R Romo Vázquez

H Vélez-Pérez

R Ranta

V Louis Dorr

D Maquin

L Maillard

Blind source separation, wavelet denoising and discriminant analysis for EEG artefacts and noise cancelling

Keywords: EEG, artefact elimination, BSS, supervised classification, wavelet denoising, medical validation

This paper proposes an automatic method for artefact removal and noise elimination from scalp electroencephalogram recordings (EEG). The method is based on blind source separation (BSS) and supervised classification and proposes a combination of classical and news features and classes to improve artefact elimination (ocular, high frequency muscle and ECG artefacts). The role of a supplementary step of wavelet denoising (WD) is explored and the interactions between BSS, denoising and classification are analyzed. The results are validated on simulated signals by quantitative evaluation criteria and on real EEG by medical expertise. The proposed methodology successfully rejected a good percentage of artefacts and noise, while preserving almost all the cerebral activity. The "denoised artefact-free" EEG presents a very good improvement compared with recorded raw EEG: 96% of the EEGs are easier to interpret.

Introduction

The electrical activity produced by the brain is recorded by the electroencephalogram (EEG) using several electrodes placed on the scalp, generally according to predefined international standards (10-20 for example). Signals characteristics vary from one state to another, such as wakefulness/ sleep or normal/ pathological. Classically, five major brain waves can be distinguished by their frequency ranges: delta (δ) 0.5 -4Hz, theta (θ) 4 -8Hz, alpha (α) 8 -13Hz, beta (β) 13 -30Hz and gamma (γ) 30 -128Hz [START_REF] Sanei | EEG Signal Processing[END_REF].

The informative cortically generated signals are contaminated by extracerebral artefact sources: ocular movements, eye blinks, electrocardiogram (ECG), muscular artefacts. Generally the mixture between brain signals and artefactual signals is present in all sensors, although not necessarily in the same proportions (depending on the spatial distribution). Moreover, the EEG recordings are also affected by other unknown basically random signals (instrumentation noise, other physiological generators, external electromagnetic activity, etc) which can be modeled as additive random noise. These phenomena make difficult the analysis and interpretation of the EEGs, and a first important processing step would be the elimination of the artefacts and noise.

Several methods for artefact elimination were proposed in the literature, a brief review being presented in the next section. Most of them consists in two main steps: artefact extraction from the multichannel recorded signals, generally using some signal separation methods, followed by signal classification (visual or automatic) and "clean EEG" reconstruction. Our goal is to contribute to EEG artefact rejection by proposing an original and more complete automatic methodology consisting in an optimized combination of several signal processing and data analysis techniques.

This paper is organized as follows: the second section presents a brief state of the art of the EEG artefact rejection solutions proposed in the literature, and concludes with the main original contributions of this paper. The third section is dedicated to our proposed approach. This section consists in a first part that briefly introduces the methodological steps included in our approach: BSS, supervised classification and wavelet denoising WD. A second part discusses their mutual interactions and proposes an optimal combination. The fourth section presents the main results and it is also divided in two parts: the first one aims to choose an optimal BSS -WD combination algorithm using a set of semi-simulated realistic EEG signals, while the second one is dedicated to a comparative medical validation on large database of real EEGs. Finally, conclusion and research perspectives are given.

In order to define the framework of this paper, we must specify that we address here classical scalp EEGs, as recorded in clinical routine. More precisely, we deal with signals recorded using the 10-20 international system, with the reference electrode placed at the Fpz position, close to the nasion (see figure 1).

State of the art

The most common artefact rejection method is based on linear regression and aims to eliminate the most frequent artefact, due to eye movement or blinking. This method is capable of estimating the influence of the simultaneously measured electrooculogram (EOG) signals in the EEG and to remove them [START_REF] Croft | Removal of ocular artifact from the EEG: a review[END_REF]. Still, as the EOG electrodes are frequently placed close to the EEG electrodes, they contain a certain amount of brain activity. Thus, removing these signals might cause distortions in the EEG signals. Besides, this method needs supplementary channels for EOG recording and, of course, does not deal with other artefacts.

Source separation. More complete methods, based on linear decomposition of the multichannel EEG recordings, were proposed in the literature. The most common method is the blind source separation (BSS). The main BSS hypothesis states that the artefact sources are independent from brain sources, either normal or pathologic; the goal is to recover the original sources (brain and artefactual), given only sensor observations. Several algorithms for BSS were developed in the last years, either using high order statistics (HOS) and thus explicitly addressing the 'independence' (Independent Component Analysis -ICA) or second order statistics (SOS) on time delayed or windowed signals, as well as combined (ICA + SOS) approaches (see for example [START_REF] Cichocki | Adaptive Blind Signal and Image Processing Learning Algorithms and Applications[END_REF] for a review).

In the EEG artefact identification setups, there is no consensus for a best BSS algorithm. Several ICA based algorithms [START_REF] Delorme | Enhanced detection of artifacts in EEG data using higher-order statistics and independent component analysis[END_REF][START_REF] Greco | Renyi's entropy and independent component scalp maps for the automatic artifact rejection from EEG data[END_REF][START_REF] Li | Automatic removal of the eye blink artifact from EEG using an ICA-based template matching approach[END_REF][START_REF] Levan | A system for automatic artifact removal in ictal scalp EEG based on independent component analysis and Bayesian classification[END_REF][START_REF] James | Temporally constrained ICA: an application to artifact rejection in electromagnetic brain signal analysis[END_REF] have been applied. However, some more restrictive (but realistic) assumptions allow the use SOS only: if the sources have different non-random temporal structures, these methods proved efficient. Indeed, as it was pointed out by different authors [START_REF] Kierkels | A model-based objective evaluation of eye movement correction in EEG recordings[END_REF][START_REF] Romero | A comparative study of automatic techniques for ocular artifact reduction in spontaneous EEG signals based on clinical target variables: A simulation case[END_REF][START_REF] Escudero | Artifact removal in magnetoencephalogram background activity with independent component analysis[END_REF][START_REF] Ting | Automatic correction of artifact from single-trial event-related potentials by blind source separation using second order statistics only[END_REF][START_REF] Klemm | Independent component analysis: comparison of algorithms for the investigation of surface electrical brain activity[END_REF]] SOBI [START_REF] Belouchrani | A blind source separation technique using second-order statistics[END_REF] is an appropriate algorithm to separate the EEG signals. This SOS algorithm is based on the 'joint diagonalization' of an arbitrary set of time delayed covariance matrices of the measured signals.

It allows the separation of Gaussian sources. The SOBI-RO algorithm is adapted for noisy signals by introducing a robust orthogonalization step [START_REF] Belouchrani | Robust whitening procedure in blind source separation context[END_REF].

Feature extraction and classification. In the artefact elimination framework, BSS is used to separate cerebral and extra-cerebral sources. After separation, the identification of the artefact sources can be done by visual inspection [START_REF] Vigario | Extraction of ocular artefacts from EEG using independent component analysis[END_REF][START_REF] Melissant | A method for detection of Alzheimer's disease using ICA-enhanced EEG measurements[END_REF], but this approach becomes very impractical when processing many EEGs.

Recently, several methods for automatic identification of artefact sources were proposed. During the feature extraction step, the main source characteristics employed in the literature are:

• Statistical characteristics as kurtosis, entropy, trends or extreme values. The kurtosis is used to detect peaky activity distributions characterizing specific artefacts (i.e. ocular and cardiac). The entropy also helps to identify the signals concentrated in small temporal intervals, therefore likely to be artefacts [START_REF] Delorme | Enhanced detection of artifacts in EEG data using higher-order statistics and independent component analysis[END_REF][START_REF] Greco | Renyi's entropy and independent component scalp maps for the automatic artifact rejection from EEG data[END_REF].

• Template signals. If available, artefact measured signals are used as templates (EOG, ECG). A high correlation between a source and the template will indicate an artefact [START_REF] Levan | A system for automatic artifact removal in ictal scalp EEG based on independent component analysis and Bayesian classification[END_REF][START_REF] Wallstrom | Automatic correction of ocular artifacts in the EEG: a comparison of regression-based and component-based methods[END_REF][START_REF] James | Temporally constrained ICA: an application to artifact rejection in electromagnetic brain signal analysis[END_REF][START_REF] Li | Automatic removal of the eye blink artifact from EEG using an ICA-based template matching approach[END_REF][START_REF] Nicolaou | Automatic artefact removal from event-related potentials via clustering[END_REF][START_REF] Shao | Automatic EEG Artifact Removal: A Weighted Support-Vector-Machine Approach With Error Correction[END_REF].

• Frequency characteristics. The sources can be characterized by the energy contained in the different frequency bands [START_REF] Levan | A system for automatic artifact removal in ictal scalp EEG based on independent component analysis and Bayesian classification[END_REF][START_REF] Romero | A comparative study of automatic techniques for ocular artifact reduction in spontaneous EEG signals based on clinical target variables: A simulation case[END_REF].

• Spatial characteristics. The features based on the mixing characteristics are connected to the scalp topography: the projection strength of the signals onto the scalp allows the examination of its biological origin [START_REF] Romero | A comparative study of automatic techniques for ocular artifact reduction in spontaneous EEG signals based on clinical target variables: A simulation case[END_REF][START_REF] Li | Automatic removal of the eye blink artifact from EEG using an ICA-based template matching approach[END_REF].

Often, these features are used to determine, with the help of human expertise, specific thresholds for every artefact type. These 'expert systems' are further on used to label specific sources as artefacts. More elaborated methods tend to automatically determine the frontiers between artefact and informative brain sources using different classifiers (Bayes rule based linear or quadratic discriminant analysis [START_REF] Levan | A system for automatic artifact removal in ictal scalp EEG based on independent component analysis and Bayesian classification[END_REF] or support vector machines [START_REF] Shao | Automatic EEG Artifact Removal: A Weighted Support-Vector-Machine Approach With Error Correction[END_REF]). Similar methods, based on BSS and supervised classification, were equally proposed for magnetoencephalographic signals (MEG) [START_REF] Escudero | Artifact removal in magnetoencephalogram background activity with independent component analysis[END_REF][START_REF] Dammers | Integration of amplitude and phase statistics for complete artifact removal in independent components of neuromagnetic recordings[END_REF]. In all methods, after separation and classification, the artefactual sources are removed and the EEG is reconstructed with the informative brain sources only. As for all classification problems, the accuracy of the solution depends both on the features and on the classifier thresholds.

Our approach follows the same general idea: EEG signals are processed by BSS, a set of features is extracted from the obtained sources, these features are fed into a classifier and the artefact sources are eliminated from the reconstruction. The originality of our work consists in several aspects:

• we perform an extended evaluation of several BSS algorithms on physiologically plausible EEGs;

• we propose an original feature set for source classification, containing physiologically significant features extracted from the estimated mixing matrix and from time and frequency characteristics of the sources. The proposed method does not need EOG electrodes, as required by most of the methods presented in the literature. The electrocardiogram signal, used as reference signal for the characteristics extraction is routinely recorded simultaneously with the EEG.

• we introduce a wavelet denoising (WD) step and we analyze its interactions with the two other classical elements of the processing chain (BSS and classification), proposing an optimal sequencing of these three processing steps;

• finally, we perform a throughout validation of the processing chain on a large database of real EEGs, using both objective criteria (classification rate) and a systematic medical evaluation.

Proposed EEG artefact rejection methodology

As said in the introduction, this section is divided in two parts: the first one briefly recalls the individual methodological steps included in our method (BSS, Bayes classifier, wavelet denoising), while the second one analysis their interactions and proposes an optimal order of these processing steps.

Methodological steps 3.1.1. Blind Source Separation -BSS

The goal of the BSS is to recover original sources, given only sensor observations. The most simple and widely used assumption in EEG processing is the linear instantaneous mixing: source signals reach the sensors simultaneously [START_REF] Sanei | EEG Signal Processing[END_REF].

The noisy mixture in this case is written as:

X = AS + N (1)
where X is the matrix of the mixed signals (x i corresponds to a row of X, i.e., a sensor signal), A is the unknown nonsingular mixing matrix, S is the matrix of independent sources (s i corresponds to a source), N is an additive noise matrix.

The aim of BSS is to find a linear transformation B of the sensor signals X that makes the outputs as independent as possible:

Y = BX = BAS + BN ( 2
)
where Y is the estimation of the sources S. We assume here that the number of sources is equal to the number of sensors Q. In this case, A ∈ R Q×Q and the ideal separation is obtained when B = A -1 and, consequently, Y is a (noisy) estimate of S. In practice, BSS algorithms search a B matrix such as the product BA is a permuted diagonal and scaled matrix. Therefore, original sources can be recovered except for their order (permutation) and their amplitude (scale): the estimated sources Y will be permuted and normalized to unitary standard deviation.

BSS evaluation. On simulated signals, one can validate the BSS results by using the separability index SI [START_REF] Cichocki | Adaptive Blind Signal and Image Processing Learning Algorithms and Applications[END_REF][START_REF] Escudero | Consistency of the blind source separation computed with five common algorithms for magnetoencephalogram background activity[END_REF][START_REF] Melissant | A method for detection of Alzheimer's disease using ICA-enhanced EEG measurements[END_REF]. This index is computed from the transfer matrix G = BA between the original sources and the estimated ones.

The SI is computed starting from the absolute values of the G elements. The rows g i and the columns g j of this matrix are normalized to obtain g i and g j respectively:

g i = |g i | max |g i | g j = |g j | max |g j | (3)
The SI 1 and the SI 2 are obtained from the elements of the resulting Q × Q matrix G :

SI 1 = Q i=1 Q j=1 (G (i, j)) -1 Q(Q -1) SI 2 = Q j=1 Q i=1 (G (i, j)) -1 Q(Q -1)
A synthetic separability index SI writes as:

SI = SI 1 + SI 2 2 , ( 4
)
its purpose being to measure the degree to which G is close to a permutation matrix. For perfect source recovering SI = 0.

Wavelet denoising -WD

Nowadays a classical solution for noise removal from non-stationary signals is WD. The decomposition of a noisy signal on a wavelet basis (discrete orthogonal wavelet transform, DWT) have the property to "concentrate" the informative signal in few wavelet coefficients having large absolute values without modifying the noise random distribution. Therefore, denoising can be achieved by thresholding the wavelet coefficients.

Consider the model x(k) = c(k) + n(k), where x(k) is the noisy discretetime signal (length M ), c is the noise-free unknown version of x(k) and n(k) the noise. For the EEG application, the x signal corresponds to a single EEG channel (a measurement electrode). As the DWT is a linear transform, the wavelet coefficient vectors of x, c and n are related by:

w x = w c + w n (5)
Denoising is performed by separating the wavelet coefficients w x by thresholding. Generally, the wavelet coefficients corresponding to low frequencies (approximation coefficients) remain unchanged. The main problem is to estimate the threshold T between small and large wavelet coefficients (i.e., noise w n and informative w c respectively). Several algorithms have been proposed in the last years, and an extensive review can be found in [START_REF] Antoniadis | Wavelet estimators in nonparametric regression: a comparative simulation study[END_REF][START_REF] Antoniadis | Wavelet methods in statistics: Some recent developements and their applications[END_REF].

The most widely used is the universal threshold

T U = σ n √ 2 log N pro-
posed by Donoho and Johnstone in their algorithm VisuShrink [START_REF] Donoho | Ideal spatial adaptation via wavelet shrinkage[END_REF] (σ n is an estimate of the noise standard deviation). VisuShrink is used to achieve complete asymptotic elimination of the normal Gaussian noise. Consequently, it might also lead to a less precise reconstruction of the signal of interest.

A different approach is proposed by the SureShrink algorithm [START_REF] Donoho | Adapting to unknown smoothness via wavelet shrinkage[END_REF] (Stein Unbiased Risk Estimator ), that aims to estimate as precisely as possible the "clean" signal by minimizing an estimate of the mean squared error (MSE ) between the denoised signal and the original one. The obtained threshold T S (or thresholds, as the method is usually implemented by scale) are lower than the T U .

In the EEG case, not loosing information potentially useful to medical diagnosis is of great importance. Moreover, as in EEG the signal to noise ratio is weak, the wavelet coefficients of neuronal signals can have small values, comparable to noise. Therefore, algorithms with a low thresholding as Sure are the most appropriate for our application: theoretically, it insures the closest possible reconstruction (in a mean squared error sense) of the informative signal.

Feature extraction

Several sets of features listed in the literature (see section 2) were investigated and a combination of spatial, frequency and template correlation characteristics was selected. The retained features cover the spectral content of the sources, their spatial projections and their correlation to a template routinely recorded signal (ECG).

Frequency characteristics. Spectral analysis was performed for all estimated sources. The power spectral density for the 5 frequency bands of each source y j was calculated. After normalization using the total energy (frequency range 1 -128Hz), the 5 features are no longer independent, so only 4 are considered in the sequel: E δ j , E α j , E β j and E γ j . For each source, the main frequency f m j (estimated from the maximum value of the power spectral density) was also calculated. An example for a real EEG recording is depicted in figure 2. Spatial characteristics. In practice, an EEG signal is the measure of the potential difference between the measure and reference electrodes, which plays Frequency (Hz) (c) separated sources (frequency spectra) an important role in the mixing matrix coefficients. In this work, the reference is placed near the eyes at Fpz (figures 1 and 3(b)), so it records the eye activity also. Consequently, there is a strong presence of ocular artefacts in all measured signals. After BSS, the sources are normalized and the strong presence of a source in a measured signal is reflected by an important absolute value of the corresponding mixing matrix coefficient. In particular, the elements of the column corresponding to the ocular artefact source should have significantly higher and more constant values than the other columns (figures 3(a) and 3(b)). After BSS estimation of the mixing matrix A, it is possible to evaluate the strength of an source y j by computing the average a j of the coefficient absolute values of column a j .

a j = 1 Q Q i=1 | a ij | j = 1, 2, . . . , Q (6)
The normalized standard deviation σ j of each column a j indicates the spreading: As mentioned above, these spatial features are influenced by the reference electrode: if the reference electrode is different to FPz (and thus the eye artefacts do not highly contaminate it), the EEG must be re-referenced.

σ j = σ j a j (7)
Template correlation characteristic. The ECG is usually recorded simultaneously with the EEG, therefore it can be used as a template signal. The correlations between the template and the separated sources y j write:

ρ ecg,j = cov(ecg, y j ) σ ecg σ y j (8)
Finally, each estimated source is characterized by 8 features: 5 spectral features (E δ j , E α j , E β j , E γ j and f m j ), 2 spatial features (the normalized standard deviation σ j and the average projection on the electrodes a j ) and one template correlation feature (ρ ecg,j ).

Classification

The extracted features aim to code and quantify medical expertise. A common solution would be a rule based expert system: according to the feature extraction paragraph, one can expect a rather good identification of the ocular artefact AO and of the ECG artefact AECG using only the spatial and template correlation characteristics respectively. Nevertheless, parameterizing this system is not trivial and not all the source types are addressed (high frequency muscle and noise artefacts HFA, brain B ) 1 . We have therefore implemented in this paper two classification methods based on the classical the Bayes classifier, as described next.

After feature extraction, the sources y are viewed as a vector sf of dimension d (number of features). These vectors are fed to the classifier. A classical approach is the discriminant analysis, derived from the general Bayes rule. For a vector sf, the probability of belonging to the class C j is written:

p(C j |sf) = p(sf|C j )p(C j ) p(sf) , with p(sf) = k j=1 p(sf|C j )p(C j ), (9)
where p(sf|C j ) is the conditional probability of sf given C j . Considering Gaussian classes and after some manipulation, one decides if a vector sf belongs to the class C j by minimizing:

d B (sf, C j ) = 1 2 (sf -µ j ) T Σ j -1 (sf -µ j ) + 1 2 ln |Σ j | -ln p(C j ), (10)
The mean µ j , the covariance matrix Σ j and the a priori probability p(C j ) are estimated from the training classes defined by the experts. This training set was consensually constructed by two neurologists, which identified the 4 types of sources. Although not usually performing source visual analysis, they were able to identify artefact sources by comparing their time courses with the recorded EEGs (bipolar and referential montages). To preserve all information potentially useful to medical diagnosis, only the obvious artefact sources were selected.

A simplified version of ( 10) is the Mahalanobis distance:

d(sf, C j ) = 1 2 (sf -µ j ) T Σ j -1 (sf -µ j ) (11)
Source classification evaluation. Classification methods are classically evaluated using the number of the true positive (TP ), true negative (TN ), false negative (FN ) and false positive (FP ) detections. The values are used to compute the sensitivity (Sen), the specificity (Spe) and the false positive rate (FPR) of the classifier (eq. 12). Alternatively, one can compute the positive predictive value (PPV) and the negative predictive value (NPV), who give a complementary view on the results (eq. 13).

Sen = T P T P +

F N Spe = T N T N + F P F P R = 1 -Spe ( 12
)
P P V = T P T P + F P N P V = T N T N + F N (13)

Interactions and optimal ordering

This subsection analyses the interaction between the three processing steps previously described (BSS, classification and WD) and proposes an optimized implementation, both in terms of chosen algorithms and in terms of ordering.

BSS and WD

Clearly, the first processing step must be chosen between BSS (to identify artefact sources) and denoising (to eliminate additive noise). Naturally, source separation algorithms perform better in no noise situations (even if specific algorithms as SOBI-RO were designed to deal with the noise), therefore a first approach would be to denoise the raw EEG signals before BSS. On the other hand, the WD step might lead to a loss of information by eliminating also a part of the informative signal, possibly useful for the BSS and/or for the classification steps.

Our first aim is thus to study the interaction between BSS and WD. Rather few references combine them, either for ECG [START_REF] Vigneron | Fetal electrocardiogram extraction based on non-stationary ICA and wavelet denoising[END_REF] or for EEG preprocessing [START_REF] Berryman | Techniques for noise removal from EEG, EOG, and airflow signals in sleep patients[END_REF][START_REF] Rong-Yi | Blind source separation of multichannel electroencephalogram based on wavelet transform and ICA[END_REF][START_REF] Castellanos | Recovering EEG brain signals: artifact suppression with wavelet enhanced independent component analysis[END_REF][START_REF] Ghandeharion | A fully automatic ocular artifact suppression from eeg data using higher order statistics: Improved performance by wavelet analysis[END_REF]. However, the only detailed study on the interaction is presented in [START_REF] Rivet | Wavelet Denoising for Blind Source Separation in Noisy Mixtures[END_REF].

First, observe that both techniques are linear, and thus the mixing equation can be combined to the wavelet transform to obtain the mixture of wavelet coefficients:

W x = AW s + W n , (14)
with W x , W s and W n being the wavelet coefficients matrices of the measured signals, sources and noise respectively. In particular, the vector of the wavelet coefficients of the ith measured signal w x,i (row i of w x ) can be written as a noisy linear combination of the wavelet coefficients of the sources w s,j :

w x,i = [w x,i (1), w x,i (2), . . . w x,i (M )] = a i      w s,1 w s,2
. . .

w s,N      + w n,i (15)
with a i the corresponding row of the mixing matrix A.

Denoising this signal implies thresholding of the wavelet coefficients vector w x,i using a threshold T to obtain the wavelets coefficients of the denoised estimate w c,i . In a matrix form, thresholding can be written as:

w c,i = w x,i F T,x i = w x,i        f (w x,i (1)) 0 0 . . . 0 0 f (w x,i (2)) 0 . . . 0 0 0 f (w x,i (3)) . . . 0 . . . . . . . . . . . . . . . 0 0 0 . . . f (w x,i (M ))        (16
) with f (w x ) being the thresholding (shrinkage) function implementing the chosen threshold (see for example [START_REF] Antoniadis | Wavelet estimators in nonparametric regression: a comparative simulation study[END_REF] for details).

Considering the mixing equation ( 14), one obtains:

w c,i = w x,i F T,x i = a i      w s,1 w s,2 . . . w s,P      F T,x i + w n,i F T,x i (17)
In other words, thresholding the wavelet coefficients of x i implies applying the same threshold to all the sources contributing to it. Which means that the individual sources risk to be distorted by the threshold, adapted to the mixture but not to the sources characteristics.

For example, a source that has a small contribution to the measured signal (i.e., a small mixing coefficient) risks to be lost or highly distorted after thresholding. According to this analysis, if there is a distortion risk (depending on the value of the threshold), it seems better to insert the WD step after the BSS. In order to confirm the presented analysis, we performed several simulations, the results being presented in the next section.

Classifier position

A last issue is the position of the classifier in the processing chain. In our opinion, there is no general answer: as for the BSS case, denoising might distort the signals and mislead both the experts and the automatic classification. Indeed, to avoid possible interpretation errors 2 , clinical experts need all the available information to do a correct source identification. Consequently, we propose to place the classification step immediately after the BSS. It is noteworthy that, in order to preserve the coherence of the method, the training set was also constructed from non denoised sources.

Results

This section consists on two parts: the first one presents simulated signals and leads to the final design of the processing chain. The second one focuses on real EEGs and on medical validation.

Simulation

The goal of this simulation step is to validate the analysis presented in section 3.2.1: which is the optimal BSS-WD combination?

Nine (Q=9) semi-simulated sources were used (figure 4(a)):

• 6 brain sources (S1, S2, S3, S4, S5 and S6) extracted from an intracerebral (depth) encephalogram (SEEG) recording. As the SEEG signals are recorded by electrodes placed inside the brain, we can safely assume that these signals are artefacts free. In order to insure maximum independence, these 6 sources were extracted from different brain locations and different time windows.

• 3 artefacts sources (one ocular artefact source (S7), an ECG artefact source (S8) and a high frequency artefact source (S9)) were also used as semi-simulated sources. These sources were extracted from scalp EEG recordings (different patients) by source separation. They were identified by the clinicians as artefacts.

The semi-simulated sources (figure 4(a)) were mixed using a random matrix (uniform distribution in [-1, 1]) (see example in figure 4(b)). Several BSS algorithms (ICAlab and EEGlab toolbox [START_REF] Cichocki | ICAlab toolboxes[END_REF][START_REF] Delorme | EEGLAB Wikitorial[END_REF]) were tested on ideal and on noisy simulated mixtures, with 4 SNR values (5dB, 10dB, 15dB, 20dB). Both white and colored noises were used, with similar results. The noises were independently generated for the 9 measures (spatially white noise). The results for the best 14 algorithms are presented in table 1 (average values over 1000 simulations).

Analyzing this table, we can see that the combined algorithm (ICA + SOS) COMBI is the most performant for the noise free signals (SI = 0.0428). For low noise level (SNR=20dB), it is the EEGLab's RUNICA (Extended Infomax) algorithm that presents the best results (SI = 0.1065), however, this result is close to the result of the SOBI-RO algorithm (SI = 0.1118). On the other hand, SOBI-RO has the best performance for higher noise levels (15dB → SI = 0.1247, 10dB → SI =0.1452 and 5dB → SI =0.1757). From these results we can conclude that the COMBI algorithm is the best adapted for the noise free signals, while SOBI-RO is the most performant for noisy EEG signals. 0.0962 0.1398 0.1502 0.1652 0.1877 RUNICA [START_REF] Makeig | Independent component analysis of electroencephalographic data[END_REF] 0.0744 0.1065 0.1280 0.1634 0.2191 JADE [START_REF] Cardoso | Blind beamforming for non Gaussian signals[END_REF] 0.1533 0.1798 0.1947 0.2131 0.2370 JADE-TD [START_REF] Müller | Jadetd: Combining higher-order statistics and temporal information for blind source separation with noise[END_REF] 0.1857 0.2160 0.2300 0.2465 0.2664 EFICA [START_REF] Koldovský | Efficient variant of algorithm fastica for independent component analysis attaining the cramér-rao lower bound[END_REF] 0.0815 0.1162 0.1351 0.1622 0.2032 COMBI [START_REF] Tichavský | Blind signal separation by combining two ica algorithms: Hos-based efica and time structure-based wasobi[END_REF] 0.0428 0.1266 0.1509 0.1777 0.2029 MULTICOMBI [START_REF] Tichavský | A hybrid technique for blind non-gaussian and time-correlated sources using a multicomponent approach[END_REF] 0.1219 0.1553 0.1817 0.2091 0.2300

The BSS algorithms were next tested in combination with the WD. Denoising was implemented before and after BSS. As for the BSS only, the combination BSS-WD was evaluated using the SI (eq. 4) averaged over 1000 simulations (mixing matrices). Mean SI values are presented in table 2. For conciseness, only the two best algorithms are presented, the best for the no noise situation (COMBI) and the best for the noisy signals (SOBI-RO) (see example figure 4). Also, only the results for the Sure algorithm [START_REF] Donoho | Adapting to unknown smoothness via wavelet shrinkage[END_REF], known to minimally distort the informative signals (see section 3.1.2) are presented here. More detailed results can be found in [START_REF] Romo-Vázquez | EEG ocular artefacts and noise removal[END_REF][START_REF] Romo-Vàzquez | Contribution à la détection et à l'analyse des signaux eeg épileptiques : débruitage et séparation de sources[END_REF].

From these results we can conclude that:

• For the COMBI algorithm, the denoising insertion distorts the informative sources (even with a low threshold algorithm), so the SI increases. • Inserting the denoising before BSS damages the SI obtained without denoising by SOBI-RO also, and for all noise levels, confirming the previous analysis (probable source distortion).

• Without denoising, the results obtained with SOBI-RO are higher than those obtained with COMBI, both for denoised and noisy signals. Considering the discussion section 3.2.2, the final order of the three processing steps is BSS → Classification → Denoising.

Real EEG validation

This subsection is dedicated to the evaluation of the presented method on a database of real signals. As said previously, two types of validation are possible: the first one aims to quantitatively evaluate the source classification performances, while the second is clinically oriented (blind medical validation of the "clean" reconstructed EEGs).

Data base. Thirty-eight scalp EEGs from 19 epileptic adults (aged 16 to 51), were recorded using a Micromed system at CHU-Nancy (2 by patient, 24 electrodes, 10-20 system, common reference at Fpz, notch filter at 50 Hz). Sampling frequency was 256 Hz. The data-base contains one sleep recording. Since the very low frequency artefacts (baseline shifts, slow ocular movements) perturb the source classification, a high-pass filter with a cut-off frequency of 1 Hz was applied.

The proposed method was applied on 20 seconds EEG sequences, in order to have a sufficient number of samples and thus a reliable BSS result. All recordings were seizure and inter-ictal spikes free.

By clinical inspection, the experts identified and labeled artefact and brain informative sources for the 38 electroencephalograms. Half of them were included in the training set, the other half being used to evaluate the performances of the classification.

Quantitative evaluation: source classification performances

The classifiers were evaluated using the sensitivity (Sen) and the false positive rate (FPR) (eq. 12), both on training and on testing subsets. Tables 3(a) and 3(b) show the global performances, all classes included, and the detailed performances by class ((a) Malahanobis distance, (b) Bayes classifier). As it can be seen in tables 3(a) and 3(b), the two methods are quite performant (and thus implicitly validate our features choice). The global performances slightly better for the classifier based on Mahalanobis distance, who shows both the best Sen and the best FPR. This observation is valid both for testing and for training data, although the performances are slightly different.

For a more precise analysis of the two automatic methods, a detailed analysis by class is presented in tables 3(a) and 3(b). This analysis shows for the AO that the two classification methods make a good identification of the artefactual sources however, the Bayes classifier method increases the good artefactual source identification but the false detections also (highest Sen and highest FPR). These observations are valid both for testing and training data, with of course better performances on the training subset.

The two automatic methods were also analyzed for the high frequency artefact source identification. However, in this case, the 2 methods have very similar sensitivity results. The Mahalanobis distance method presents the smallest FPR (less false detections), whereas the Bayes method presents the higher Sen (better artefactual source identification). Some of the sources identified by the experts as HFA are classified in other classes. In particular, there is an important FPR for the brain class: this result indicates that the two classes (HFA and B ) are close in the feature space. This drawback should be nuanced, as the main objective is to have a minimal loss of brain information (although some of the EEGs reconstructed from the sources classified as brain might still be noisy).

For the ECG artefact identification the two methods in both subsets, testing and training groups, have an excellent performance with a good Sen rate. The FPR is equal to 0 for all the cases for the ECG artefact source identification. It must be noted here that very few ECG sources were identified by the experts, so this "perfect" classification should be validated on a larger data-base.

Finally, for the brain sources identification, the Bayes method has the smallest FPR (as well as the smallest Sen), that is this method identifies just a few false brain sources. On the opposite, the Mahalanobis distance method identifies correctly more brain sources than the Bayes method (highest Sen) but has a FPR slightly higher than the Bayes classifier. Interestingly, for the (only) EEG recording without artefacts (sleep), the classifier identified all sources as brain (no loss of information) 3 .

As the classes are rather unbalanced (very few ECG artefact sources, midsized ocular and high-frequency artefact classes and a big brain class), one might use the PPV and the NPV (eq. 13) values to have a complementary view.

The PPV and NPV values presented in tables 4(a) and 4(b) confirm the previous Sen/FPR analysis and offer a complement of information. The most interesting case is the ocular artefact class (AO). According to the PPV Regardless of the classifier and of the employed criteria, global performances reflect mostly the brain source classification. This is quite expected, as the brain sources largely outnumber the artefact sources, so their good or bad classification rate highly influence the global classification.

A detailed comparison of the the two discriminant analysis classifiers (Bayes and Mahalanobis) reveals that for all 3 artefact classes, the Bayes classifier has a higher Sen but a highest FPR also (more artefacts are detected, but more brain sources are also labeled as artefacts). For brain sources, the situation is inverted (as expected). Generally, we can conclude that Bayes classifier should be used when 'brain only' sources are needed in the reconstruction (i.e. all artefacts must be eliminated). When this procedure is too rough (i.e. when all information should be preserved), the Mahalanobis based classifier is the best choice. Therefore, for the medical validation step (final validation of the processing chain), we used the reconstructed EEG after the Mahalanobis distance classifier.

Qualitative evaluation: medical validation of the reconstructed EEG

This last subsection presents the medical validation results in terms of visual interpretation of the reconstructed denoised artefact-free EEGs. A last issue is then the reconstruction method. The EEG reconstruction was made using the estimated matrix A ( Â) and the estimates sources Y that is:

EEGrec = i∈R âi ŷi (18)
where R represent the indices of the sources classified as brain sources. For consciousness, denoising was implemented either on the selected sources ŷ or on the reconstructed EEG signals. Both versions were visually analyzed by the neurologists, who found them completely equivalent (we remind that the this validation was made consensually by two neurologists).

Three versions of cleaned EEGs were reconstructed and compared to the raw EEG: after BSS and visual identification of the artefact sources by the experts (clinical inspection), after BSS and Mahalanobis classifier (BSSC) and after BSS, Mahalanobis classifier and wavelet denoising (BSSCD). All processing steps were developed using MATLAB 7.9.0. The processing time for each EEG (20 seconds long) was 2 seconds using an Intel CORE T M 2 duo processor.

The clinical validation was made by blindly comparing the improvement between the raw EEG and each cleaned EEG (clinicians had no information on the noise and artefact removal method). The improvement was measured in two ways: the artefact removal quality and the physiological interpretation improvement. Clearly, they have a strong relation: an artefact free EEG allows a better interpretation.

As expected, the artefact sources having a good sensitivity (AO et ECG) were more easily eliminated. Still, the clinically validated results offer a complement of information, as they globally classify 24 channels reconstructed EEGs and not individual sources. For example, if all misclassified artefact sources belong to a single EEG, it would indicate that this particular EEG had a recording or separation problem. On the contrary, if the misclassified artefact sources are equally distributed over the whole EEG data-set, all reconstructions would be affected and none would be easier to interpret.

Consequently, clinicians noted the reconstructed EEGs, from an artefact elimination point of view, with: 1 no elimination, 2 partial elimination, 3 complete elimination, and, from an interpretation point of view, with: 1 much harder to interpret (loss of information), 2 harder (partially removed artefacts confusing the interpretation), 3 equal, 4 easier and 5 much easier. The raw EEG was always noted 3.

The percentage of EEGs by category is presented in the following table [START_REF] Greco | Renyi's entropy and independent component scalp maps for the automatic artifact rejection from EEG data[END_REF]. The AECG artefact elimination validation is not presented, as all these sources were completely eliminated (Sen=1, tables 3(a) and 3(b), to compare with the results from [START_REF] Shao | Automatic EEG Artifact Removal: A Weighted Support-Vector-Machine Approach With Error Correction[END_REF], where the ECG was reduced in 98.4% of the EEGs). A first conclusion appears from table 5: the denoising doesn't contribute to the AO elimination (98% completely or partially eliminated both by BSSC and BSSCD). Similar results were obtained by [START_REF] Shao | Automatic EEG Artifact Removal: A Weighted Support-Vector-Machine Approach With Error Correction[END_REF] (96.8%), but with the help of an electrooculogram. On the contrary, the HFA was the most difficult to identify (as it was for the experts also). The results obtained by clinical inspection and BSSC are very similar (79% and 84% respectively), with a slightly better performance for the latter. On the contrary, the denoising step improves considerably the HFA elimination. As it can be seen, the percentage of EEG showing a total elimination of the HFA (noted 3) increases from 21% to 63% and the percentage of the overall improvement (categories 2 and 3) increases from 84% to 98%.

Concerning the facility of interpretation, BSSC seems to offer better performances than the clinical inspection method (87% compared to 71%). This rather surprising result is coherent with the artefact elimination results from the same table 5: some of the artefact sources were not visually identified by the experts during the labelling step, but the automatic method correctly classified them. This can be explained, as said previously, by the fact that clinical experts have only chosen the evident artefact sources to avoid potential loss of information (see also quantitative results of Sen, FPR, PPV and NPV in the previous subsection). As for HFA elimination, further denoising (BSSCD) increases the percentage of EEGs noted 5 from 24% to 48% and the overall improvement percentage (categories 4 and 5) increases from 87% to 96%.

An example of EEG processing is shown in figure 5.

Conclusion and future research

In this paper, we propose a method for eliminating several types of artefacts and noise based on blind source separation (SOBI-RO), wavelet denoising (SureShrink ) and supervised classification (Mahalanobis). The analysis of the interaction between the three methods yielded an optimal preprocessing chain, validated on simulated and real signals. In particular, we show that BSS must be performed on the noisy raw signals, i.e. before wavelet denoising. Concerning the choice of the BSS algorithm, our simulations (on highly realistic signals) led to the conclusion that in normal clinical setups (noisy environment) second order statistics algorithms perform better than HOS algorithms. This conclusion is supported by extensive simulation results (see also recent studies by [START_REF] Klemm | Independent component analysis: comparison of algorithms for the investigation of surface electrical brain activity[END_REF][START_REF] Escudero | Consistency of the blind source separation computed with five common algorithms for magnetoencephalogram background activity[END_REF]).

The obtained preprocessing chain was applied on inter-ictal EEG and was compared with a semi-automatic approach based on BSS and visual classification. The results show a significant improvement of both artefact elimination and EEG interpretation. According to the clinicians, high frequency artefact sources (muscles and noise) are difficult to identify (visually, thus also by supervised classification). Moreover, it is also possible that BSS fails to separate these sources from the brain activity. The WD step introduction addresses this problem, with very good results from an interpretation point of view (with only 2% of the EEGs showing a loss of information, compared to 11% for clinical inspection).

The proposed method can be applied on any EEG window, seizure included. First results of "clean" ictal EEG, obtained using the same feature space and training set as for the inter-ictal case, are very encouraging. Moreover, the method can be adapted further, in order to take into account the specificities of the seizure signals (i.e., new classes or new features dedicated to seizure sources).

Figure 1 :

 1 Figure 1: International 10-20 system

Figure 2 :

 2 Figure 2: Example of raw EEG and estimated sources by SOBI-RO. Vertical lines in (c) delimit physiological frequency bands

Figure 3 :

 3 Figure 3: Topographic characteristics

Table 1 :

 1 Comparison of BSS algorithms on semi-simulated EEG (no noise and noisy)

	Algorithme SAS	no noise 20dB	15dB	10dB	5dB
	AMUSE [36]	0.0565	0.2410 0.2726 0.2946 0.3098
	SOBI-RO [15]	0.0941	0.1118 0.1247 0.1452 0.1757
	EVD [37]	0.0600	0.2219 0.2553 0.2803 0.2968
	SOBI [38, 14]	0.0882	0.1407 0.1673 0.1989 0.2322
	SOBI-BPF[39]	0.0753	0.1124 0.1346 0.1663 0.2085
	WASOBI [40]	0.0654	0.1874 0.2119 0.2348 0.2507
	EWASOBI [41]	0.0614	0.1563 0.1881 0.2246 0.2555
	SEONS2[42]

Table 2 :

 2 Comparison of BSS algorithms on simulated EEG, before and after denoising

		COMBI	SOBI-RO
	no noise	0.0428	0.0941
	SNR	Noisy Denoised Noisy Denoised
	20dB	0.1266	0.1861	0.1118	0.1309
	15dB	0.1509	0.2173	0.1247	0.1424
	10dB	0.1777	0.2616	0.1452	0.1608
	5dB	0.2029	0.3126	0.1757	0.1867
	Therefore, our proposed method is based on the SOBI-RO (for this algorithm
	100 time delays were considered) separation and the Sure denoising, with BSS
	applied on the raw signals (before denoising).

Table 3 :

 3 Classifier performances (Sen/FPR) (a) Distance de Mahalanobis classifier (b)

	Bayes classifier
			(a)
		Training	Testing
		Sen	FPR	Sen	FPR
	global 85.3% 4.9% 82.2% 5.9%
	AO	95.4% 2.5% 85.2% 4.4%
	HFA 77.6% 10% 68.1% 7.7%
	AECG 100%	0%	100%	0%
	B	87.4% 14.9% 89.0% 21.8%
			(b)
		Training	Testing
		Sen	FPR	Sen	FPR
	global 80.2% 6.6% 78.3% 7.6%
	AO	100% 6.4% 88.9% 7.9%
	HFA 80.8% 13.6% 71.5% 11.9%
	AECG 100% 0.2% 100%	0%
	B	78.1% 10.4% 80.5% 16.1%

Table 4 :

 4 Classifier performances (PPV/NPV ) (a) Distance de Mahalanobis classifier (b) number of false positives (FP ) in the AO class is bigger for the Bayes classifier than for the Mahalanobis distance (as said previously). But one can notice that, quantitatively, there are more FP (false positives) than TP (true positives) in this class when using Bayes (this is not the case for the Mahalanobis classifier)! Considering the values for the other classes, one can conclude that a certain amount of brain labeled signals were classified as AO. The problem might be important, as it might lead to some information loss (i.e. brain sources elimination). Still, in practice, this phenomenon has very little influence on the final results (see also next subsection): first of all, as classes are unbalanced, rather few brain labeled sources are misclassified (high Sen for the brain class); second, this analysis deals with sources labeled by the neurologists and, as explained before, they avoided to label as artefacts sources that were not obviously artefacts. In other words, both automatic classifiers classed as AO sources having rather ambiguous characteristics, some of them maybe real ocular artefacts not selected by the neurologists.

	Bayes classifier
		(a)
		Training	Testing
		PPV NPV PPV NPV
	global 85.3% 95.1% 82.2% 94.1%
	AO	65.6% 99.8% 54.8% 99.0%
	HFA 74.6% 91.4% 80.3% 86.2%
	AECG 100% 100% 100% 100%
	B	92.0% 77.5% 86.8% 81.4%
		(b)
		Training	Testing
		PPV NPV PPV NPV
	global 80.2% 93.4% 78.3% 92.8%
	AO	44.0% 100% 41.4% 99.2%
	HFA 69.2% 92.3% 73.6% 81.0%
	AECG 87.5% 100% 100% 100%
	B	93.6% 67.6% 89.0% 72.6%

Table 5 :

 5 Artefact elimination and facility of interpretation performances

		Identification methods
	category Clinical inspection	BSSC	BSSCD
		AO elimination
	3	42% (16)	50% (19) 50% (19)
	2	50% (19)	48% (18) 48% (18)
	1	8% (3)	2% (1)	2% (1)
		HFA elimination
	3	13% (5)	21% (8) 63% (24)
	2	66% (25)	63% (24) 35% (13)
	1	21% (8)	16% (6)	2% (1)
		Facility of interpretation
	5	32% (12)	24% (9) 48% (18)
	4	39% (15)	63% (24) 48% (18)
	3	18% (7)	8% (3)	2% (1)
	2	11% (4)	5% (2)	2% (1)
	1	0%	0%	0%

Such a rule based classifier was implemented in[START_REF] Romo-Vàzquez | Contribution à la détection et à l'analyse des signaux eeg épileptiques : débruitage et séparation de sources[END_REF], but the results were less convincing than the ones presented in this paper.

According to our tests on real EEGs, this problem mainly occurs for muscle artefacts containing high frequency components, often distorted by denoising.

The sources for this EEG (represented by the 8 dimensional feature vector sf ) are in the middle of the B class.


Wim Delva

Kristien Michielsen

Bert Meulders

Sandy Groeninck

Edwin Wasonga

Pauline Ajwang

Marleen Temmerman

Bart Vanreusel

AIDS Impact special issue 2009: HIV prevention through sport: the case of the Mathare Youth Sport Association in Kenya

Keywords: HIV prevention, sport, youth, Kenya, East Africa HIV prevention, sport, youth, Kenya, East Africa

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In Kenya, the prevalence of HIV among adults declined from 10% in the late 1990s to under 7% in 2003 [START_REF] Cheluget | Evidence for population level declines in adult HIV prevalence in Kenya[END_REF]. A downward trend in HIV prevalence among female sex workers was also observed over the period 1985-2005[START_REF] Kimani | Reduced rates of HIV acquisition during unprotected sex by Kenyan female sex workers predating population declines in HIV prevalence[END_REF].

Peer-mediated interventions in these groups have shown to result in a reduction in unprotected sex [START_REF] Luchters | Impact of five years of peer-mediated interventions on sexual behavior and sexually transmitted infections among female sex workers in Mombasa, Kenya[END_REF]. However, high HIV incidence rates continue to affect young people and other vulnerable populations in Kenya, and the most recent figures from the Kenya AIDS Indicator Survey (KAIS) show an increased HIV prevalence among 15-49 year olds from 6.7 % in 2003 to 7.8 % in 2007. The risk for infection is highest among young women and girls. Young women aged 15 to 24 are 4 times more likely to be infected than young men (6.1 percent compared to 1.5 percent) (Ministry of Health Kenya, 2008). Biological factors, large age differences between young women and their sexual partners, as well as the low likelihood of condom use in such relationships, may explain this disparity in the risk of HIV infection between the sexes. [START_REF] Brabin | Hormonal markers of susceptibility to sexually transmitted infections: are we taking them seriously[END_REF][START_REF] Chersich | Vulnerability of women in southern Africa to infection with HIV: biological determinants and priority health sector interventions[END_REF][START_REF] Hargreaves | Characteristics of sexual partnerships, not just of individuals, are associated with condom use and recent HIV infection in rural South Africa[END_REF][START_REF] Luke | Confronting the 'sugar daddy' stereotype: age and economic asymmetries and risky sexual behavior in urban Kenya[END_REF].

The Mathare Youth Sport Association (MYSA) has been on the forefront of grassroots HIV prevention for vulnerable young people. Established in 1987, this non-governmental organisation has been active in and around Mathare Valley -one of the poorest slum areas in Africa. The population of Mathare Valley is estimated at 180 000 people, living in an area of less than five square kilometres. There are only a few schools for the 70 000 children in Mathare Valley, and more than one in five people in Mathare is thought to be HIV positive. (Médecins Sans Frontières, 2008).

MYSA links sports with environmental clean-ups, HIV prevention, leadership training, awareness raising and other community service activities. Over the years, it has grown to be the largest self-help youth sports and community service organisation in Africa, with approximately 14 775 male and 4 275 female members in 2008 (Mathare Youth Sport Association, 2009). MYSA's strategy to prevent new HIV infections is grounded in the Social Learning Perspective [START_REF] Bandura | Self-efficacy: toward a unifying theory of behavioral change[END_REF]. Social Learning Theories claim that people 3 acquire and maintain certain behavioural patterns through a constant interaction between three factors: the individual, his environment, and his behaviour. Behaviour is not simply the result of the environment and the individual, just as the environment is not simply the result of the individual and his behaviour. The environment provides models for behaviour [START_REF] Glanz | Health Behavior and Health Education. Theory, Research and Practice[END_REF]. MYSA uses peer educators to spread information and creates a healthy environment in which behaviour change can take place. To that end, MYSA employs a scheme that integrates sport and life skills through peer education, peer counselling, games, music, drama, puppetry and other cultural and recreational activities. Children may choose which activities they wish to join and MYSA meetings have an open door policy.

Within the sport-for-development movement, a loosely connected coalition of organisations promoting development through sport, sport is generally perceived as a valid instrument in the fight against HIV and AIDS. The rationale behind the use of sport in HIV prevention programmes is based on claims that sport can provide an attractive and accessible platform to disseminate health information, and that it can foster life skills that are necessary to translate knowledge, attitudes and behavioural intentions into actual behaviour [START_REF] Koss | Essay: HIV/AIDS prevention and peace through sport[END_REF].

Empirical evidence of the effectiveness of sport-based HIV prevention programmes is, however, sorely lacking, and efforts to scale up these programmes are mainly based on the intuitive judgement of sport enthusiasts, rather than sound monitoring and evaluation [START_REF] Delva | Determinants of the effectiveness of HIV prevention through sport In[END_REF]. In order to address this research gap, we conducted a cross-sectional survey assessing sexual behaviour and determinants thereof among MYSA members and a control group of non-MYSA members. In addition, we determined whether there is a dose-effect of exposure to MYSA's HIV prevention activities on indicators of risky sexual behaviour. In the Rotational Facilitation, peer educators and peer counsellors visit teams in one of the 16 MYSA zones to educate youth about topics affecting people in that particular zone. The peer educators talk for 10 to 30 minutes in an interactive way to the youngsters. In the School Outreach Programme, the peer educators mainly use group discussions as a tool to deliver their message. Each session in a school takes two to three hours. The topics of discussion are chosen in dialogue with the pupils. The Movement Games are done with younger children up to the age of 14. In this component of the HIV/AIDS Prevention and Awareness Project, sport and play are used in a more direct way. Through various forms of play knowledge is conveyed to youngsters and awareness is created about HIV and AIDS. A peer counsellor is always present in the Resource Centre to provide individual information and advice. Books and videos about sexual and reproductive health issues including HIV, gender, drugs and teenage pregnancy are available for consultation. Lastly, the volunteers from the HIV/AIDS Project often take the opportunity to give information and education during MYSA football tournaments.

METHODS

The intervention

F

Effectiveness assessment

Study design

The impact of the MYSA HIV/AIDS Prevention and Awareness Project was assessed using a cross-sectional study design with an intervention and control group. Participants were eligible if they were between 12 and 24 years old. For the intervention group, people from all the MYSA zones and all MYSA programmes were eligible for participation and candidate respondents were approached during different MYSA activities.

In order to reduce socio-demographic differences between the intervention and the control group, the control respondents had to live in the same geographical region. To 5 select the control respondents, venues and locations where youth meet (i.e. youth clubs, schools, social organisations) were selected in the 16 MYSA zones. In these sites, all young people within the age range of 12 to 24 were invited to participate. Data collection was done from July to October 2007. Data collection took place in private rooms of the participating organisations and no person who could be perceived as an authority by the young people was present during survey administration.

All subjects were asked to sign an informed consent in which they confirmed that their participation in the study was voluntary and anonymous. In the case of a subject being younger than 18 years, a supervisor (e.g. MYSA peer educator) was asked to sign as well.

Theoretical framework

The theoretic framework used for this evaluation and analysis is the Theory of Planned Behaviour [START_REF] Ajzen | Perceived behavioral control, self-efficacy, locus of control, and the theory of planned behavior[END_REF]. As illustrated by Figure 1, this model identifies behavioural intention as the main determinant of behaviour. Intention is in turn influenced by the person's attitude towards the behaviour, the subjective norm and his or her perceived behavioural control. [START_REF] Ajzen | Perceived behavioral control, self-efficacy, locus of control, and the theory of planned behavior[END_REF]. [START_REF] Harvey | Evaluation of a drama-in-education programme to increase AIDS awareness in South African high schools: a randomized community intervention trial[END_REF][START_REF] Iriyama | AIDS health beliefs and intention for sexual abstinence among male adolescent students in Kathmandu, Nepal: a test of perceived severity and susceptibility[END_REF][START_REF] James | Young people, HIV/AIDS/STIs and sexuality in South Africa: the gap between awareness and behaviour[END_REF][START_REF] O'leary | Social Cognitive Predictors of Sexual Risk Behavior Change Among STD Clinic Patients[END_REF][START_REF] Olley | Gender differences in condom use behaviour among students in a Nigerian university[END_REF][START_REF] Slaymaker | A critique of international indicators of sexual risk behaviour[END_REF]UNAIDS, 2001;[START_REF] Visser | Life skills training as HIV/AIDS preventive strategy in secondary schools: evaluation of a large-scale implementation process[END_REF]. The questionnaire was divided into two sections: one section to be answered by all subjects, the other to be answered only by those who reported to have previously had sexual intercourse. The questionnaire was piloted among 25 MYSA members. Following this pilot study small corrections were made in layout and answer categories and a translation was provided in Kiswahili for specific terms. Selfadministration of the questionnaire took between 20 and 45 minutes.

Data collection method

Statistical methods

Data analysis was performed with R version 2.9.0 [START_REF] Ihaka | R: A language for data analysis and graphics[END_REF]R Development Core Team, 2005). First, chi²-tests were used in bivariate analyses to compare attitudes, norms, self-efficacy, intentions and sexual behaviour between MYSA members and youth from the control group, and to identify factors associated with MYSA membership. Sexual behaviour was measured by several outcome variables: sexual experience (having had vaginal and/or anal intercourse), age at sexual debut, condom use at first/last sex act, history of concurrent relationships, condom use with current/last partner and number of partners in the last year. Next, the potentially confounding effects of age, sex, religion, ethnicity, exposure to media, social capital and perceptions of body and health on the association between MYSA membership and the outcome variables of interest status were assessed via multiple (ordinal) logistic regression models. Lastly, we constructed a MYSA activity score, ranging from 0 (no participation in any of the HIV prevention activities) to 12 (intensive participation in all components of the project), to measure to which degree individuals had been exposed to the MYSA HIV/AIDS Prevention and Awareness Project. For outcome variables

RESULTS

Data from 892 questionnaires were considered: 474 in the MYSA group and 418 in the control group. Subjects from the control group who had been involved in the MYSA School Outreach programme (93 subjects) were excluded from the analysis. After filtering for age inclusion criteria and inconsistent responses, 772 questionnaires were used for further analysis: 318 control and 454 MYSA.

Socio-demographic characteristics

Respondents had a mean age of 16.2 years. Both groups had a similar mean age: 16.1 years in the MYSA group and 16.4 years in the control group (p=0.18). The MYSA group contained significantly more male respondents than the control group (73.6% versus 57.6%; p<0.001). Christianity was by far the dominant religion in both groups: 90.5% in the MYSA group and 93.9% in the control group (p=0.15). Schooling levels in respondents in the MYSA group (80.5%) were comparable to those in the control group (79.5%) (p=0.81). The MYSA group contained significantly more respondents of the Luo ethnic group, while Kikuyu were more present in the control group (p<0.001). The socioeconomic situation of the respondents was assessed through questions regarding the roofing and flooring material of the houses the respondents were living in and no significant differences between the MYSA and control group were found.

Attitudes, norms, self-efficacy and intentions

Attitudes, norms, self-efficacy and intentions, considered to be associated with sexual behaviour according to the Theory of Planned Behaviour, were measured using 4-point Likert-scales. Each factor was measured by two questions, which resulted in sum scores between 0 and 8. Wilcoxon tests showed no significant differences between the MYSA group and the control group on compiled factors for attitudes towards risk avoiding behaviour (median score=6, p=0.97), subjective norms on virginity and responsibility (median score=6, p=0.49), nor for behavioural intentions concerning condom use and remaining faithful to a partner (median score=6, p=0.22). For behavioural control concerning condom use (having one or more condoms with and not having difficulty finding a place to buy a condom) respondents from the MYSA group scored better than their counterparts from the control group (median MYSA score=4, median control group score=3, p=0.003).

Confounding factors

As shown in Table 1, the MYSA group contained significantly more boys than the control group, and there were also ethnic differences between the two groups.

Furthermore, MYSA members were found to have greater exposure to media (newspapers, television, radio), had a greater social capital and were more aware of the importance of taking care of their body and health. We performed multivariate regression analyses to control for these potentially confounding variables. The associations between MYSA membership and ever having had sex, number of sexual partners in the last year,

history

Dose-effect

As evident from Figure 2, only a minority of MYSA members had been maximally exposed to the organisation's HIV prevention activities while about one in six (69/419) had not participated in any of these. We performed additional regression analyses to investigate whether MYSA members with higher activity scores were more likely to use condoms at first sex and to use condoms more frequently. The analyses showed a lack of evidence for a dose-effect of the project. For condom use at first sex, the OR for the dose-effect, adjusted for the effect of MYSA membership, was 1.00; 95% CI: 0.87-1.14. The OR for the dose-effect on the frequency of condom use with the current/last partner, adjusted for media exposure and MYSA membership, was 0.97; 95% CI: 0.62-1.50.

DISCUSSION

This survey showed no significant differences between MYSA and non-MYSA members regarding attitudes towards risk avoiding behaviour, subjective norms on virginity and members reported stronger habits of having one or more condoms with them and had less difficulty finding a place to buy condoms. These results seem consistent with the initial bivariate analysis of sexual behaviour and MYSA membership. This analysis indicated that the sexual behaviour of MYSA members did not differ significantly from that of non-MYSA members, except that MYSA members were more likely to use condoms at first and last sex and that they used condoms more frequently with the current or last sexual partner. In the multivariate analysis none of the candidate confounding factors were independently associated with condom use at first sex after adjusting for the effect of MYSA. Adjusting for exposure to media reduced the effect size of MYSA membership on condom use at last sex and the frequency of condom use with the current/last partner, rendering the former association statistically insignificant. However, the respective point estimates for the effect sizes (OR=1.56 and OR=1.64) were still relatively large, and the wide confidence intervals around these estimates may be due to insufficient statistical power rather than lack of effect.

These findings concur with the results of a previous study in a South African mining community, which showed that young women who belonged to sports clubs were more likely to use condoms with casual partners than non-members [START_REF] Campbell | Is social capital a useful conceptual tool for exploring community level influences on HIV infection? An exploratory case study from South Africa[END_REF]. To our knowledge -our study is the first to report differences in frequency of condom use associated with an HIV prevention programme through sports as the two previously published evaluations of soccer-based programmes merely reported on changes in knowledge, attitudes and intentions [START_REF] Clark | An adolescent-targeted HIV prevention project using African professional soccer players as role models and educators in Bulawayo, Zimbabwe[END_REF] or used a composite scale to describe changes in condom experience [START_REF] Maro | Using sport to promote HIV/AIDS education for at-risk youths: an intervention using peer coaches in football[END_REF]. The analysis presented in this paper begs two key questions: Does the association of MYSA membership with increased condom use point to a causal effect? And if so, are the observed differences large enough to confer a sizeable impact on HIV incidence (averted HIV infections)? Prevention and Awareness Project, we would expect a dose-effect of the project according to Hill's criteria for causation [START_REF] Hill | The Environment and Disease: Association or Causation?[END_REF]. In contrast, we found that respondents who had been highly exposed to the programme were not more likely to use condoms than those who reported never having participated in the programme.

A first explanation for this may be self-selection bias [START_REF] Westhoff | Epidemiologic studies: pitfalls in interpretation[END_REF]. Individuals who are more likely to avoid unprotected sex, may be guided to do so by a greater sense of control over their own future or stronger feelings of responsibility towards the health of themselves and their sexual partners. The decision to join MYSA may be driven by the same underlying motives. This corresponds with the finding that MYSA members had a significantly higher perceived behavioural control than control respondents. Interestingly, attitudes towards avoiding risk behaviour, subjective norms on virginity and responsibility and intention concerning condom use and faithfulness were not significantly different between study groups as the median scores for these variables were very high (6/8 for all variables) in both groups. This could mean that there is a high awareness of the consequences of risky sexual behaviour and an acceptance of protective behaviour in the general population, but that the MYSA members have less difficulty putting these beliefs into practice. Our study attempted to measure and adjust for the potentially confounding effects of differential exposure to media, social capital, and perceptions of body and health. It is possible however, that other, unmeasured confounding factors explain the association between MYSA membership and condom use at first sex and higher frequency of condom use with the current/last partner.

Alternatively, it may be so that the mere fact of becoming a MYSA member, and not the other sexually transmitted infections and was associated with an increased risk of gonococcal and chlamydial infections [START_REF] Ahmed | HIV incidence and sexually transmitted disease prevalence associated with condom use: a population study in Rakai, Uganda[END_REF][START_REF] Katz | Why has HIV stabilized in South Africa, yet not declined further? Age and sexual behavior patterns among youth[END_REF][START_REF] Pettifor | Young people's sexual health in South Africa: HIV prevalence and sexual behaviors from a nationally representative household survey[END_REF]. Our results indicate that the goal of consistent condom use among youth in Mathare is far from reached, and that more is needed to effectively reverse the HIV epidemic.

The financial and human resources available for health care -and HIV prevention in particular -are not unlimited, and it is therefore crucial to prioritise and allocate resources according to the proven or estimated effectiveness of HIV prevention programmes [START_REF] Creese | Cost-effectiveness of HIV/AIDS interventions in Africa: a systematic review of the evidence[END_REF][START_REF] Lasry | Multi-level resource allocation for HIV prevention: A model for developing countries[END_REF][START_REF] Zaric | Optimal investment in a portfolio of HIV prevention programs[END_REF]. A recent meta-analysis that combined results of 28 behavioural interventions for young people in sub-Saharan Africa showed only a significant impact on condom use at last sex among males (risk ratio: 1.46; 95% CI: 1.31-1.64) [START_REF] Michielsen | Effectiveness of HIV-prevention for youth in sub-Saharan Africa: systematic review and meta-analysis of randomised and nonrandomised trials[END_REF]. Next to problems with implementation of interventions, the limited effectiveness might point to problematic underlying assumptions of HIV risk reduction interventions. Even though unprotected intercourse is the main mode of HIV transmission in sub-Saharan Africa, most intervention programmes use a reverse logic and assume that HIV-related knowledge and beliefs are the main determinants of sexual behaviour.

However, many other factors on different levels influence sexual behaviour, including gender inequality, ethnicity, poverty, educational systems, policy and cultural practices [START_REF] Bronfenbrenner | The Ecology of Human Development: Experiments by Nature and Design[END_REF]. effects on the social cohesion and empowerment of its members, thus facilitating a shift towards social norms that foster the adoption of efficacious biomedical interventions [START_REF] Delva | Is scaling up enough to curb the HIV epidemic in southern Africa?[END_REF][START_REF] Kippax | Understanding and integrating the structural and biomedical determinants of HIV infection: a way forward for prevention[END_REF]. Secondly, MYSA may have a risk reducing effect through unmeasured variables: While the number of partners and the level of consistent condom use may stay relatively unchanged, it is possible that MYSA members make safer partnership choices, for instance by choosing partners within their own age group. Further evaluations are needed to explore this hypothesis. Thirdly, evidence which proves that sport-for-development initiatives like MYSA may have many other benefits to the individual and the society, beyond HIV prevention, is steadily increasing [START_REF] Burnett | Building Social Capital Through an 'Active Community Club[END_REF].

Limitations of our survey mainly relate to the study design and validity constraints of self-reported sexual behaviour. Firstly, the survey adopted a cross-sectional study design, making it is difficult to draw causal links between MYSA membership and study outcomes. Given that MYSA's HIV prevention project was established in 1994 random assignment to the intervention and control conditions was impossible. Therefore, we cannot rule out pre-existing differences between the two groups on the outcome variables. The analysis took account of these issues through controlling for possible confounding factors. Secondly, no process evaluation was done. We therefore have no data on how well the programme was implemented on the field. Lastly, reported sexual behaviour might be different from the actual behaviour. However, it can be expected that reporting bias would be equally present in the intervention and the control group.

In conclusion, our study fills a gap in the evidence base for HIV prevention through

  /AIDS Prevention and Awareness Project consists of several components; the main components are the Rotational Facilitation, School Outreach Programme, Movement Games and the Resource Centre. The main facilitators in all of these programmes are MYSA-trained volunteer peer educators and peer counsellors.

Figure 1 .

 1 Figure 1. Path diagram of the Theory of Planned Behaviour[START_REF] Ajzen | Perceived behavioral control, self-efficacy, locus of control, and the theory of planned behavior[END_REF].

  using a self-administered questionnaire of closed-ended questions in English. The questionnaire was based on existing and validated questionnaires and included sections about the demographic profile of the respondents, exposure to MYSA activities, knowledge about HIV/AIDS, attitudes and perceptions towards HIV/AIDS, sexual behaviour, VCT experience, sexual intentions, social capital and perceptions of body and health

  membership, the MYSA activity score was included in a secondary regression analysis to assess the evidence for a significant dose-effect of the project.

Figure 2 .

 2 Figure 2. Exposure to the MYSA HIV/AIDS Prevention and Awareness Project among MYSA members.

  behavioural intentions concerning condom use and remaining faithful to a partner. Vis-à-vis behavioural control concerning condom use, however, MYSA

  use in MYSA members was caused by the MYSA HIV/AIDS

  that we should reconsider investing in MYSA and other sport-based behavioural HIV prevention programmes? Not necessarily. Firstly, social and structural interventions such as the MYSA HIV prevention project may have long-term beneficial

Figure 2 .

 2 Figure 2. Exposure to the MYSA HIV/AIDS Prevention and Awareness Project among MYSA members.

Table 1 .

 1 Socio-demographic characteristics of the respondents.

		All	MYSA	Control
	Age (mean)	16.2	16.1	16.4
	(2-sample t-test: p=0.18)
	Gender (% male)	67.0% (514/767)	73.6% (332/451)	57.6% (182/316)
	(Chi²-test: p<0.001)
	Religion (Chi²-test:
	p=0.15)

Table 2 .

 2 Differences in sexual activity between MYSA respondents and control group.The fraction reporting to have ever had sex was similar in the MYSA (38.6%; 160/414) and control (34.0% (102/300) group (p=0.23). Furthermore, in both groups boys reported more frequently to have had sex than girls. The mean age at sexual debut was 14.4 years for the MYSA group and 15.2 years for the control group (p=0.08). Within the sexually active group of the respondents, no significant differences were found in the number of sexual partners between MYSA members and subjects of the control group (p=0.58).Among the sexually active members of MYSA, 55.8% (87/156) reported to have had no or one sexual partner during the last year, versus 52.0% (52/100) of the subjects in the control group. The percentage of respondents reporting to have ever had concurrent relationships was not significantly different either for MYSA members compared to their counterparts in the control group (p=0.23). Among MYSA respondents however, boys reported concurrent partners more frequently than girls, while the opposite was true in the control group.

		All respondents	MYSA	Control group
	Sexually active (p=0.23)	36.7% (262/714)	38.6% (160/414)	34.0% (102/300)
	Girls (p=0.24)	26.3% (64/243)	22.3% (25/112)	29.8% (39/131)
	Boys (p=0.18)	42.1% (197/468)	44.5% (134/301)	37.7% (63/167)
	Partners in last year* (p=0.58)
	0 partners	13.7% (35/256)	16.0% (25/156)	10.0% (10/100)
	1 partner	41.4% (106/256)	39.7% (62/156)	42.0% (42/100)
	2 partners	18.6% (48/256)	18.6% (29/156)	19.0% (19/100)
	>2 partners	27.0% (69/256)	25.6% (40/156)	29.0% (29/100)
	Concurrent partners* (p=0.23)	27.0% (65/241)	29.6% (42/142)	23.2% (23/99)
	Boys (p=0.29)	27.5% (50/182)	30.3% (37/122)	21.7% (13/60)
	Girl (p=0.79)	25.4% (15/59)	25.0% (5/20)	25.6% (10/39)
	Mean age at sexual debut*
	(p=0.08)	14.7	14.4	15.2
	* among those reporting ever having had sex

Table 3 .

 3 Differences in condom use between MYSA respondents and control group.

		All respondents	MYSA	Control group
	Condom use first sex*	25.5% (61/239)	30.6% (45/147)	17.4% (16/92)
	(p=0.033)
	Condom use last sex*	50.8% (123/242)	56.4% (84/149)	41.9% (39/93)
	(p=0.040)
	Frequency of condom use with
	current/last partner* (p=0.037)
	Always	20.9% (53/254)	23.2% (36/155)	17.2% (17/99)
	Most of the time	15.4% (39/254)	17.4% (27/155)	12.2% (12/99)
	Sometimes	29.1% (74/254)	31.6% (49/155)	25.3% (25/99)
	Never	34.6% (88/254)	27.7% (43/155)	45.5% (45/99)

* among those reporting ever having had sex Significantly more MYSA members (30.6%) reported to have used a condom during the first sexual intercourse compared to respondents from the control group (17.4%)

  95% CI: 1.10-3.99), none of the candidate confounding factors were independently associated with condom use at first sex. For condom use at last sex and frequency of condom use with the current or last partner, we found that the positive effect

	(OR=2.10; of MYSA was reduced after adjusting for exposure to media, rendering it insignificant for
	the former (from the unadjusted OR=1.79; 95% CI: 1.06-3.02 to the adjusted OR=1.56;
	95% CI: 0.90-2.71) and borderline significant for the latter (from the unadjusted
	o F OR=1.86; 95% CI: 1.17-2.98 to the adjusted OR=1.64; 95% CI: 1.01-2.68).
	r
	P
	e e r
	R e v i e w
	O n
	l y
	11

of concurrency and age of sexual debut remained statistically insignificant when adjusted for these candidate confounding factors. Adjusting for the effect of MYSA

Table 1 .

 1 sport. Although the MYSA HIV/AIDS Prevention and Awareness Project may have some positive effects on condom use, it is unlikely to result in a large reduction of the HIV incidence in youth in Mathare. Given a growing interest in HIV prevention through sport programmes, it is important that more rigorous evaluations of sport programmes are When possible, programmes should be preceded by baseline assessments, trends in risk behaviour of the intervention group should be compared to those of a control group, and protocols for data collection and analysis should include measuring of and adjusting for potentially confounding factors. Socio-demographic characteristics of the respondents.

	conducted.
	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	17

Table 2 .

 2 Differences in sexual activity between MYSA respondents and control group.

	All respondents	MYSA	Control group
	Sexually active (p=0.23)
	Girls (p=0.24)
	Boys (p=0.18)

Table 3 .

 3 Differences in condom use between MYSA respondents and control group.Figure 1. Path diagram of the theory of planned behaviour[START_REF] Ajzen | Perceived behavioral control, self-efficacy, locus of control, and the theory of planned behavior[END_REF].

	All respondents	MYSA	Control group
	Condom use first sex*
	(p=0.033)

http://mc.manuscriptcentral.com/ac-phm-vcy Health Sciences

http://mc.manuscriptcentral.com/ac-phm-vcy

Acknowledgements

We are indebted to the research assistants of the Mathare Youth Sport Association for their continued dedication. In addition, we wish to express our sincere thanks to the youth of Mathare that participated in this study.