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# Linear Models: Statistical Analysis of Regional Imaging Data

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# Linear Models: Statistical Analysis of Regional Imaging Data

Advanced statistical techniques based on linear statistical model are implemented in the PMOD R interface. These solutions have been developed by Prof Karl Herholz, University of Manchester, UK, who is a renowned expert and consultant in the field of neuroimaging, with particular interest in dementia and brain tumors. His statistical expertise was sharpened as the coordinator of multiple international multicenter studies, and by the development of automated image analysis procedures, such as the one employed in PMOD’s PALZ module.

Images provide a wealth of information. They are essential for demonstration and analysis of normal and pathological anatomy and function in medicine and biomedical sciences. Computerized tomography (CT) and related techniques, such as magnetic resonance imaging (MRI) and positron emission tomography (PET), have made huge progress in the recent decades. They are frequently being used to provide diagnostic images interpreted visually by trained observers (e.g., radiologists).

Recently, it is increasingly being recognized that some images can also be regarded as data sets representing a quantitative parameter measured simultaneously in a large number of anatomical regions. Particularly, as each region in an image (with image pixels or voxels as the smallest regions that could potentially be studied) provides a separate dependent variable, their number may be very large and will often exceed the number of individuals under study. This situation creates a particular statistical challenge, which will be addressed in the current section.

These challenges can best be addressed by procedures which:

take into account that regional data originating from the same individual are not independent from each other, and describe their dependency by a covariance matrix;

provide tests for comparing the experimental effects between regions;

provide proper correction for multiple comparisons.

The procedures are based on linear statistics models. Two approaches fulfilling these requirements will be described:

1.Repeated measures and multivariate analysis of variance (rm-ANOVA, MANOVA)

2.Linear mixed effect models (LME).

The table below summarizes the benefits and limits of the two linear statistics models:

 MANOVA LME Analytical minimization of residual variance within groups for general linear model Iterative minimization of residual variance for general linear model Analytical separation of variance components for within-subject and between-subject factors Fitting the mean effects for all specified experimental factors, and the variance of a random factor associated with individuals Automatic inclusion of interactions between within and between-subject factors All interactions need to be specified in the model for inclusion May fail if too many highly correlated regions are included in model Can accommodate a large number of regions Requires a balanced design (groups of equal size) for correct separation of variance components Works for balanced and unbalanced designs Does not allow missing values In presence of missing values effect sizes can still be fitted, but statistical tests to determine their significance may fail