use the T test in PLS for testing moderation Multigroup on GSCA. T test only requires sample size, estimate path coefficient, and standard error of each group that are already available on the output of GeSCA and the formula is simple so the user does not need a long time for analysis.