Abdullah Almasri

Tests for Trend: a Simulation Study

Keywords: Discrete Wavelet Transform, Periodogram, Long Memory Process

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Tests for Trend: a Simulation Study

Introduction

A common issue in time series analysis is the decomposition of the different components of variation. In some applications, it is important to decompose a time series into a low frequency (trend) component, and a high frequency (noise and periodicity) component. The multiresolution analysis is a convenient setting for decomposing and describing the different scales of variation in the data, and the periodogram is a simple way for decomposing the variation into low and high frequencies. It seems natural to turn the attention to other tests which are based on the low frequency part; in wavelet domain as well as in frequency domain. In this study we use the wavelet analysis to construct a test statistic to test for the existence of a trend in the series. We also propose a new approach for testing the presence of trend based on the periodogram of the data. Since we are also interested in the presence of a long-memory process among the data, we study the properties of our test statistics under different degrees of dependency. We compare the results when using the band periodogram test and the wavelet test with results obtained by applying the ordinary least squares (OLS) method under the same conditions. A major problem in practice is the discrimination of an FD(d) process with trend from an FD(d) process without trend, since FD(d) processes for 0 < d < 1 2 usually look like having some trends. This makes it hard to distinguish between these processes. Several authors have considered this problem. [START_REF] Smith | Long-Range Dependence and Global Warming[END_REF] adapts the OLS estimator to test for trend in temperature time series. [START_REF] Deo | Linear Trend with Fractionally Integrated Errors[END_REF] investigate the use of OLS estimators to estimate the linear trend for a time series in the presence of additive LM noise. [START_REF] Künsch | Discrimination between Monotonic Trends and Long-Range Dependence[END_REF] provides a method to discriminate between small monotonic trends and LM processes by examining the distribution of the periodogram. [START_REF] Brillinger | Some River Wavelets[END_REF] and [START_REF] Brillinger | Some Uses of Cumulants in Wavelet Analysis[END_REF] apply the wavelet transform by using the Haar wavelet to provide pointwise confidence intervals for a trend estimation. [START_REF] Craigmile | Wavelet-Based Estimation for Trend Contaminated Long Memory Processes[END_REF] and [START_REF] Almasri | Some Aspects of Wavelet Analysis in Time Series[END_REF] use the Daubechies wavelet filters for testing the trend in the presence of the FD processes. In the present paper we develop tests for trend which are based on on the low frequency part; in wavelet domain as well as in frequency domain. The paper is organised as follows: section 1 gives an introduction. The methodology introduced in section 2, in section 3 we define the trend and trend tests while in section 4 we present a simulation study, and finally, we give a short summary and conclusions in section 5.

Methodology

In this section we will introduced the theory that has been used in this study.

Fractional Difference Processes

The autoregressive fractionally integrated moving average (ARFIMA) processes introduced by [START_REF] Granger | An Introduction to Long-Memory Time Series Models and Fractional Differencing[END_REF] and [START_REF] Hosking | Fractional Differencing[END_REF] are the most widely used class of long-memory models. A process {X t } follows an ARFIMA(p,d,q) process if

Φ(B)(1 -B) d X t = Θ(B) t ,
where { t } are identically independent distributed (i.i.d) with zero mean and σ 2 variance and where

Φ(B) = 1 -φ 1 B -. . . -φ p B p and Θ(B) = 1-θ 1 B -. . .-θ q B q
are polynomials of order p and q in the backshift operator B, i.e., BX t = X t-1 , and d is the difference parameter and is allowed to take fractional values. In this work we study the simplest type of ARFIMA(p,d,q) process, i.e., ARFIMA(0,d,0), which is called the Fractional Difference (FD) process

(1 -B) d X t = t , (1)
and denoted FD(d). When 0 < d < 1 2 the process is called a stationary Long-Memory process (LM). The spectrum has a pole at zero frequency, and the process exhibits slowly decaying auto-covariances. When d = 0 in (1), an FD process becomes a white noise process. When d ≥ 1 2 the process is a non-stationary process. Such process will not be considered further here.

The periodogram

The periodogram was first introduced by Schuster (1898) and was used to search for hidden periodicities and, naturally, it became a tool for testing the presence of periodic components.

Consider a stationary process {Z t } -which we assume has zero mean and absolutely continuous spectral density function (SDF) given by S(f )with autocovariance sequence (acvs) given by s τ , τ = 0, ±1, ±2, . . .. The following relationship between the spectral density and autocovariance sequence holds,

S(f ) = ∞ τ =-∞ s τ e -i2πf τ for f ∈ (- 1 2 , 1 2 ] (2)
This relation holds if the auto-covariance sequence (acvs) s τ is square summable, i.e., if

∞ τ =-∞ s 2 τ < ∞. ( 3
)
For LM processes the acvs is not necessarily a square summable sequence, so that the relation (3) does not always hold.

A naïve estimator of the spectrum is given by the periodogram, in which the autocovariance in (2) is replaced by a biased estimator, The periodogram is hence given by

ŝτ = 1 N N -|τ | t=1 Z t Z t+|τ | , for |τ | ≤ N -1 0, for τ > N -1.
Ŝ(f ) = N -1 τ =-(N -1) ŝτ e -i2πf τ = 1 N N t=1 Z t e -i2πf t 2 , f ∈ (- 1 2 , 1 2 ].
The periodogram is often evaluated at the Fourier frequencies

ϕ k = k/N, k = -N -1 2 , . . . , N 2
, where x is the greatest integer less than or equal to x. The periodogram can be a good approximation to the true spectrum in cases with small spectral range, in other cases it can be an extremely poor estimate of the spectrum. The disadvantages of the periodogram are well documented, readers are referred to Priestley (1981, Ch. 6) and Percival and Walden (1993, Ch. 6). A modification that improves the properties of the periodogram is tapering. Tapering is a common technique to reduce the bias of the periodogram. In this paper we will work with the raw periodogram without taking into account the tapering technique. The technique can however be extended in the future by using such improving techniques.

The band Periodogram

In this section we introduce the band periodogram that has been introduced by [START_REF] Almasri | Some Aspects of Wavelet Analysis in Time Series[END_REF]. This approach can help us in analysing the FD processes. The main idea behind this approach is to divide the Fourier frequencies into different frequency intervals or bands, matching the band-pass of the DWT, i.e. (2 -(j+1) , 2 -j ]. Each band in this case of the FD process might be regarded as a bounded spectrum of a stationary process. We shall now investigate the properties of the spectrum and its estimate at different bands. Before we study the band spectrum and the band periodogram, we have to define the spectral density function (SDF) and the periodogram. For a stationary process {Y t } with a SDF S(f ) that is continuous over the Nyquist range, it can be shown that, subject to the finiteness of certain high order moments,

Ŝ(f ) d = S(f )χ 2 2 /2, for 0 < f < f (N ) S(f )χ 2 1 , for f = 0 or f (N ) (4
Ŝ(f )} = S(f ) 2 , for 0 < f < f (N ) 2S(f ) 2 , for f = 0 or f (N ) (5) cov{ Ŝ(f ), Ŝ(f )} = 0, 0 ≤ f < f < f (N ) , (6)
asymptotically as N → ∞. Hence, for a N large enough the periodogram ordinates at the grid of Fourier frequencies are all approximately pairwise uncorrelated; i.e., cov{

Ŝ(ϕ k ), Ŝ(ϕ l )} ≈ 0, k = l and 0 ≤ k, l ≤ N/2 , ( 7
)
For more details about the spectral analysis, readers are referred to [START_REF] Priestley | Spectral Analysis and Time Series[END_REF] and [START_REF] Percival | Spectral Analysis for Physical Applications[END_REF]. Let us now define the band decomposing of the spectrum of the process {X t } with the following spectrum

S(f ) = J j=1 S j (f ) (8) S j (f ) = S(f )I (2 -(j+1) ,2 -j ] (f ) j = 1, . . . , J -1 S(f )I [0,2 -j ] (f ) j = J (9)
where I [.] is an indicator function, the first part in the right of ( 9) collectively represents the high-frequency spectrum S H (f ) and the second part represents the low-frequency spectrum S L (f ).

The basic estimator of S(.) is the periodogram and in the same way we define the band decomposition of the periodogram

Ŝj (f ) = Ŝ(f )I [2 -(j+1) ,2 -j ] (f ) j = 1, . . . , J -1 Ŝ(f )I [0,2 -j ] (f ) j = J (10)
We call the first part of (10) the high-frequency band periodogram ŜH (f ) =

J-1 j=1 Ŝj (f ) and the second part the low-frequency band periodogram ŜL (f ).

The Discrete Wavelet Transform

The key idea of the discrete wavelet transform (DWT) is to decompose a series orthogonally into different new series. Let X = (X 0 , . . . , X N -1 ) be a data vector of length N, where we assume that N is an integer divisible by 2 J , where J is a positive integer. The wavelet and scaling filters are used in parallel to define the DWT i.e., we have two types of coefficients in the DWT based on these two types of filter: the scaling coefficients and the wavelet coefficients. The pyramid algorithm, introduced by [START_REF] Mallat | A Theory for Multiresolution Signal Decomposition: The wavelet Representation[END_REF], uses linear filtering operations. The first stage of the pyramid algorithm for computing DWT consists of transforming the time series X into the N/2 first level scaling coefficients and the N/2 first level wavelet coefficients. There are J -1 subsequent stages of the pyramid algorithm. The scaling coefficients for level j (j = 1, . . . , J) are given by

V j,k = L-1 l=0 g l V j-1,2k+1-l mod N j-1 for k = 0, . . . , N j -1, (11)
and the wavelet coefficients for level j are given by

W j,k = L-1 l=0 h l V j-1,2k+1-l mod N j-1 for k = 0, . . . , N j -1, (12)
where g l is the scaling filter, h l is the wavelet filter, V 0 ≡ X and N j ≡ N2 -j . The modulus operator in ( 11) and ( 12) is required in order to deal with the boundary of a finite length vector of observations. This operator circularly filters the data, by using a fast filtering algorithm of order O(N). We see from ( 12) and ( 11) that at each step we filter the previous level scaling coefficients using either the scaling or wavelet filter, and then subsample the resulting sequence. The DWT can be defined also by matrix calculation. Let W j ≡ [W j,0 , W j,1 , . . . , W j,N j -1 ] T , j = 1, 2, . . . , J, and

V J ≡ [V J,0 , V J,1 , . . . , V J,N J -1 ] T .
The elements of the subvectors W j correspond to that in (12) and the subvector V J correspond to that in (11). We then have the analysis equation where W contains the DWT coefficients, i.e.,

W = WX,
W = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ W 1 W 2 . . . W j . . . W J V J ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
, and W is an orthonormal N × N real-valued matrix whose rows depend on the wavelet filter h l , i.e., W -1 =W T , so W T W = WW T = I N , see [START_REF] Percival | Wavelet Methods for Time Series Analysis[END_REF]. We can reconstruct our time series from the wavelet coefficients W by using

X = W T W.
We partition the columns of W commensurate with the partitioning of W to obtain

W T = [W 1 W 2 . . . W j . . . W J V J ],
where W j is an N × N/2 j matrix and V J is an N × N/2 J matrix. Now, we can define the multiresolution analysis of a series by expressing W T W as a sum of several new series, each of which is related to variations in X at a certain scale:

X = W T W = J j=1 W j W j + V J V J = J j=1 D j + S J . ( 13
)
The terms in (13) constitute a decomposition of X into orthogonal series components D j (detail) and S J (smooth) at different scales and the length of D j and S J coincides with the length of X (N × 1 vector). Because the terms at different scales represent components of X at different resolutions the approximation is called multiresolution decomposition. [START_REF] Daubechies | Ten Lectures on Wavelets[END_REF] introduces two types of wavelets, the extremal phase D(L) and the least asymmetric LA(L). The difference between them lies only in their phase functions, i.e., θ (G) (.) in the polar representation The Haar wavelet or D(2), is a filter of width L=2, that can be defined through its wavelet filter,

G(f ) = [G (D) (f )] 1/2 e iθ (G) (f ).
h 0 = 1 √ 2 and h 1 = -1 √ 2 ,
or, equivalently, through its scaling filter,

g 0 = g 1 = 1 √ 2 .
The scaling coefficients for the LA(8) and other Daubechies wavelets are given in [START_REF] Daubechies | Ten Lectures on Wavelets[END_REF].

Trend

We describe the trend here as a long term change in the underlying mean level per unit time. For example, recent concerns about the possibility of climate change have focused attention on temperature series. A crucial question raised by these data is whether the temperature rise of around 0.5 • C could be interpreted as a trend over the last hundred years, see [START_REF] Bloomfield | Climate Spectra and Detecting Climate Change[END_REF]. This trend can be a start of a systematic warming, or an effect of natural variability. The most difficult problem when testing for linear trend is the presence of dependence among the residuals. Because the residuals are dependent, the tests for trend based on the classical OLS regression will be inappropriate. A plausible statistical model for temperature series can consist of a mean level, a possible trend plus a noise term which can be a FD process. However, there are different models for describing various forms of trend, both linear and non-linear, and both stochastic and deterministic.

In this work we will study only the model that represents the time series by using a pth-order polynomial function, that is

T t = β 0 + β 1 t + β 2 t 2 + . . . + β p t p .
When p = 0, there is no long-run increase or decline in the time series over time, and p = 1, implies that there is a straight-line long-run growth (if β 1 > 0) or decline (if β 1 < 0) over time. These simple linear trends are often called a deterministic linear trends.

Trend tests

In this section we will provide three methods for testing the trend:

• the OLS test,

• the wavelet based test and,

• the band periodogram based test. [START_REF] Yajima | On Estimating of a Regression Model with Long-Memory Stationary Errors[END_REF] considered a polynomial regression consisting of a polynomial trend with p = 1 and a stationary process with long memory. Based on that we consider the following model

Z t = T t + X t = a + βt + X t for t = 0, . . . N -1, (14)
where X t is a FD(d) process.

Ordinary least squares method for testing the trend

In this method we attempt to estimate the parameter β by using the OLS method, i.e. by regressing Z t on t in ( 14), and we consider the following two cases: Case 1: d = 0. That is, the X t is a zero mean white noise process of constant variance σ 2 X . It is well known that the least squares estimator of β in this case is given by

β = N -1 t=0 (t -t)Z t N -1 t=0 (t -t) 2 with standard error se( β) = σ 2 X N -1 t=0 (t -t) 2
In this case and under the null hypothesis H 0 that β = 0 (against the alternative hypothesis H 1 that β = 0), we consider the following test statistic which approximately follows the N(0, 1) distribution. Case 2: 0 < d < 1 2 . [START_REF] Yajima | On Estimating of a Regression Model with Long-Memory Stationary Errors[END_REF] has shown that, for 0 < d < 1 2 , the estimator β is inefficient. By normalising the above estimate β by N d , we get the same convergence as for Case 1, see [START_REF] Beran | Statistics for Long-Memory Processes[END_REF] and [START_REF] Craigmile | Wavelet-Based Estimation for Trend Contaminated Long Memory Processes[END_REF]. In Section 4 we will calculate corrected critical values for the LS test for different d's via a Monte Carlo method.

LS ≡ β se( β) , ( 15

A wavelet-based test for testing the trend

We investigate here the wavelet-based approach for testing the trend. In section 2 we introduced the DWT coefficients and we have seen that these can be divided into two different types: scaling coefficients V and wavelet coefficients W . Percival and Bruce (1998) and [START_REF] Craigmile | Wavelet-Based Estimation for Trend Contaminated Long Memory Processes[END_REF] have shown the ability of the Daubechies wavelet filters to identify trend contaminated FD processes due to of the inherent differencing operations in the filters. This property implies that a Daubechies wavelet filter can transform a FD process of order L/2 or less into • a stationary process, i.e., a process with a lower dependency than the original data series, or

• can annihilate a polynomial of order less than L/2.

This result only applies to the non-boundary coefficients.

Thus we can rewrite ( 14) in terms of the inverse wavelet and scaling coefficients as

Z = S J + J j=1 D j , ( 16
)
where S J represents the trend and J j=1 D j represents the residuals. The above form is valid only for the Haar wavelet since there are no boundary coefficients in the Haar wavelet. [START_REF] Craigmile | Wavelet-Based Estimation for Trend Contaminated Long Memory Processes[END_REF] has generalised (16) for where W BD is the non-boundary coefficients matrix, T captures the trend and X represents the residuals. For more details about the statistical properties of the trend estimate, see [START_REF] Craigmile | Wavelet-Based Estimation for Trend Contaminated Long Memory Processes[END_REF]. The idea of the wavelet based test for trend is simple. We would like to test the null hypothesis H 0 : T t = 0 t = 0, . . . , N -1.

L > 2. If W = W BD W + W S W + W BI W , then we can write Z = W T W = W T (W BD + W S )W + W T W BI W
(17) [START_REF] Craigmile | Wavelet-Based Estimation for Trend Contaminated Long Memory Processes[END_REF] presented a test statistics for discriminating between this null hypothesis and the alternative hypothesis

H 1 : T t = 0 for some t = 0, . . . , N -1. ( 18
)
The test statistic is defined by

W T = V 2 + W BD 2 W BI 2 . ( 19
)
Almasri ( 2000) introduced a test statistic for discriminating between the null hypothesis ( 17) and the alternative hypothesis ( 18) in the same way as in ( 19), but by taking into account all the wavelet and scaling coefficients. An alternative test statistic introduced by [START_REF] Craigmile | Wavelet-Based Estimation for Trend Contaminated Long Memory Processes[END_REF] and is given by

W T * = Z -Z 2 W BI 2 . ( 20
)
In each case the null hypothesis is rejected for large values of the test statistics.

A band-periodogram test for trend

In this section we will describe tests which based on the periodogram to assess the significance of trend in the FD processes. Time series analysts often identify periodicities and trends in the spectral density of a time series. As we have seen in section 2, we can partition the periodogram into two parts, the high frequency part ŜH (.) (identifies periodicities) and the low frequency part ŜL (.) (identifies trends). These two parts can help us build new tests for the trend. To illustrate the impact of the trend on the periodogram of the FD(d) process, Figure In each case we have a sample length of N = 64. We note that the trend has the strongest effect on the low frequency part of the periodogram only.

The idea of the tests is simple. We want to know whether the contribution of the low frequency part of the periodogram to the high frequency part is significant. Under the null (17) we expect that the contribution of the low frequency part to the high frequency part is negligible. Hence we propose the test statistic

BT = ŜL (f ) ŜH (f ) = N/2 J q=1 Ŝ(f q ) J-1 j=1 m i=N/2 j+1 Ŝ(f i ) , ( 21
)
where N = 2m + 1 if N odd and N = 2m + 2 if N even. We reject the null for large values of BT . In a similar manner as in Section 3.3, we propose a test to examine the existence of a trend. Define

BT * = N -1 t=0 (Z t -Z) 2 J-1 j=1 m i=N/2 j+1 Ŝ(f i ) . ( 22
)
When d = 0, the test statistic ( 21) has approximately an F distribution since the numerator and the denominator are independent and follow approximately χ 2 distributions.

The size and the power of the tests

This section describes the results of a Monte Carlo study designed to assess the size and the power properties of the tests described in the previous section. We calculate the corrected critical values for the LS test for different d (LS * ) by using a Monte Carlo simulation study. The critical values for the BT , BT * and W T have also been obtained by simulation. [START_REF] Almasri | Some Aspects of Wavelet Analysis in Time Series[END_REF]

Empirical size

Here we present our main results along with results of our Monte Carlo experiment regarding the dominating effects on the size of the above tests. We calculate the estimated size by observing how many times the null is rejected in repeated samples under conditions where the null is true, which called for type 1 error. We simulate 10000 FD(d) processes with no trend (using different seed than the critical values simulation), and calculate how many times the null is rejected where the null is true. Table 2 gives the results of the size for the LS * , BT , BT * and W T , where J = 8 and by using Haar wavelet for the W T test. The results have shown that the tests performs well as regarding the size when using the simulated critical values in Table 2

Empirical power

In this sub-section we discuss the most interesting results of our Monte Carlo experiment, regarding the power of the above tests which means the rejection of the null when null is false. The power results are estimated by calculating rejection frequencies from 1000 replication for different trend parameters (β), different d and N = 1024, where J = 8 and by using LA(8) wavelet for the W T * and Haar wavelet for the W T , see Figure 2 and Figure 3. We can see from Figure 2 that the power of the W T (using LA(8) wavelet) and BT is less than that of the LS test, when d = 0 and d = 0.2. The W T performs better than LS and BT when d = 0.4 and d = 0.49. However, the BT performs reasonably well when d = 0.49, but is quite a bit less than W T . Figure 3 shows that the LS * performs better than other tests for d = 0, d = 0.20 and d = 0.40. We can also see that the BT * performs better than W T * (using Haar wavelet). In summary, the LS * and LS tests perform better when the FD parameter is smaller, and the wavelet based tests and the band periodogram based tests are more better as d approximate 1 2 .

F

6

  Page 7 of 19 URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.

  (1) shows a periodogram for two FD(d) processes with (boxestrend (circles) and when d = 0 and d = 0.4, respectively.

Figure 1 :

 1 Figure 1: (a) The periodogram for a realisation when d = 0, 2 with trend (b = 1/64) and • without trend. (b) The periodogram for a realisation when d = 0.4, 2 with trend (b = 1/64) and • without trend.

Figure 2 :Figure 3 :

 23 Figure 2: Figures show a comparison of the power of the test for trend for various slopes and a d. The sample size used was 1024, with a DWT using the LA(8) filter based on the Craigmile's critical values and analysing to J = 8 levels.

  we introduced two tests for testing the trend in LM processes, based on the wavelet and band periodogram. These tests have been compared with the OLS based test. The results have shown that the LS * and LS tests perform better when the FD parameter is smaller, and the wavelet based tests and the band periodogram based tests are much better as d approximate 1 2 .

) 4 Page 5 of 19 URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.ca Communications in Statistics -Simulation and Computation

	F o
	r
	P
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asymptotically as N → ∞. Furthermore, Ŝ(f ) and Ŝ(f ) are asymptotically independent. We thus have var{

mcmaster.ca Communications in Statistics -Simulation and Computation

  obtaines the critical values for the W T but by taking into account the boundary coefficients. For the W T * test we use the critical values that have been listed inCraigmile (2000, page 108). For the LS * , BT , BT * and W T tests we obtain the critical values by simulation. We simulate a 10000 of FD(d) processes with no trend, and calculated the resulting test statistic for the LS * , BT , BT * and W T . The length of the series is 1024. Table1lists the upper quantiles of the distribution of the LS * , BT , BT * and W T

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13 Page 14 of 19 URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.ca Communications in Statistics -Simulation and Computation

	test d	p=0.90 p=0.95 p=0.99
	BT 0	0.0109 0.0133 0.0178
	0.20 0.1076 0.1405 0.1961
	0.40 2.0942 2.8262 4.3252
	BT * 0	2.0176 2.0214 2.0304
	0.20 2.0975 2.1218 2.1648
	0.40 2.5310 2.6763 2.9604
	W T 0	0.013	0.014	0.019
	0.20 0.087	0.105	0.136
	0.40 1.183 LS * 0 1.282 0.20 4.749 o F 0.40 25.621 32.852 46.202 1.559 2.329 1.645 2.326 6.184 8.715
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Table 1 :

 1 Table of the 90th, 95th and 99th quantiles of the BT , BT * , W T and LS * , tests for various values d. The evaluation of the distribution was based on 10000 simulations of a FD process using a DH algorithm. for different d, where J = 8 using Haar wavelet. As we can see from the table that the critical values of the tests increases with d.

. 14 Page 15 of 19 URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.ca Communications in Statistics -Simulation and Computation

	test d	p=0.10 p=0.05 p=0.01
	BT 0	0.101	0.052	0.014
	0.20 0.104	0.050	0.017
	0.40 0.094	0.049	0.012
	BT * 0	0.113	0.055	0.010
	0.20 0.112	0.053	0.015
	0.40 0.121	0.056	0.013
	W T 0	0.109	0.067	0.012
	0.20 0.125	0.063	0.020
	0.40 0.100 LS * 0 0.084 0.20 0.010 o F 0.40 0.097	0.053 0.0516 0.052 0.049	0.014 0.011 0.010 0.011
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Table 2 :

 2 Empirical sizes for BT , BT

* , W T and LS * .

URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.caCommunications in Statistics -Simulation and Computation


MD Manuele ; Furnari

MD Andrea Parodi

MD Lorenzo Gemignani

PhD Edoardo G Giannini

MD Simona Marenco

MD Edoardo Savarino

MD Lorenzo Assandri

MD Valentina Fazio

MD Daria Bonfanti

MD Simona Inferrera

MD Vincenzo Savarino

The Association Between Rifaximin And Partially Hydrolyzed Guar Gum Is More Effective Than Rifaximin Alone In Eradicating SIBO

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

Abnormal intestinal clearance is involved in the pathogenesis of small intestinal bacterial overgrowth (SIBO). It is known that partially hydrolyzed Guar gum (PHGG) affects intestinal motility. Eradication therapy of SIBO is based on antibiotic treatment: no data are available about the role of fibers supplementation in eradicating SIBO.

Aims:

To assess whether the association between PHGG plus rifaximin is more effective than rifaximin alone in the treatment of SIBO. Methods: 50g-glucose breath test (GBT) was given to 500 consecutive patients. Patients with positive GBT and predisposing conditions to SIBO entered into the study, and were randomized to receive rifaximin 1200mg/die or rifaximin 1200mg/die plus PHGG 5g/die for 10 days. Patients completed a symptom questionnaire and GBT both in basal condition and 1 month after withdrawal of therapy.

Results:

Seventy-seven patients had SIBO. SIBO eradication rate was 62.1% in the rifaximin group (both on per-protocol and intention-to-treat analyses), and 87.1% (per-protocol, p=0.017) and 85.0% (intention-to-treat, p=0.036) in the rifaximin-plus-PHGG group. Clinical improvement was observed in 86.9% and 91.1% of eradicated cases in rifaximin and rifaximin-plus-PHGG groups, respectively (p=0.677).

Conclusion:

The association between rifaximin and PHGG seems to be more useful in eradicating SIBO compared to rifaximin alone.

INTRODUCTION

Small intestinal bacterial overgrowth (SIBO) is a condition mainly characterized by diarrhoea, bloating, flatulence and abdominal pain due to an abnormal amount of bacteria in the small intestine [START_REF] Husebye | The pathogenesis of gastrointestinal bacterial overgrowth[END_REF][START_REF] Gregg | Enteric bacterial flora and bacterial overgrowth syndrome[END_REF][START_REF] Sherman | Small bowel bacterial overgrowth syndrome[END_REF][START_REF] Bouhnik | Bacterial populations contaminating the upper gut in patients with small intestinal bacterial overgrowth syndrome[END_REF]. Gastric acid production, anatomical integrity of intestinal wall and peristaltic motility are main factors in preserving the fine equilibrium between host and bacteria.

Therefore, predisposing conditions that alter the above mentioned mechanisms could heighten the number of bacteria in the small intestine and lead to the development of this syndrome.

Furthermore, it has been proposed that gut microflora could play a role in the modulation of some inflammatory diseases. This was suggested by the higher incidence of SIBO among patients with Rheumatoid Arthritis [START_REF] Henriksson | Small intestinal bacterial overgrowth in patients with rheumatoid arthritis[END_REF] and Non Alcoholic Steatohepatitis [START_REF] Drenick | Hepatic steatosis after intestinal bypass-prevention and reversal metronidazole, irrespective of protein-calorie malnutrition[END_REF] and by improvement of Rosacea after eradicating SIBO [START_REF] Parodi | Small intestinal bacterial overgrowth in rosacea: clinical effectiveness of its eradication[END_REF]. Although severe forms presenting remarkable malabsorption can be seen occasionally, the majority of clinical manifestations of SIBO are generally mild and make it hardly distinguishable from other conditions such as Irritable Bowel Syndrome (IBS) or Lactose Intolerance. This difficulty is clearly underlined by the heterogeneous results of several studies that reported IBS comorbidity with SIBO ranging widely from 10% to 80% [START_REF] Lin | Small intestinal bacterial overgrowth: a framework for understanding irritable bowel syndrome[END_REF][START_REF] Parodi | Positive glucose breath testing is more prevalent in patients with IBS-like symptoms compared with controls of similar age and gender distribution[END_REF][START_REF] Pimentel | The effect of nonabsorbed oral antibiotic (rifaximin) on the symptoms of the irritable bowel syndrome: a randomized trial[END_REF][START_REF] Posserud | Small intestinal bacterial overgrowth in patients with irritable bowel syndrome[END_REF][START_REF] Ford | Small intestinal bacterial overgrowth in irritable bowel syndrome: systemic review and meta-analysis[END_REF][START_REF] Grover | Small intestinal bacterial overgrowth in irritable bowel syndrome: association with colon motility, bowel symptoms, and psychological distress[END_REF].

The presence of at least 10⁵ cfu/ml in jejunal aspirate culture is considered the gold standard test to diagnose SIBO, especially when colonic-type bacteria are isolated [START_REF] Husebye | The pathogenesis of gastrointestinal bacterial overgrowth[END_REF][START_REF] Gregg | Enteric bacterial flora and bacterial overgrowth syndrome[END_REF][START_REF] Sherman | Small bowel bacterial overgrowth syndrome[END_REF][START_REF] Bouhnik | Bacterial populations contaminating the upper gut in patients with small intestinal bacterial overgrowth syndrome[END_REF][START_REF] Corazza | The diagnosis of small bowel bacterial overgrowth. Reliability of jejunal culture and inadequacy of breath hydrogen testing[END_REF]. However, hydrogen breath tests are commonly used in clinical practice, being more acceptable to patients and giving quicker information to the clinician [START_REF] Peralta | Small intestine bacterial overgrowth and irritable bowel syndrome-related symptoms: experience with rifaximin[END_REF]. Among them, Glucose Breath Test (GBT) has proved to have the highest accuracy in diagnosing SIBO [START_REF] Corazza | The diagnosis of small bowel bacterial overgrowth. Reliability of jejunal culture and inadequacy of breath hydrogen testing[END_REF][START_REF] Parodi | H2-breath testing for small-intestinal bacterial overgrowth[END_REF]. Once the bacterial overgrowth is diagnosed it can be successfully treated by locally active non absorbable antibiotics. Various studies have shown that rifaximin is successful in eradicating SIBO with no or minimal side effects when compared to systemic antibiotics [START_REF] Parodi | Small intestinal bacterial overgrowth in rosacea: clinical effectiveness of its eradication[END_REF][START_REF] Peralta | Small intestine bacterial overgrowth and irritable bowel syndrome-related symptoms: experience with rifaximin[END_REF][START_REF] Majewski | Efficacy of rifaximin, a nonabsorbed oral antiobiotic, in the treatment of small intestinal bacterial overgrowth[END_REF][START_REF] Lauritano | Rifaximin dose finding study for the treatment of small intestinal bacterial overgrowth[END_REF][START_REF] Scarpellini | High dosage rifaximin for the treatment of small intestinal bacterial overgrowth[END_REF][START_REF] Pimentel | Review of rifaximin as treatment for SIBO and IBS[END_REF][START_REF] Parodi | Small intestinal bacterial overgrowth in patients suffering from scleroderma: clinical effectiveness of its eradication[END_REF]. Of the predisposing conditions involved in SIBO pathogenesis, hypomotility seems to play a relevant role by impairing intestinal clearance and, as a consequence, the intestinal bacteria distribution [START_REF] Parodi | Small intestinal bacterial overgrowth in patients suffering from scleroderma: clinical effectiveness of its eradication[END_REF][START_REF]Bacterial overgrowth[END_REF][START_REF] Resmini | Evidence of prolonged orocecal transit time and small intestinal bacterial overgrowth in acromegalic patients[END_REF][START_REF] Lauritano | Association between hypothyroidsm ans small intestinal bacterial overgrowth[END_REF]. Thus, we have hypothesized that adding a prebiotic such as partially hydrolyzed guar gum (PHGG) to rifaximin can be of help in the decontamination of small bowel. In fact, it can have a beneficial effect on intestinal motility and therefore, a synergic interaction between rifaximin and PHGG may lead to a higher eradication rate of SIBO. The primary end point of our study was to assess whether the association of rifaximin and PHGG was more effective than rifaximin alone in eradicating SIBO, while the secondary end point was to evaluate whether the combined treatment allowed to obtain a greater symptomatic improvement than rifaximin alone.

MATERIALS AND METHODS

Patients

From May 2007 to March 2010, 500 consecutive patients were referred to our centre to perform GBT because of gastrointestinal symptoms, such as modification in stool frequency, abdominal pain, bloating, flatulence, tenesmus, nausea and vomiting. In these subjects, the predisposing conditions for SIBO were: impaired intestinal motility due to medications (i.e. antidepressant drugs) (n=20), hypothyroidism (n=5), diabetes mellitus (n=4), Scleroderma (n=1), and Crohn's Disease (n=3); acquired anatomical conditions such as resection of the ileum-cecal valve (n=3) or partial gastrectomy (n=1), adhesions due to major abdominal surgery (n=2). Also Rosacea (n=5), Non Alcoholic Steatohepatitis (n=4) and Rheumatoid Arthritis (n=1) were considered as disorders related to SIBO. Patients that underwent a previous treatment for SIBO and patients with basal H₂ sample >10ppm were excluded from the study. Moreover, patients had to take neither antibiotic or Proton Pump Inhibitors (PPI), nor pre or probiotics for at least 10 days before the examination. Among these, we evaluated 390 patients who had both performed GBT and answered our questionnaire based on gastrointestinal symptom. In this investigation, we included the 77 patients (male/female: 15/62; mean Age 54; range 26-84 years) who had a positive GBT. These patients were randomized, by using a computer generated random list, to receive rifaximin 1200mg daily for 10 days or rifaximin 1200mg daily plus PHGG 5g/die for 10 days. All patients completed the questionnaire both in basal condition and 1 month after therapy. Adverse events were investigated during and 1 month after the end of treatment. Eradication of SIBO was assessed 1 month later after the end of treatment by a further GBT. The study was evaluated and approved by our Institutional Review Board.

Glucose Breath Test

The evening before GBT patients followed a diet containing boiled rice, meat and water alone.

Then they fasted until the end of the test. Glucose was given in a dose of 50 g dissolved in 250ml of water. Breath hydrogen concentration, in parts per million (ppm), was measured by gas-chromatography (Quintron MicroLizer model DP plus, Milwaukee, USA) on samples of end expiratory air collected every 15 minutes for 2 hours. A basal sample was taken before glucose intake. Patients were asked to avoid cigarette smoking, food intake and physical exercise during test. A single peak of hydrogen excretion higher than 12 ppm was the cut-off value for test positivity.

Questionnaire

All patients completed an interview questionnaire, according to previous studies performed by our group [7,9,21] and by other Authors [START_REF] Latella | Rifaximin improbe symptoms of acquired uncomplicated diverticular disease of the colon[END_REF][START_REF] Papi | Efficacy of rifaximin in the treatment of symptomatic diverticular disease of the colon. A multicentre double-blind placebo controlled trial[END_REF][START_REF] Mario | Efficacy of mesalaxine in the treatment of symptomatic diverticular disease[END_REF], based on 10 variables (diarrhea, upper and lower abdominal pain/discomfort, bloating, flatulence, abdominal tenderness, weight loss, nausea, constipation, and tenesmus) scored from 0 (no symptoms) to 3 (severe), providing a global symptomatic score (GSS), calculated as the sum of all symptom scores, with a range from 0 to 30. A decrease of 50% in global symptomatic score after the end of therapy was arbitrarily considered as a significant improvement of symptoms, in agreement with other studies carried out by our group on this topic [START_REF] Parodi | Small intestinal bacterial overgrowth in rosacea: clinical effectiveness of its eradication[END_REF][START_REF] Parodi | Positive glucose breath testing is more prevalent in patients with IBS-like symptoms compared with controls of similar age and gender distribution[END_REF][START_REF] Parodi | Small intestinal bacterial overgrowth in patients suffering from scleroderma: clinical effectiveness of its eradication[END_REF].

Statistical analysis

Data are shown as mean values, ranges and rates. Data were assessed on both per-protocol (PP) and intention-to-treat (ITT) analyses. Fisher's exact test was used to evaluate if the difference between the two groups was statistically significant in terms of both SIBO eradication rates and symptomatic relief. A p value <0.05 in a two-tailed test was considered significant. Statistical analysis was performed with GraphPad Software, QuickCalcs [San Diego, CA, USA], and with GNU Software, PSPP [Boston, MA, USA].

RESULTS

Table 1 shows the main demographic and clinical characteristics of the study population subdivided according to treatment received. There were no statistically differences between the two groups. Overall, eradication of SIBO was achieved in 57/77 patients (74.0%). In particular, SIBO eradication was obtained in 23/37 patients (62.1%; both PP and ITT analysis) treated with rifaximin alone, and in 34/39 (87.1%; PP) and 34/40 (85.0%; ITT) patients treated with rifaximin plus PHGG. SIBO eradication rates were significantly different between the two treatment arms on both PP (p=0.017; OR=0.241; 0.075, 0.781) and ITT (p=0.036; OR 0.289; 0.095, 0.884) analyses. No serious adverse events were reported during treatment.

DISCUSSION

In patients diagnosed with SIBO, a broad-spectrum antibiotic therapy is recommended in order to obtain eradication of intestinal bacterial overgrowth. Rifaximin is a locally active non absorbable antibiotic whose efficacy in eradicating SIBO has been demonstrated by several studies [START_REF] Parodi | Small intestinal bacterial overgrowth in rosacea: clinical effectiveness of its eradication[END_REF][START_REF] Peralta | Small intestine bacterial overgrowth and irritable bowel syndrome-related symptoms: experience with rifaximin[END_REF][START_REF] Majewski | Efficacy of rifaximin, a nonabsorbed oral antiobiotic, in the treatment of small intestinal bacterial overgrowth[END_REF][START_REF] Lauritano | Rifaximin dose finding study for the treatment of small intestinal bacterial overgrowth[END_REF][START_REF] Scarpellini | High dosage rifaximin for the treatment of small intestinal bacterial overgrowth[END_REF][START_REF] Pimentel | Review of rifaximin as treatment for SIBO and IBS[END_REF][START_REF] Parodi | Small intestinal bacterial overgrowth in patients suffering from scleroderma: clinical effectiveness of its eradication[END_REF]. Its use is often preferred to other antibiotics such as levofloxacin and metronidazole because of its topical action and absence of adverse events [START_REF] Lauritano | Antibiotic therapy in small intestinal bacterial overgrowth: rifaximin versus metronidazole[END_REF]. In this study, we aimed at evaluating whether adding PHGG to rifaximin was able to increase SIBO eradication rate. Our hypothesis was based on the fact that antibiotics act only on intestinal bacteria, but do not solve the conditions predisposing to SIBO. On the other hand, impaired intestinal motility, by decreasing intestinal clearance, might promote the development of unfavourable habitat for physiologic gut microflora and the invasion of small bowel lumen by colonic bacteria.

Our results show that the association of PHGG and rifaximin was significantly more effective than rifaximin alone in the eradication of SIBO. Thus, this association reached an eradication rate of 87.1%, resulting significantly higher than rifaximin alone (62.1%). This finding suggests that fiber supplementation positively interacts with rifaximin in SIBO treatment.

Several studies have shown a beneficial effect on intestinal motility by use of alimentary fibers [START_REF] Muller-Lissner | Effect of wheat bran on weight of stool and gastrointestinal transit time: a meta-analysis[END_REF]. In fact, alimentary fibers increase fecal mass and transit time, easing defecation.

They could be generally distinguished into two categories. Unsoluble fiber is minimally modified in the intestinal lumen and mechanically increases fecal mass by retaining water, thus decreasing transit time and improving defecation. Otherwise, soluble fiber is metabolized in the large bowel, thus producing short chain fatty acids and leading to selective stimulation of microbial growth which influences secondarily bowel functions [START_REF] Stephen | Mechanism of action of dietary fibre in the human colon[END_REF]. This is an important distinction because several studies conducted on IBS populations have shown that the global amelioration of IBS symptoms is mainly associated with the use of soluble fibers rather than with the insoluble ones. It was also found that insoluble fiber was no better than placebo at improving IBS and, rather surprisingly, that a large amount of insoluble fiber may worsen IBSrelated symptoms [START_REF] Bijkerk | Systematic review: the role of different types of fibre in the treatment of irritable bowel syndrome[END_REF][START_REF] Francis | Bran and irritable bowel syndrome: time for a reappraisal[END_REF]. In this study we used PHGG, a vegetable, water-soluble, dietary fiber that is derived from guar gum with a lower molecular weight than the original guar gum, whose safety has been largely proved [START_REF] Lina | Sub-chronic (13 week) oral toxicity study with Sunfiber and Sunfiber ST in rats[END_REF][START_REF] Takahashi | Effect of partially hydrolyzed guar gum on fecal output in human volunteers[END_REF][START_REF] Giaccari | Gomma guar parzialmente idrolizzata: una fibra come coadiuvante nella sindrome del colon irritabile[END_REF]. Noteworthy, PHGG increases fecal acetate content and the colonic concentration of Lactobacilli and Bifidobacteria thus providing an important prebiotic action [START_REF] Giannini | Role of partially hydrolyzed guar gum in the treatment of irritable bowel syndrome[END_REF][START_REF] Takahashi | Influence of partially hydrolyzed guar gum on constipation in women[END_REF][START_REF] Tuohy | The prebiotic effects of biscuits containing partially hydrolyzed guar gum and fructo-oligosaccharides-a human volunteer study[END_REF][START_REF] Gibson | Dietary modulation of the human colonic microfloraintroducing the concept of prebiotics[END_REF][START_REF] Weaver | Dietary guar gum alters colonic microbial fermentation in azoxymethane-treated rats[END_REF][START_REF] Okubo | Effects of partially hydrolyzed guar gum intake on human intestinal microflora and its metabolism[END_REF]. As PHGG is not used by these bacteria in vitro, it has been proposed that PHGG is degraded in human colon providing substrates that favour the selective growth of Bifidobacteria and Lactobacilli [START_REF] Okubo | Effects of partially hydrolyzed guar gum intake on human intestinal microflora and its metabolism[END_REF]. This is an important mechanism because it is proved that loss of anaerobes is associated with a depletion in short chain fatty acids and an increase in stool pH, allowing overgrowth of other bacteria which may contribute to altering intestinal function [START_REF] Lupp | Host-mediated inflammation disrupts the intestinal microbiota and promotes the overgrowth of Enterobacteriaceae[END_REF]. Moreover, acetate is one of the most important energy resources for colonocytes and is necessary to sustain colonic epithelial cell proliferation [START_REF] Philips | Physiology and pathophysiology of the colon: relationship to constipation[END_REF]. These factors are useful to preserve the mucosal integrity and to support its repairing process and, when altered, could lead to develop SIBO.

GBT and Lactulose Breath Test (LBT) are the most commonly utilized tests for SIBO. Although there is no universal agreement about which test should be performed to diagnose SIBO, in our study we used GBT because it is easier to interpret and more accurate in diagnosing SIBO than LBT [START_REF] Corazza | The diagnosis of small bowel bacterial overgrowth. Reliability of jejunal culture and inadequacy of breath hydrogen testing[END_REF]. This has been recently confirmed by the 1 st Rome Consensus Conference that reported higher diagnostic accuracy for GBT with respect to LBT (71% vs 55%) [START_REF] Parodi | H2-breath testing for small-intestinal bacterial overgrowth[END_REF]. In fact, glucose is highly absorbed in the proximal small bowel and rarely reaches the colon, showing a single "early" H₂ peak in case of SIBO. On the other hand, lactulose passes unabsorbed through the small bowel and reaches the large bowel where it is metabolized by colonic bacteria. Thus, lactulose investigates bacterial fermentation through the whole gut and can also be used as a measure of orocaecal transit. Nevertheless, being a non-absorbable carbohydrate, lactulose itself can accelerate small bowel transit that is a condition in which the "early" peak can merge with the late "colonic" peak, thus making impossible to distinguish SIBO from colonic fermentation. Moreover, different portions of the given substrate might reach the colon at different times, thus causing two or more peaks in H₂ excretion that simulate SIBO [START_REF] Riordan | The lactulose breath hydrogen test and small intestinal bacterial overgrowth[END_REF]. GBT is associated with a lower incidence of false positive results when compared with LBT, and in healthy volunteers GBT shows an optimal intra-individual reproducibility [START_REF] Rocco | Intra-individual reproducibility of the glucose hydrogen breath test in a cohort of healthy subjects[END_REF].

Recently, studies on SIBO diagnosed by GBT and treated with rifaximin reported that the progressive increase in rifaximin dosage (from 600mg/day up to 1600mg/day for 7 days) may lead to an important gain in terms of SIBO eradication without enhancing the occurence of side-effects [START_REF] Lauritano | Rifaximin dose finding study for the treatment of small intestinal bacterial overgrowth[END_REF][START_REF] Scarpellini | High dosage rifaximin for the treatment of small intestinal bacterial overgrowth[END_REF]. Similar results were also achieved by Lombardo et al. [START_REF] Lombardo | Increased incidence of small intestinal bacterial overgrowth during proton pump inhibitor therapy[END_REF] by prolonging high dose (1200 mg daily) rifaximin treatment to 14 days. These Authors studied two specific groups and achieved an eradication rate as high as 87% in PPI users and 91% in IBS patients.

Although the setting of our study was slightly different (i.e, we included patients with all the predisposing conditions to SIBO, given the frequent coexistence of different GI disorders in them), nevertheless we obtained similar SIBO eradication rates by combining a shorter course of antibiotic treatment (1200 mg/day rifaximin for 10 days) with the supplementation of a soluble fiber such as PHGG. Lastly, we observed that, although symptom improvement was higher among patients who obtained SIBO eradication with the combined therapy, this tendency failed to achieve statistical significance. This could be due to the fact that both groups underwent an active treatment, rifaximin, whose efficacy has been already proved, and therefore, clinical amelioration was very high in both groups.

In conclusion, the combined use of rifaximin with PHGG allows us to obtain a higher eradication of SIBO as compared with the use of rifaximin alone. Therefore, the prebiotic effect of PHGG is

Figure 1

 1 Figure1shows the flow of patients within the study, SIBO eradication rates and symptoms

  a synergistic action with rifaximin inside the bowel lumen, by improving intestinal clearance and favoring the microflora balance. Furnari was responsible for writing the manuscript, contributed data acquisition and partecipated in the statistical analysis; Dr Andrea Parodi designed the study and participated in the statistical analysis; Dr Vincenzo Savarino and Dr Edoaardo Giannini participated in the writing of the manuscript and partecipated in the statistical analysis; Dr Lorenzo Gemignani partecipated in the writing of the manuscript and contributed to data acquisition; Dr Simona Marenco, Dr Edoardo Savarino, Dr Lorenzo Assandri, Dr Valentina Fazio, Dr Simona Inferrera, and Dr Daria Bonfanti partecipated in patient management and data collection. All authors have seen and approved the final version of the manuscript. All authors declare that they have no conflicts of interest and that the work is original.

Table 1 .

 1 Main demographic and clinical characteristics of the study population subdivided according to treatment receive. Flow diagram of the progress through the phases of a randomised trial of two groups (patients within the study, SIBO eradication rates, symptom improvement).Figure 1 Flow diagram of the progress through the phases of a randomised trial of two groups (patients within the study, SIBO eradication rates, symptom improvement). GBT: glucose breath test; GSRS: gastrointestinal symptom rating scale. 184x159mm (96 x 96 DPI)Results13a For each group, the numbers of participants who were randomly assigned, received intended treatment, and Harms 19 All important harms or unintended effects in each group (for specific guidance see CONSORT for harms) 7

	Tab. 1		rifaximin	rifaximin + PHGG
	patients (n)		37	40
	gender (male/female)		8/29	7/33
	mean age (years)		55 [26-79]	52.5 [36-84]
	BMI (kg/m²)		24.3 [18-29]	24.5 [18-31]
	symptoms n (%):
	-diarrhoea (d) -constipation (c) F o r -alternating d/c	13 (35%) 6 (16%) 4 (11%)	12 (30%) 7 (17.5%) 5 (12.5%)
	-abdominal pain	P	21 (57%)	24 (60%)
	-bloating	e	25 (68.5%)	28 (70%)
	-flatulence	e r	14 (38%)	17 (42.5%)
	-nausea -tenesmus	6 (16.2%) R e 4 (11%)	5 (12.5%) 3 (7.5%)
	v i e n: number of patients; BMI: body mass index; M: male; F: female.
			w
	Figure 1


M.D Joaquin Marticorena
email: jmarticorena@gmail.com

M.D Mario R Romano

M.D Heinrich Heimann

M.D Theodore Stappler

M.D Kurshid S Gibran

M.D Carl Groenewald

M.D Ian Pearce

David Wong

Intravitreal bevacizumab for retinal vein occlusion and early growth of epiretinal membrane: a possible secondary effect?

Keywords: vein occlusion, epiretinal membrane, ischaemia

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Retinal vein occlusion (RVO) is a vascular disease that can be subdivided into central retinal vein occlusions (CRVO) and branch retinal vein occlusions (BRVO). Both diseases are associated with an up-regulation of vascular endothelial growth factor (VEGF) mRNA and with increased intraocular levels of VEGF, especially in those where neovascularization is present. [START_REF] Boyd | Correlation of increased vascular endothelial growth factor with neovascularization and permeability in ischemic central vein occlusion[END_REF] The presence of macular oedema in patients with RVO has also been associated with higher levels of VEGF and retinal ischemia. Inhibiting the effect VEGF would be a rationale therapy to reduce macular oedema, retinal ischemia and to prevent neovascularization in eyes with RVO. Bevacizumab (Avastin, Genentech, Inc, San Francisco, California) is a full-length humanized monoclonal non-selective antibody against VEGF approved by the Food and Drug Administration for the treatment of metastatic colorectal cancer in combination with chemotherapy. Since the first report of a patient with CRVO treated with intravitreal bevacizumab by Rosenfeld et al, [START_REF] Rosenfeld | Optical coherence tomography findings after an intravitreal injection of bevacizumab (avastin) for macular edema from central retinal vein occlusion[END_REF] several studies have described functional and anatomic improvement in patients affected with RVO treated with this anti-VEGF therapy. [START_REF] Kreutzer | Intravitreal bevacizumab for the treatment of macular oedema secondary to branch retinal vein occlusion[END_REF][START_REF] Prager | Intravitreal bevacizumab (avastin) for macular oedema secondary to retinal vein occlusion: 12-Month results of a prospective clinical trial[END_REF][START_REF] Wu | Comparison of two doses of intravitreal bevacizumab as primary treatment for macular edema secondary to branch retinal vein occlusions: results of the Pan American Collaborative Retina Study Group at 24 months[END_REF][START_REF] Spaide | Prospective study of intravitreal ranibizumab as a treatment for decreased visual acuity secondary to central retinal vein occlusion[END_REF] This novel therapy seems to be well tolerated even after numerous retreatments. However, a rebound of macular oedema associated with deterioration of visual acuity has been described and an increase of retinal ischaemia in a patient with CRVO has been reported in relation to the administration of intravitreal bevacizumab. [START_REF] Matsumoto | Rebound macular edema following bevacizumab (Avastin) therapy for retinal venous occlusive disease[END_REF][START_REF] Kim | Ischaemic change after intravitreal bevacizumab (Avastin) injection for macular oedema secondary to non-ischaemic central retinal vein occlusion[END_REF] The purpose of this study is to describe the early onset of secondary epiretinal membrane (ERM) in eyes with RVO treated with intravitreal bevacizumab.

Material and Methods

A retrospective, interventional and non-comparative case series study was conducted with the approval of the Institutional Ethics Committee. Patients with CRVO or BRVO were offered to be treated with an intravitreal injection of bevacizumab. In all cases a signed informed consent was obtained. Evaluation with best corrected visual acuity (BCVA) with Snellen charts, non-contact intraocular pressure (IOP) measurement, slit lamp examination of the anterior segment, exploration of the fundus by biomicroscopy and macular thickness measurement using optical coherence tomography (OCT; OCT Stratus, Carl Zeiss Meditec, Dublin, California) was done at baseline and thereafter approximately every 6 weeks. In 8 patients a fluorescein angiography was performed at baseline. All patients with previous therapy for RVO (i.e. laser photocoagulation, intravitreal triamcinolone) and/or intraocular surgery within the previous 6 months, patients with history of uveitis or other pathologies that may affect the macula (i.e. diabetic retinopathy) were excluded from this study.

Each dose of 2.5mg/0.1ml bevacizumab was prepared in the pharmacy of the hospital under sterile conditions and administered as an intravitreal injection in theatre.

All patients received topical chloramphenicol 0.5% four times a day for 3 days after the injection.

A positive response to intravitreal bevacizumab was normally assumed if there was an increase in BCVA of 2 or more Snellen lines together with a decrease equal or greater than 100 ⎧m of central macular thickness. Retreatment criteria was at discretion of the specialist, but generally it was indicated if: (1) after an initial positive response there was persistent intra or subretinal fluid, (2) after an initial positive response there was a decrease of 2 or more BCVA lines with or without increase of central macular thickness (3) absence of positive response to the initial injection. In those patients that showed no positive response after 2 consecutive treatments, the administration of further bevacizumab injections was discarded.

The diagnosis of ERM was established by biomicroscopy and by an OCT image

showing the presence of a highly reflective layer on the inner retinal surface at the macular area.

For the statistical analysis, BCVA was converted into logMAR units. All continuous variables are expressed as mean ± standard deviation. Serial changes in BCVA and macular thickness were compared with Wilcoxon paired test. All data were analyzed with SPSS 13.0 (SPSS Inc., Chicago, IL). A P value < 0.05 was considered to be significant.

Results

Twenty-five eyes of 25 patients, 14 male and 11 female, were included in this study. In 16 eyes (64%) the diagnosis of CRVO was done, while 9 eyes (36%) were catalogued as having BRVO. Mean age at baseline was 64 ± 14 years (range, 38 -84).

Before intravitreal bevacizumab, in the group of patients with BRVO, 2 eyes had been treated with argon laser macular grid photocoagulation, 1 eye with intravitreal triamcinolone acetonide (IVTA) and 2 eyes with IVTA and grid laser. In the group of patients with CRVO, 2 of them had 1 previous IVTA injection and 1 patient received argon laser panretinal photocoagulation. All these treatments were administered at least 6 months before the bevacizumab injection.

Patients were followed for 8.3 ± 3.3 months (range, 4.5 -13.5). The mean time period between the beginning of the symptoms related to RVO and the administration of bevacizumab was 15 ± 24 months (range, 0.5 -97.5). Eleven patients were treated with a single initial injection, 8 patients with 2 injections and 6 patients with 3 injections, resulting in an average of 1.8 injections per eye.

At baseline, mean BCVA was 1.00 ± 0.57 logMAR and an improvement in BCVA was observed throughout the follow-up. The increase in BCVA was statistically significant compared with baseline at week-6, week-12, week-30, week-36 and week-54 visits (Table 1).

Mean initial central macular thickness measured with OCT was 463 ± 204 ⎧m and a statistically significant decreased was observed at week-6, week-12, week-24, week-30, week-36 and week-54.

In the subgroup analysis, patients with BRVO showed an initial mean BCVA of 0.67 ± 0.38 logMAR and central retinal thickness of 347 ± 133 ⎧m. During follow-up, there were no statistically significant differences in these two variables compared with baseline. Patients with CRVO showed an initial mean BCVA of 1.18 ± 0.58 logMAR and a significant increase was observed after 6 weeks (p < 0.01), 12 weeks (p = 0.01), 30 weeks (p = 0.02) and 36 weeks (p = 0.02). Initial mean central macular thickness was 529 ± 211 ⎧m and a statistically significant decrease was observed after 6 weeks (p = 0.03), 24 weeks (p = 0.02), 30 weeks (p = 0.02) and 36 weeks (p = 0.02). Baseline BCVA and central retinal thickness were statistically different between BRVO and CRVO subgroups and no further comparisons were done between them.

Four patients (3 with CRVO and 1 with BRVO) developed an ERM following the administration of intravitreal bevacizumab (Figures 123). Characteristics of these patients are described in Table 2.

Increase of central retinal thickness and deterioration of BCVA in 1 or more lines compared with baseline occurred in 3 cases (12%), 1 patient with BRVO and 2 patients with CRVO. This rebound was detected after 6 to 18 weeks from previous bevacizumab injection. One of these patients did not receive further therapy and no anatomical or functional improvement was observed during the following 12 weeks. The second patient showed an improvement of BCVA and a decrease in central macular thickness compared with baseline after being retreated. The third patient with rebound developed an ERM and corresponds to Case 1 of Table 2.

No other ocular or systemic complications related to the use of intravitreal bevacizumab were observed during this study.

Discussion

The results of the present study are congruent with several previous reports in which repeated intravitreal bevacizumab injections have been associated with short-term anatomical and functional improvement in patients with RVO, needing repeated injections to maintain this transient benefit in most of the patients. [START_REF] Kreutzer | Intravitreal bevacizumab for the treatment of macular oedema secondary to branch retinal vein occlusion[END_REF][START_REF] Prager | Intravitreal bevacizumab (avastin) for macular oedema secondary to retinal vein occlusion: 12-Month results of a prospective clinical trial[END_REF][START_REF] Wu | Comparison of two doses of intravitreal bevacizumab as primary treatment for macular edema secondary to branch retinal vein occlusions: results of the Pan American Collaborative Retina Study Group at 24 months[END_REF][START_REF] Spaide | Prospective study of intravitreal ranibizumab as a treatment for decreased visual acuity secondary to central retinal vein occlusion[END_REF] Subgroup analysis showed significant improvement of BCVA and decrease of macular oedema in patients with CRVO treated with bevacizumab, but not in those with BRVO. We believe that the lack of benefit observed in the BRVO group may be related to the sample size.

Recurrence of macular oedema appears to be a frequent situation despite the use of fixed initial retreatments and high rate of reinjections of bevacizumab. In our series, we observed not only recurrence of macular oedema, but also rebound of cystoid macular oedema with deterioration of visual acuity compared with baseline in 3 patients.

In 2 of these eyes, retreatment with bevacizumab produced a new decrease in central macular thickness due to reabsorption of macular oedema and increase in BCVA.

Previous reports of intravitreal bevacizumab for RVO have described the reabsorption of macular oedema by measuring the central macular thickness with OCT, but few details regarding the qualitative changes of the macula have been given. It is known that OCT is a very useful tool for the diagnosis of ERM especially in cases where macular edema and intraretinal hemorrhages may difficult the diagnosis by biomicroscopy. In our study, an incidence of 16% of secondary ERM was observed, similar to the 16.1% observed by the Blue Mountains Study in eyes with RVO. [START_REF] Mitchell | Prevalence and associations of epiretinal membranes. The blue mountains eye study, australia[END_REF] Interestingly, there is no description in the literature of ERM growth in patients with RVO treated with bevacizumab despite the numerous studies recently published. On possible explanation to this situation may be that most of these studies are centered in the description of quantitative changes of central macular thickness measured with OCT, but few data is given about the qualitative changes of the macula during follow-up. Due to the characteristics of our study it is difficult to determine a cause-effect relationship between intravitreal bevacizumab and early development of secondary ERM, but there are some elements that allows us to establish this possibility. First, in an early report done by Wise G, 10 the development of "preretinal folds" occurred between 6 and 12 months after the diagnosis of RVO. These folds are not other than the tractional forces of the contracted ERM on the retinal surface. The growth and contraction ERM is though to be a slow process, but in our study ERM rapidly appeared 6-7 weeks after the injection of bevacizumab in eyes with RVO diagnosed 5.5 to 12.5 months before.

Another case with history of 44.5 months of CRVO, developed a premacular membrane only 7 weeks after a second injection of bevacizumab, suggesting that this treatment might be related with this change in the evolution of the disease and beginning of premacular proliferation. But, how can bevacizumab participate in the development of ERM in eyes with RVO? The administration of an anti-VEGF therapy does not only block the pro-angiogenic stimulus of VEGF, it changes the relation, expression and activity of numerous cytokines, growth factors and mediators present in the retinal tissue, retinal vessels and retinal surface. A rise in the levels of VEGF produces an increase in nitric oxide (NO) production by endothelial cells. [START_REF] Hood | VEGF upregulates ecNOS message, protein, and NO production in human endothelial cells[END_REF] NO is involved in controlling retinal blood flow during hypoxia and constitutes a main pathway to stimulate endothelial cell proliferation, migration, release of proteases and increase in capillary permeability. [START_REF] Namba | Angiogenesis induced by endothelial nitric oxide synthase gene through vascular endothelial growth factor expression in a rat hindlimb ischemia model[END_REF][START_REF] Yuan | Histamine increases venular permeability via a phospholipase C-NO synthase-guanylate cyclase cascade[END_REF][START_REF] Ziche | Nitric oxide promotes DNA synthesis and cyclic GMP formation in endothelial cells from postcapillary venules[END_REF][START_REF] Ziche | Nitric oxide promotes proliferation and plasminogen activator production by coronary venular endothelium through endogenous bFGF[END_REF] In an experimental model, Donati et al observed that a decrease in NO production causes an arteriolar constriction in eyes with BRVO, contributing to maintain the hypoxia. [START_REF] Donati | Decreased nitric oxide production accounts for secondary arteriolar constriction after retinal branch vein occlusion[END_REF] It has been proposed that anti-VEGF therapy could reduce the capacity of the endothelium to produce NO. [START_REF] Hood | VEGF upregulates ecNOS message, protein, and NO production in human endothelial cells[END_REF] Therefore, despite the anti-oedematous and anti-angiogenic role of bevacizumab, it could also produce an increase in retinal ischemia by reducing NO production. Clinically, the transformation of a non-ischaemic CRVO into a ischaemic CRVO after intravitreal bevacizumab have been recently described. [START_REF] Kim | Ischaemic change after intravitreal bevacizumab (Avastin) injection for macular oedema secondary to non-ischaemic central retinal vein occlusion[END_REF] Apart from VEGF there are some other factors like platelet-derived growth factor A and tumour necrosis factor-alfa that participate in the growth of ERMs. [START_REF] Campochiaro | Platelet-derived growth factor is an autocrine growth stimulator in retinal pigmented epithelial cells[END_REF][START_REF] Chen | Localisation of vascular endothelial growth factor and its receptors to cells of vascular and avascular epiretinal membranes[END_REF][START_REF] Gardiner | Inhibition of tumor necrosis factoralpha improves physiological angiogenesis and reduces pathological neovascularization in ischemic retinopathy[END_REF] An increase of such factors, as a consequence of persistent ischemia, could explain the development of ERM in patients with RVO treated with bevacizumab. In our study, visual acuity remained stable in 2 of the patients with ERM after bevacizumab compared with baseline, while in the other 2 patients there was an improvement of vision. Even when ERM can limit visual recovery, vitrectomy and peeling of the membrane was not indicated since ERM was not associated with further deterioration of visual acuity or metamorphopsia.

It is well known that in ischemic retinopathies VEGF is up-regulated while pigment epithelium-derived factor (PEDF), an angiostatic and neurothophic factor, is decreased. [START_REF] Aiello | Vascular endothelial growth factor in ocular fluid of patients with diabetic retinopathy and other retinal disorders[END_REF] Therefore, the administration of an anti-VEGF agent produces an imbalance towards the effect of PEDF. In addition, PEDF production by retinal glial cells is increased under a marked hypoxia environment. [START_REF] Lange | Regulation of pigmento epithelium-derived factor production and release by retinal glial (Müler) cells under hypoxia[END_REF] Enhanced expression and location of PEDF, as well as its capability of being stimulated by transforming growing factor beta (TGF-β), has been observed in progressive fibrotic pathologies. [START_REF] Cosgrove | Pigment epithelium-derived factor in idiopathic pulmonary fibrosis: a role in aberrant angiogenesis[END_REF] It suggests that a relative increase in PEDF after intravitreal bevacizumab may promote fibrotic changes of ERM in eyes with retinal ischemia. Hypoxia can also promote the expression of TGF-β in Muller cells, [START_REF] Behzadian | Effects of hypoxia on glial cell expression of angiogenesis-regulating factors VEGF and TGF-b[END_REF] and consequently the presence of connective tissue growth factor (CTGF), an important mediator of retinal fibrosis and development of ERM. [START_REF] He | Connective tissue growth factor as a mediator of intraocular fibrosis[END_REF] In other tissues VEGF has shown to inhibit the expression of CTGF in a complex mechanism in which is also involved TGF-β. [START_REF] Szeto | Differential effects of transforming growth factor-beta on the synthesis of connective tissue growth factor and vascular endothelial growth factor by peritoneal mesothelial cell[END_REF] We may hypothesize that the blockage of VEGF through bevacizumab may increase the relative effect of factors such as PEDF and CTGF. This may produce a rapid development of the fibrotic component of an early ERM. Fibrosis, contraction and wrinkling of the ERM make more evident the presence of the epimacular tissue, facilitating the diagnosis of previously undetected lesions.

In conclusion, bevacizumab appears as a symptomatic treatment for vasoocclusive diseases since recurrence of macular oedema is a frequent situation, even after repeated injections. The early development of secondary ERM in eyes with RVO may constitute a secondary effect of intravitreal bevacizumab considering the time effect relationship observed in the present study and the theoretical basis that can explain this phenomenon. We describe different mechanism that may promote the growth ERM in eyes with RVO, as well as an increase in fibrosis and secondary contraction of epimacular tissue after intravitreal bevacizumab. Although intravitreal bevacizumab is emerging as one of the possible treatments in retinal venous disease, we encourage the cautious administration of this therapy until randomized masked clinical trials determine the safety and efficacy of this treatment.

Legends

Figure 1 .

 1 Figure 1. Case 1. (A) Baseline horizontal OCT scan showing cystoid macular edema

Figure 2 .

 2 Figure 2. Case 2. Right eye of a patient with initial BCVA of 20/200 and central macular

Figure 3 .

 3 Figure 3. Case 4. (A) Baseline OCT scan shows the presence of cystoid macular

Table 1 . Progression of Visual Acuity and Central Macular Thickness During Follow-up.

 1 BCVA: Best corrected visual acuity; * Wilcoxon signed rank test. Values are expressed as mean ± standard deviation. ± 0.57 0.83 ± 0.62 0.87 ± 0.69 0.79 ± 0.48 0.62 ± 0.44 0.68 ± 0.69 0.45 ± 0.35 0.50 ± 0.43 0.17 ± 0.23 0.47 ± 0.41

		Baseline	6 weeks	12 weeks	18 weeks	24 weeks	30 weeks	36 weeks	42 weeks	48 weeks	54 weeks
	N	25	25	23	25	12	11	12	6	3	5
	BCVA (logMAR) 1.00 P Value*	---	.005	.023	.139	.071	.012	.005	.285	.180	.042
	Central Macular Thickness (μm) 463 ± 204	355 ± 175	375 ± 136	417 ± 173	331 ± 133	298 ± 84	293 ± 95	417 ± 247	224 ± 14	223 ± 20
	P Value*		---	.007	.031	.178	.008	.012	.004	.593	.109	.043
	Retreatments		---	6	3	7	3	---	---	1	---	---

No grants or funds have been involved in the development of this study.