SPM software - Statistical Parametric Mapping
Statistical Parametric Mapping refers to the construction and assessment of spatially extended statistical processes used to test hypotheses about functional imaging data. These ideas have been instantiated in software that is called SPM.The SPM software package has been designed for the analysis of brain imaging data sequences. The sequences can be a series of images from different cohorts, or time-series from the same subject. The current release is designed for the analysis of fMRI, PET, SPECT, EEG and MEG.
Statistical parametric mapping is generally used to identify functionally specialized brain responses and is the most prevalent approach to characterizing functional anatomy and disease-related changes. The alternative perspective, namely that provided by functional integration, requires a different set of [multivariate] approaches that examine the relationship among changes in activity in one brain area others. Statistical parametric mapping is a voxel-based approach, employing classical inference, to make some comment about regionally specific responses to experimental factors. In order to assign an observed response to a particular brain structure, or cortical area, the data must conform to a known anatomical space. Before considering statistical modeling, this chapter deals briefly with how a time-series of images are realigned and mapped into some standard anatomical space (e.g. a stereotactic space). The general ideas behind statistical parametric mapping are then described and illustrated with attention to the different sorts of inferences that can be made with different experimental designs.
fMRI is special, in the sense that the data lend themselves to a signal processing perspective. This can be exploited to ensure that both the design and analysis are as efficient as possible. Linear time invariant models provide the bridge between inferential models employed by statistical mapping and conventional signal processing approaches. Temporal autocorrelations in noise processes represent another important issue, specific to fMRI, and approaches to maximizing efficiency in the context of serially correlated errors will be discussed. Nonlinear models of evoked hemodynamics are considered here because they can be used to indicate when the assumptions behind linear models are violated. fMRI can capture data very fast (in relation to other imaging techniques), affording the opportunity to measure event-related responses. The distinction between event and epoch-related designs will be discussed and considered in relation to efficiency and the constraints provided by nonlinear characterizations.
Before considering multivariate analyses we will close the discussion of inferences, about regionally specific effects, by looking at the distinction between fixed and random-effect analyses and how this relates to inferences about the subjects studied or the population from which these subjects came. The final section will deal with functional integration using models of effective connectivity and other multivariate approaches.
Functional mapping studies are usually analyzed with some form of statistical parametric mapping. Statistical parametric mapping entails the construction of spatially extended statistical processes to test hypotheses about regionally specific effects (Friston et al 1991). Statistical parametric maps (SPMs) are image processes with voxel values that are, under the null hypothesis, distributed according to a known probability density function, usually the Student's T or F distributions. These are known colloquially as T- or F-maps. The success of statistical parametric mapping is due largely to the simplicity of the idea. Namely, one analyses each and every voxel using any standard (univariate) statistical test. The resulting statistical parameters are assembled into an image - the SPM. SPMs are interpreted as spatially extended statistical processes by referring to the probabilistic behavior of Gaussian fields (Adler 1981, Worsley et al 1992, Friston et al 1994a, Worsley et al 1996). Gaussian random fields model both the univariate probabilistic characteristics of a SPM and any non-stationary spatial covariance structure. 'Unlikely' excursions of the SPM are interpreted as regionally specific effects, attributable to the sensorimotor or cognitive process that has been manipulated experimentally.
Over the years statistical parametric mapping has come to refer to the conjoint use of the general linear model (GLM) and Gaussian random field (GRF) theory to analyze and make classical inferences about spatially extended data through statistical parametric maps (SPMs). The GLM is used to estimate some parameters that could explain the spatially continuos data in exactly the same way as in conventional analysis of discrete data. GRF theory is used to resolve the multiple comparison problem that ensues when making inferences over a volume of the brain. GRF theory provides a method for correcting p values for the search volume of a SPM and plays the same role for continuous data (i.e. images) as the Bonferonni correction for the number of discontinuous or discrete statistical tests.
The approach was called SPM for three reasons; (i) To acknowledge Significance Probability Mapping, the use of interpolated pseudo-maps of p values used to summarize the analysis of multi-channel ERP studies. (ii) For consistency with the nomenclature of parametric maps of physiological or physical parameters (e.g. regional cerebral blood flow rCBF or volume rCBV parametric maps). (iii) In reference to the parametric statistics that comprise the maps. Despite its simplicity there are some fairly subtle motivations for the approach that deserve mention. Usually, given a response or dependent variable comprising many thousands of voxels one would use multivariate analyses as opposed to the mass-univariate approach that SPM represents. The problems with multivariate approaches are that; (i) they do not support inferences about regionally specific effects, (ii) they require more observations than the dimension of the response variable (i.e. number of voxels) and (iii), even in the context of dimension reduction, they are less sensitive to focal effects than mass-univariate approaches. A heuristic argument, for their relative lack of power, is that multivariate approaches estimate the model’s error covariances using lots of parameters (e.g. the covariance between the errors at all pairs of voxels). In general, the more parameters (and hyper-parameters) an estimation procedure has to deal with, the more variable the estimate of any one parameter becomes. This renders inferences about any single estimate less efficient.
Multivariate approaches consider voxels as different levels of an experimental or treatment factor and use classical analysis of variance, not at each voxel (c.f. SPM), but by considering the data sequences from all voxels together, as replications over voxels. The problem here is that regional changes in error variance, and spatial correlations in the data, induce profound non-sphericity[1] in the error terms. This non-sphericity would again require large numbers of [hyper]parameters to be estimated for each voxel using conventional techniques. In SPM the non-sphericity is parameterized in a very parsimonious way with just two [hyper]parameters for each voxel. These are the error variance and smoothness estimators (see Figure 2.htm). This minimal parameterization lends SPM a sensitivity that surpasses multivariate approaches. SPM can do this because GRF theory implicitly imposes constraints on the non-sphericity implied by the continuous and [spatially] extended nature of the data. This is something that conventional multivariate and equivalent univariate approaches do not accommodate, to their cost.
Some analyses use statistical maps based on non-parametric tests that eschew distributional assumptions about the data. These approaches are generally less powerful (i.e. less sensitive) than parametric approaches (see Aguirre et al 1998). However, they have an important role in evaluating the assumptions behind parametric approaches and may supercede in terms of sensitivity when these assumptions are violated (e.g. when degrees of freedom are very small and voxel sizes are large in relation to smoothness).
The Bayesian alternative to classical inference with SPMs rests on conditional inferences about an effect, given the data, as opposed to classical inferences about the data, given the effect is zero. Bayesian inferences about spatially extended effects use Posterior Probability Maps (PPMs). Although less commonly used than SPMs, PPMs are potentially very useful, not least because they do not have to contend with the multiple comparisons problem induced by classical inference. In contradistinction to SPM, this means that inferences about a given regional response do not depend on inferences about responses elsewhere.
More detail and software available at:
[url]http://www.fil.ion.ucl.ac.uk/spm/[/url]
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