Quantified Neurophysiology with mapping: Statistical ... - Springer Link

Brain Topography, Volume 3, Number 1, 1990

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Quantified Neurophysiology with Mapping: Statistical Inference, Exploratory and Confirmatory Data Analysis Frank H. Duffy,* Kenneth Jones,** Peter Barrels,*** Marilyn Albert,* Gloria B. McAnulty, *+ and Heidelise AIs+++

Summary: Topographic mapping of brain electrical activity has become a commonly used method in the clinical as well as research laboratory. To enhance analytic power and accuracy, mapping applications often involve statistical paradigms for the detection of abnormality or difference. Because mapping studies involve many measurements and variables, the appearance of a large data dimensionality may be created. If abnormality is sought by statistical mapping procedures and if the many variables are uncorrelated, certain positive findings could be attributable to chance. To protect against this undesirable possibility we advocate the replication of initial findings on independent data sets. Statistical difference attributable to chance will not replicate, whereas real difference will reproduce. Clinical studies must, therefore, provide for repeat measurements and research studies must involve analysis of second populations. Furthermore, Principal Components Analysis can be employed to demonstrate that variables derived from mapping studies are highly intercorrelated and data dimensionality substantially less than the total number of variables initially created. This reduces the likelihood of capitalization on chance. The need to constrain alpha levels is not necessary when dimensionality is low and/or a second data set is available. When only one data set is available in research applications, techniques such as the Bonferroni correction, the "leave-one-out" method, and Descriptive Data Analysis (DDA) are available. These techniques are discussed, clinical and research examples are given, and differences between Exploratory (EDA) and Confirmatory Data Analysis (EDA) are reviewed. Key words: Electroencephalography (EEG); Evoked potentials (EP); Quantified electroencephalography (qEEG); Brain electrical activity mapping (BEAM); Significance probability mapping (SPM); Principal components analysis (PCA).

Introduction T h e p a s t d e c a d e h a s w i t n e s s e d a n increase in the a p plication of m o d e m a n a l y t i c t e c h n i q u e s to the b r o a d field

*Associate Professor of Neurology, Harvard Medical School and The Children's Hospital, Boston, Massachusetts, **JohnStein Professor of Social Research Brandeis University, Waltham, Massachusetts, ***Professor, Optical Sciences Center, University of Arizona, Tucson, Arizona, +Associate Professor of Psychiatry and Neurology, Harvard Medical School and The Massachusetts General Hospital, Boston, Massachnsetts, **Research Associate in Neurology Harvard Medical School and The Children's Hospital, Boston, Massachusetts, +++ Associate Professor of Psychology (Psychiatry), Harvard Medical School and The Children's Hospital, Boston, Massachusetts Accepted for publication: July 13,1990. Acknowledgements: This work was supported in part by NICHD grant ROIHD18761 to F. H. Duffy, ROIHD18654 to H. AIS, NIA program project POIAG04953 to M. Albert and the Mental Retardation Program Project P30I-ID18655to C. F. Barlow. We would like to thank our research assistants and secretaries for their unflagging support, and D. McAnulty for his editorial review. Correspondence and reprint requests should be addressed to F. H. Duffy, Department of Neurology,The Children's Hospital, 300 Longwood Avenue, Boston, MA, 02115, USA. Copyright © 1990 Human Sciences Press, Inc.

of clinical n e u r o p h y s i o l o g y . Spectral a n a l y s i s (including coherence), m u l t i v a r i a t e d i s c r i m i n a n t f u n c t i o n analysis, a n d t o p o g r a p h i c m a p p i n g are b u t a f e w e x a m p l e s of n e w m e t h o d s u s e d to extract a d d i t i o n a l i n f o r m a t i o n f r o m classic s c a l p r e c o r d e d d a t a . C o m p u t e r i z e d d e v i c e s w h i c h m a p e l e c t r o e n c e p h a l o g r a p h i c (EEG) a n d e v o k e d potential (EP) d a t a are n o w relatively c o m m o n p l a c e a n d available f r o m m a n y m a n u f a c t u r e r s . W e refer to this b r o a d field as q u a n t i f i e d n e u r o p h y s i o l o g y (qNP). In add i t i o n to utilization in basic research, m a n y laboratories - i n c l u d i n g o u r o w n - h a v e b e g u n to use q N P w i t h t o p o g r a p h i c m a p p i n g in t h e e v a l u a t i o n o f clinical p a t i e n t s (Duffy 1982; 1989; D u f f y et al. 1979; G r u z e l i e r et al. 1988; Jerrett et al. 1988; J o h n et al. 1988; M a u r e r et al. 1988; N a g a t a et al. 1988; Oller et al. 1988 a n d R o n d o t et al. 1987). O n e of o u r first o b s e r v a t i o n s w a s t h a t s i m p l e inspection of t o p o g r a p h i c i m a g e s of p a t i e n t b r a i n electrical activity c o u l d lead to m o r e q u e s t i o n s t h a n a n s w e r s . Alt h o u g h significant p a t h o l o g y s u c h as b r a i n t u m o r s or v a s c u l a r accidents o f t e n s h o w well d e m a r c a t e d focal or a s y m m e t r i c a l features, it is n o t u n u s u a l for a p p a r e n t l y n o r m a l subjects to also exhibit s o m e d e g r e e of a s y m m e t r y . To assist in the d e t e r m i n a t i o n of w h e t h e r a n ob-

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served finding is, or is not, within normal limits of expected variation, we developed the technique of significance probability mapping (SPM) (Duffy et al. 1981). SPM involves the creation of a new map where a subject's data are replaced by the degree of statistical difference from a reference group. This technique calls for the use of a normative data base to facilitate mapping of statistical deviation from control group norms. Although any statistic can be employed to form SPM, we proposed the Z transformation for clinical comparisons between a patient and a group, Student's t-test for research comparisons between two groups, and the F statistic from analysis of variance for multiple group comparisons. Areas above a p r e - d e t e r m i n e d statistical threshold would be considered abnormal, deviant, or different and are designated "regions of interest" (ROI). Statistical mapping has been extensively used in our lab and elsewhere (Duffy 1982; Duffy 1986; Duffy et al. 1984a; 1984b; Duffy et al. 1981; Duffy et al. 1979; Duffy, Jensen et al. 1984; Garber et al. (in press); Gruzelier et al. 1988; John et al. 1988; Maurer et al. 1988; Morstyn et al. 1983; Rappelsberger et al. 1988 and Saletu et al. 1987) and has proven useful for clinical applications of brain electrical activity mapping. On the other hand, concerns have been raised about this approach, questioning inappropriate use of multiple statistical measures (Duffy et al. 1986; Oken et al. 1986; Samson-Dollfus et al. 1988). Multiplying the number of electrodes by the number of data values obtained from each electrode emphasizes that a large number of statistical comparisons may be involved. By chance alone some could appear significant. How can one separate the wheat from the chaff, i.e., which differences are "real" and which attributable to chance? Many articles are now appearing in the neurological and n e u r o p h y s i o l o g i c a l literature w h e r e data are presented as topographic images. It is the specific intent of this paper to discuss relevant statistical issues such articles may raise (Duffy 1988). As we shall demonstrate, the availability of additional data sets obviates concerns over capitalization on chance. Moreover, the underlying dimensionality of the data is substantially less than the number of initial variables, due to significant similarity (inter-correlation) among variables.

Multiple Statistical Comparisons Exploratory and Confirmatory Data Analysis Contemporary training of medical professionals in the uses of statistical analysis emphasizes the difficulties inherent in the use of multiple comparisons. Succinctly

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stated, the statistical evaluation of multiple independent variables predisposes to alpha inflation or type I error, where the null hypothesis is rejected although it is valid. Such "false positive" results may lead to capitalization on chance. Indeed the use of multiple Z or t tests, as used in the SPM technique, appears to violate statistical canons. Note: In a t w o g r o u p c o m p a r i s o n the "null hypothesis" is that there is no significant difference between-group means. To reject the null hypothesis is to find significant between-group difference. To fail to reject it is to find no significant group difference. Neurophysiological mapping studies are not, however, alone in this problem. According to Abt 1981, statistical problems intrinsic to multiple comparisons have long been known (Tukey 1962; 1977; 1980) but only recently have they received sufficient attention from the producers of such data. This recent evolution is attributable to the increasingly broad availability of computerized statistical software packages, with their virtually unlimited capacity to manipulate large data sets. Maus and Endresen 1979, point out that if a two group comparison involving 100 variables is performed, and if one employs the usual alpha criterion level of 0.05, then on the average 100 x .05 or five variables (2 to 8 variables at the 90% confidence level) may appear statistically significant by chance alone. In addition, these authors point out that the probability of reaching at least one false conclusion when using the P + 2.00). (A.) Eight images are shown, the t o p four representing AER activity encompassing the 92-132 msec latency e p o c h a n d the bottom four the corresponding Z statistic SPM, comparing this patent's data to an a g e appropriate normative data base. The right hand three AER-SPM pairs are formed by sequential adminsitration of 200 stimuli each. They are labeled repetition 1 (R1), repetition 2 (R2), a n d repetition 3 (R3). The left hand pair represent a summation (S) by averaging together all 600 stimulations. The maximum SPM Z score is shown'below e a c h AER-SPM pair. Note how the same left posterior deviation from normal is delineated in each of the three repetitions as well as in the summary (red arrows). Such reproducibility of results across three repetitions of the same state is called class I consistency. This adult was diagnosed as having partial complex seizures from a left temporal focus. Discharges were not present at the time the AER were formed. (B.) EEG spectral d a t a in the theta range are imaged as in A. Each repetition (R1, R2, R3) represents average theta over one minute of artifact free d a t a for sequentially gathered EEG during waking. Note how R] a n d R2 fail to show any disgnificant deviation from the control data; whereas, R3 reaches 6.52 SD from normal (right hand green arrow). In this example, class I consistency could not be demonstrated. Note, however, how the three minute summary theta-SPM d a t a pair (S) show apparent deviation from normal (left hand green arrow). This demonstrates h o w spurious d a t a c a n be better detected by examining brief sequential samples (R1, R2, R3) than by relying upon examination of a single larger sample (S). The subject was a normal adult a n d the theta excess in R3 represented the consequence of undetected state c h a n g e (drowsiness). (C.) The SPMs are shown for EEG deffa gathered from an infant in three different canditions: alert, awake, a n d interactive or "alert processing" (AP), drowsy a n d non-interactive but not asleep or "not processing* (NP), a n d trac6 atternant sleep (TA). Note how an abnormality d e t e c t e d in the left central region in AP is also demonstrated in both NP a n d TA (blue arrows). This reproducibility across states is termed class II consistency. The infant had a left intraventricular hemorrhage.

which can be found on only one of the three repetitions (green arrows) (see also also figure legend) and was attributable to intermittent drowsiness. At time of data gathering the technologist had not detected subtle EEG changes compatible with drowsiness (Santamaria et al. 1987). Second, a finding might reappear in the same region across different experimental conditions. We refer to this

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as class II consistency, an example of which is shown in Figure 1C. Note that for this infant with known grade II intraventricular hemorrhage (IVH), there is consistently augmented left central EEG delta slowing during three different conditions (blue arrows) (see also figure legend). By such similarity of results across experimental condition, the finding becomes more convincing than if seen only once. Clinical topographic mapping studies may be understood as exploratory analyses, seeking consistent regions of abnormality. The process begins by defining regions of interest (ROI) as areas exceeding a criterion level on the t-SPM, corresponding approximately to an alpha level of .05. Clearly ROI which involve many electrodes a n d / o r which demonstrate high t values (perhaps exceeding the Bonferonni correction value) are most likely to be clinically important. Lesser ROI may also prove clinically relevant if they appear on repeated measure. Accordingly, we have found it wise to repeat each state a minimum of three times and demand that similar findings be evident for each repetition. This is much like the practice of superimposing several sequentially formed averaged EP tracings, a widely recommended practice (Chiappa 1983). It is also important for similar findings to be noted in more than one state. For example, increased background theta in the eyes closed state should also be seen in the eyes open state. If not, a transient phenomenon, such as drowsiness, may be suspected. By choosing among ROI those with high t levels, those that involve several electrodes, and those that remain viable across state repetition and between states, the neurophysiologist can generally protect him/herself f r o m the effects of r a n d o m statistical noise, and capitalization upon chance. The Bonferroni correction is unnecessary ff a replication or second data set is available. Consistency, by definition, is the mark of a non-random process. Unfortunately, under some circumstances, artifact may also remain constant across replications. Recognition of artifact is an important consideration in mapping studies (Coburn et al. 1988; Duffy 1988b; Duffy 1989; Kahn et al. 1988; Nuwer et al. 1987). Fortunately, artifact produces recognizable signatures, especially when supplemental electrodes are employed to aid in its detection (Duffy 1988). Research m a p p i n g studies - descriptive d a t a analysis

In contrast to clinical studies, replication is more complex for research projects where use of all available subjects may be required to establish reasonable estimates of the underlying structure of the data set. Results of exploratory analyses, although potentially interesting, may be less convincing when not accompanied by confir-

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matory procedures. There are three solutions to this problem. The first, and clearly best, solution calls for demonstration of similar findings on a second population. For e x a m p l e , the f i n d i n g by o u r g r o u p of diminished left temporal P300 activity in a mapping study of schizophrenic patients (Morstyn et al. 1983) has recently been replicated (Faux et al. 1987). It can be difficult and time consuming to collect and analyze data from a second population. Indeed four years elapsed between the original P300 study and its replication. Because of this there is understandable pressure to make at least a preliminary or minimal statement from an initial exploratory study. An alternative to replication on a second or independent sample is the "leave-one-out" or "jackknifing" procedure of Lachenbruch and Mickey (1968). This pro6edure sequentially omits one subject at a time from analysis and calculates a discriminant function based upon the remaining subjects. It then determines how well the discriminant function classifies the "left out" subject. The process is repeated as m a n y times as there are subjects. For an example, see Morihisa et al. 1983. The procedure is "statistically independent," since the discriminant functions are not based upon the subject to be classified; however, this method of replication is not based upon an independently drawn sample from the overall population. It cannot substitute for a full replication on a new sample but provides a useful estimation of potential replicability should a second population not be available. The second solution is to restrict findings to those exceeding the Bonferroni criteria. Unfortunately, such exceedingly strict criteria may result in the absence of any statistically significant findings. Application of the Bonferroni criterion to our original P300 data (Morstyn et al. 1983) would have resulted in no reportable finding, despite the fact that its results were eventually replicated (Faux et al. 1987). Indeed, protection against type I error by lowering the alpha level ("Bonferronization") is not without cost, since it will simultaneously tend to raise type II error. Victor 1982 and Abt 1987 have previously cautioned that "Bonferronization" may serve to prevent adequate analysis by the investigator. The third solution is based upon "descriptive" data analysis (DDA), a new approach Abt proposes to fill the gap betwen CDA and EDA (Abt 1987, 1988). Although beyond the scope of this paper to describe fully, DDA allows an investigator to narrow his perspective from the entire data set and to recognize certain patterns that appear near regular and which "make sense". Abt refers to such locations of interest as Rfiger areas (Rfiger 1978). To understand this approach in the context of mapping studies we shall hypothesize a two group study where comparison is made on the basis of EEG spectral data in

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the eyes open, eyes-closed, and drowsy states. As previously mentioned, one sets a descriptive alpha level of .05 (c~) to delineate ROI. Such descriptive significances may appear in many locations and across any or all spectral bands. Assume the investigator recognizes a group difference in the central region for theta across all three states. A Riiger area is n o w defined consisting of values from five "central" electrodes (FZ, CZ, PZ, C3, C4) for all three states producing an overall N of 15. Abt then requires the investigator to choose a minimal number of unspecified null hypotheses (M), less than N, to be nominally rejected at a new, more conservative alpha level (~). Typically the value M / N is 1 / 3 to 1/2. If M / N is 1/2, then ~ = (.05)/2 - .025. Thus if any eight (15/2) values within the Riiger area individually reach the .025 level, the the overall null hypothesis is rejected for the Riiger area at the c~= .05 level. According to Victor (1982) and Abt (1987) this procedure allows one to make an "overall statement with controlled uncertainty" on an initial data set w h e n a second confirmatory population is unavailable.

Data Dimensionality To i l l u s t r a t e the h i g h i n t e r c o r r e l a t i o n of neurophysiological variables on a real data sample, we analyzed the flash VER data of 73 medically normal male subjects between the ages of 30 and 39. Dimensionality was assessed by Principal Components Analysis (PCA) a technique for reducing a set of variables to the minimum number of independent "factors" needed to explain population variability or variance. Each new factor constitutes a new variable formed by the linear combination of the original variables multiplied by a factor loading coefficient. All resulting factors are independent of one another (orthogonal). The number of factors provides a useful measure of underlying data dimensionality. Details of PCA may be found in many excellent articles including those of Seal (1964) and Bartels (1981a, 1981b). Recording techniques have been previously detailed (Duffy et al. 1984b). Subjects were stimulated with a Grass model PS-22 photic stimulator placed less than 30 cm in front of their closed eyes at intensity 8, a supranorreal level making pupillary dilation unnecessary (Skalka et al. 1986). EEG was monitored to ensure alertness. An individually adjusted voltage threshold was set to remove high voltage artifactual transients. The response to a minimum of 300 flashes was obtained with 512 msec analytic intervals (128 data points) before and after flash onset. The long pre-stimulus epoch facilitated setting zero measurement voltage, recognition of time locked artifact, and evaluation of adequacy of noise reduction by averaging. Data w e r e gathered from 20 scalp electrodes in the 10-20 format (19 standard + OZ) and

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three bipolar artifact channels placed to monitor vertical eye movement and blink, horizontal eye movement, and temporal muscle activity.

Temporal PCA Given the huge data matrix produced by each subject (23 electrodes x 128 data points = 2944 variables), traditional approaches to PCA have involved simplifying assumptions. The most common is that the VER from each electrode be considered a separate case (John et al. 1973; Kavanagh et al. 1976; RSsler and Manzey 1981; Lopes da Silva 1987). This results in factors whose loading scores may be polotted over time - we refer to this as temporal PCA. Thus, PCA is performed on 128 variables across 23 electrodes x 73 subjects = 1679 cases. For this we employed program P4M of the BMDP statistical software package (Dixon 1985) using Varimax rotation. Results are s h o w n in Figure 2. Thirteen factors demonstrated Eigenvalues of 1.0 or more explaining 94.8% of the overall variance (see Table 1). Thus there was approximately a ten-fold reduction in dimensionality from 128 to 13. Each graph in Figure 2 represents a plot of varimax rotated factor loadings (vertial axis) against original variables, the 128 time points in milliseconds (horizontal axis). These loadings are the eigenvectors of the correlation matrix multiplied by the square roots of the corresponding eigenvalues. They are the correlations of the principal components with the original variables (Dixon 1985). The "Residuals" plot in Figure 2 is the sum of the loadings for the 11 additional factors each with Eigenvalues less than 1.0, needed to explain 99% of the variance. This may be considered a noise or residual factor. The waveshapes of the loadings are often taken as representing basic EP components. Ten waveforms could be t a k e n as EP w a v e f o r m s (Fac 1,2,3,5,6,7,9,10,11,12). However, three appear to represent ERG or other artifactual contamination (Fac 4,8,13) on the basis of major loadings at latencies shorter than 50 msec.

Spatial PCA An alternative simplifying assumption in performing PCA is that each instant in time is a separate case. Thus PCA is performed on 23 variables across 128 time points x 73 subjects = 9344 cases. This results in factors whose loading scores can be imaged as topographic maps. We refer to this as spatial PCA. Results are shown for this approach in Figure 3. Four factors demonstrated Eigenvalues of 1.0 or more explaining 84.6% of the overall variance (see Table 2). Thus there was almost a six fold reduciton in dimensionality, from 23 to four. Each image in Figure 3 represents a

Quantified Neurophysiologywith Mapping

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Table 1: Temporal PCA, Factors

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In Factor Space

49.8663

0.3896

0.4110

27.2896

0.6028

0.6358

11.0084

0.6888

0.7266

6.8272

0.7421

0.7828

6.3313

0.7916

0.8350

5.7172

0.8362

0.8821

3.4153

0.8629

0.9103

2.9006

0.8856

0.9342

2.5544

0.9055

0.9552

1.8947

0.9203

0.9708

1.3853

0.9312

0.9822

1.1174

0.9399

0.9915

1.0366

0.9480

1.0000

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Table 2: Spatial PCA, Factors Figure 2: Temporal Factor Analysis of VER. This figure shows the varimax rotated factor Ioadings waveforms resulting from temporal PCA on the flash VER of 73 healthy 30 to 39 year old adults - see text for details. The vertical axis is factor loading coefficient with all waveforms similarly scaled from +1 to -1. The horizontal axis represents time in milliseconds. Fac 4, 8, and 13 load heavily before 50 msec and a p p e a r to be related to ERG or other artifact. A Residual or noise waveform is also shown - see text. Temporal PCA results in approximately a 10:1 reduction in dimensionality (128 to 13).

topographic map of a varimax rotated factor loadings versus electrode location. The three artifact channels are also shown as side bars. The "Residuals" or noise map is also shown, again representing the sum of the loading coefficients for the nine additional factors needed to explain 99% of the overall variance. Few studies have reported spatial PCA, but, Harner [personal communication] has speculated the loading coefficient maps (Figure 3) may describe general scalp regions of activity. It is of interest, therefore, that the loading pattern per factor is not random. Fac 1 loads the central region. Fac 2 loads on the frontal region yet NOT on the vertical eye movement channel. Fac 3 loads on the occipital electrodes. Fac 4 loads primarily on both the horizontal eye move-

Cumulative Pror~ortion of Variance

In Data Space

In Factor Sr~ace

13.1423

0.5714

0.6752

3.0238

0.7029

0.8305

1.9745

0.7887

0.9320

1.3244

0.8463

1.0000

ment and temporal muscle channels with minimal loading on scalp channels. Thus one of four loading coefficient maps clearly represents artifactual data. The "Residuals" load primarily on the vertical eye movement and temporal muscle channels as well as both mid to posterior temporal regions. Thus, although many variables are often available at the start of a qNP study, especially when mapping is involved, the final dimensionality is always much lower. This considerably diminishes the "too many variable" criticism and the likelihood of type I error.

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Figure 3: Spatial Factor Analysis of VER. Ten topographic images are shown in the format of Figure 1. These represent the varimax rotated factor Ioadings maps resulting from the spatiaI-PCA on the flash VER of 73 subjects - see text for details. Each m a p is displayed twice, one at coefficient scale from 0 to 1 and again scaled from zero to maximum value which is shown next to the map. Three auxiliary scaling bars are shown. The bar a b o v e the right eye corresponds to the vertical eye movement channel, at the left of the left ear to the horizontal eye movement channel, and to the right of the right ear to the temporal muscle channel. The top four pairs correspond to factors 1-4. The final pair is the Residuals map - see text. Note that the factor 4 and Residuals map load heavily on artifact channels. Spatial PCA results in approximately a 6:1 reduction in dimensionality (23 to 4).

Conclusion The acquisition of multiple variables is a natural and essential product of electrophysiological brain mapping studies whether for clinical or research purposes. The SPM technique is a simple yet powerful tool for the definition of regions of potential clinical interest (ROI). Capitalization upon chance, a theoretical danger when multiple univariate statistical tests are employed, can be successfully g u a r d e d against by requiring several replications of the same finding in either the same state a n d / o r across several states. The easy availability of replicated data diminishes the need to eliminate variables a n d / o r correct alpha levels. Our over five year experience with clinical mapping indicates that these

precautionary techniques are of great importance in fleeing the clinician from excessive constraints on one extreme and from false positives on the other. Issues are more complex for group comparison studies. If replication is not possible, limited conclusions may be drawn from either exploratory data analysis with Bonferroni correction, the "leave-one-out" procedure, or descriptive data analysis. The issue of generation of too many variables and the subsequent problem of capitalization on chance can also be approached by the use of PCA to examine actual data dimensionality. Although there have been questions as to whether, once obtained, factor derived components should be identified as r e p r e s e n t i n g f u n d a m e n t a l biological processes (Achim et al. 1988; RSsler et al. 1981; VanRotterdam 1970; Wastell 1979 and Wood et al. 1984)

Quantified Neurophysiology with Mapping

all approaches support the conclusion that data dimensionality is far less than the n u m b e r of available variables as demonstrated herein. Thus, in qNP, it is inappropriate to estimate the potential for capitalization on chance u p o n a count of initial variables. Artifactual signals, unfortunately, can remain highly consistent across replications since, although undesired, they m a y constitute real, not chance events. It should be noted in our PCA s t u d y that despite best efforts of specially trained technologists s t u d y i n g healthy subjects, a n u m b e r of factors loaded heavily u p o n auxiliary channels demonstrating persistance of artifact. At the very least this demonstrates the absolute need for artifact channel use in qNP. Confinement of artifact to discrete factors suggests that these confounding signals can be more rigorously recognized and removed statistically than by eye alone (Semlitsch et al. 1986). More efforts are required in this area.

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