Summary We review some results on the analysis of longitudinal data or, more generally, of repeated measures via linear mixed models starting with some exploratory statistical tools that may be employed to specify a tentative model. We follow with a summary of inferential procedures under a Gaussian set‐up and then discuss different diagnostic methods focusing on residual analysis but also addressing global and local influence. Based on the interpretation of diagnostic plots related to three types of residuals (marginal, conditional and predicted random effects) as well as on other tools, we proceed to identify remedial measures for possible violations of the proposed model assumptions, ranging from fine‐tuning of the model to the use of elliptically symmetric or skew‐elliptical linear mixed models as well as of robust estimation methods. We specify many results available in the literature in a unified notation and highlight those with greater practical appeal. In each case, we discuss the availability of model diagnostics as well as of software and give general guidelines for model selection. We conclude with analyses of three practical examples and suggest further directions for research.

Amyotrophic Lateral Sclerosis (ALS) is one of the most common adult-onset motor neuron disease causing a progressive, rapid and irreversible degeneration of motor neurons in the cortex, brain stem and spinal cord. No effective treatment is available and cell therapy clinical trials are currently being tested in ALS affected patients. It is well known that in ALS patients, approximately 50% of pericytes from the spinal cord barrier are lost. In the central nervous system, pericytes act in the formation and maintenance of the blood-brain barrier, a natural defense that slows the progression of symptoms in neurodegenerative diseases. Here we evaluated, for the first time, the therapeutic effect of human pericytes in vivo in SOD1 mice and in vitro in motor neurons and other neuronal cells derived from one ALS patient. Pericytes and mesenchymal stromal cells (MSCs) were derived from the same adipose tissue sample and were administered to SOD1 mice intraperitoneally. The effect of the two treatments was compared. Treatment with pericytes extended significantly animals survival in SOD1 males, but not in females that usually have a milder phenotype with higher survival rates. No significant differences were observed in the survival of mice treated with MSCs. Gene expression analysis in brain and spinal cord of end-stage animals showed that treatment with pericytes can stimulate the host antioxidant system. Additionally, pericytes induced the expression of SOD1 and CAT in motor neurons and other neuronal cells derived from one ALS patient carrying a mutation in FUS. Overall, treatment with pericytes was more effective than treatment with MSCs. Our results encourage further investigations and suggest that pericytes may be a good option for ALS treatment in the future. Graphical Abstract ᅟ.

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