G ; Imsas

R Fuentes-García

R H Mena

S G Walker
email: s.g.walker@kent.ac.uk

A New Bayesian Nonparametric Mixture Model

Keywords: Bayesian model, Mixture model, Geometric distribution, Gibbs sampler Bayesian model, Geometric weight, Gibbs sampler, Mixture model

We propose a new mixture model for Bayesian nonparametric inference. Rather than considering extensions from current approaches, such as the mixture of Dirichlet process model, we end up shrinking it, by making the weights less complex. We demonstrate the model and offer an explanation for the performance.

1. Introduction. There are two approaches to Bayesian nonparametric density estimation; the first is based on mixture models where the random density function f (y) is constructed via f (y) = K(y; θ) dP (θ), where K(y; θ) is a density function for each θ, P is a random distribution function, which is typically taken to be discrete, e.g. of the type

P (dθ) = ∞ l=1 wl δ θ l (dθ) (1)
with a prior distribution assigned to ( wl , θ l ) ∞ l=1 and where δ θ denotes the measure with mass 1 at the location θ. For example, the well known and widely used Dirichlet process results when {θ l } are independent and identically distributed (iid) from some distribution G, the prior guess at the shape of P , w1 = v 1 , and for l > 1, wl = v l k<l (1 -v k ) with the {v l } being iid from Beta(1, c), for some c > 0. See [START_REF] Sethuraman | A constructive definition of Dirichlet priors[END_REF] for the latter representation and [START_REF] Lo | On a class of Bayesian nonparametric estimates I. Density estimates[END_REF] for definition and properties of mixture of Dirichlet process models. Some sampling techniques to infer from Bayesian nonparametric mixture models can be found in [START_REF] Escobar | Estimating the means of several normal populations by nonparametric estimation of the distribution of the means[END_REF][START_REF] Escobar | Estimating normal means with a Dirichlet process prior[END_REF], [START_REF] Escobar | Bayesian density estimation and inference using mixtures[END_REF], [START_REF] Maceachern | Estimating normal means with a conjugate style Dirichlet process prior[END_REF], [START_REF] Maceachern | Estimating mixtures of Dirichlet process models[END_REF], [START_REF] Neal | Markov chain sampling methods for Dirichlet process mixture models[END_REF], [START_REF] Papaspiliopoulos | Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models[END_REF][START_REF] Papaspiliopoulos | Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models[END_REF][START_REF] Walker | Sampling the Dirichlet mixture model with slices[END_REF]. The other approach to Bayesian density estimation is based on a finite mixture model with the number of mixtures being N and a prior distribution assigned to N . So

f (y|N ) = N l=1
w l,N K(y; θ l,N ).

See, for example, [START_REF] Richardson | On Bayesian analysis of mixtures with an unknown mixture of components[END_REF]. Algorithms for estimating this latter model are based on reversible jump Markov chain Monte Carlo [START_REF] Green | Reversible jump Markov chain Monte Carlo: computation and Bayesian model determination[END_REF] or using birth and death Markov chain Monte Carlo; see [START_REF] Stephens | Bayesian Analysis of mixture Models with an unknown Number of Componentsan alternative to Reversible Jump Methods[END_REF].

The algorithm of [START_REF] Walker | Sampling the Dirichlet mixture model with slices[END_REF] for estimating the mixture of Dirichlet process (MDP) model, which is also applicable to more general stick-breaking processes, e.g. when the v l ∼ Beta(a l , b l ), starts by considering the density

f (y|u) = |A u | -1 ∞ l=1 1(u < wl ) K(y; θ l )
where A u denotes a random set defined as A u := {j : wj > u} with u a uniform random variable. Given u, this random set is clearly finite and we denote its cardinality by |A u |. It is worth emphasizing that A u is a random finite subset of the set of positive integers.

We could consider a more general idea by constructing the following random density

f (y | A) = |A| -1 l∈A K(y; θ l ) (2)
where A denotes a different, perhaps more general, random set. This is similar to the [START_REF] Richardson | On Bayesian analysis of mixtures with an unknown mixture of components[END_REF] model but with differences. First, notice that if we assume model (2) for each observation y i , then there will be a random set A i for each of them whereas in the [START_REF] Richardson | On Bayesian analysis of mixtures with an unknown mixture of components[END_REF] model the N suffices for all observations. This is one of the reasons for having complex weights and parameters specifications, (w l,N , θ l,N )'s, in their approach, i.e. to make a richer model. On the other hand for the MDP model it is sufficient to have uniform weights given A and a single sequence {θ l }. Second, the A used in the mixture of Dirichlet process model is not a consecutive sequence of integers from 1 to N , as it is with the [START_REF] Richardson | On Bayesian analysis of mixtures with an unknown mixture of components[END_REF] model. It seems clear to us that the use of consecutive sequences is likely to be more efficient when estimating the model using Markov chain Monte Carlo algorithms.

In fact, there is no point in having the A to have gaps; the real question is why would one wish A to have gaps?

The idea of this paper is to suggest the model whereby A i := {1, . . . , N i }, so where N is random, but with the same distribution for each observation; say P(N ) = q N and a prior distribution is assigned to {q N }.

f (y|N ) = N -1 N l=1
Our observation is on the choice of the {q N }, which as we will see determines the structure of the weights {w l } corresponding to a random distribution characterized by (1). In principle, any distribution supported on the set of positive integers could be used. Particularly, we look for a choice of {q N } that lead us to a manageable structure for the weights and also to simple conditionals in the corresponding Gibbs sampler algorithm. A suitable choice for these purposes turns out to be a Neg-Bin(2, λ) that, together with a beta prior distribution for λ, results in a well defined random distribution of the type (1). Our results based on this choice are remarkable considering the simplicity of the model and algorithm. In Section 2 we describe the model, resulting from our choice of random set A, in more detail and describe some properties. Section 3 details the Gibbs sampler for estimating the model and Section 4 is devoted to illustrations that aid to understand the potential and contribution of our approach. A discussion on our findings is presented in Section 5.

2. Properties of the model. If we write out the model by marginalizing over N then we have

f (y) = ∞ N =1 1 N N l=1 K(y; θ l ) q N (3)
which can be written as

f (y) = ∞ l=1
w l K(y; θ l ) = K(y; θ) dP (θ),

where

P (dθ) = ∞ l=1 w l δ θ l (dθ)
and the weights {w l } are given by

w l = ∞ N =l q N /N. (4)
These weights clearly add up to one and, in contrast to the weights corresponding to the Dirichlet process, are always decreasing. Although, this model can be seen as a nonparametric mixture model with the above random distribution, we can write it in the hierarchical form (2)

with the random set A chosen as {1, . . . , N } rather than being of the non-consecutive type as it is with the Dirichlet process model, as seen in [START_REF] Walker | Sampling the Dirichlet mixture model with slices[END_REF].

Indeed, as we mentioned in the introduction, the {q N } can be given any arbitrary distribution supported on the set of positive integers; immediate choices could fall in the Poisson, negative binomial or geometric families. However, note that an arbitrary choice for q N does not necessarily leads to a simple analytic structure for the weights. For example, if

q N = N + r -2 r -1 λ r (1 -λ) N -1 , N = 1, 2, . . .
namely a negative binomial distribution (Neg-Bin(r, λ)) supported on the set of positive integers, then the corresponding weights take the form

w l = 1 l l + r -2 r -1 λ r (1 -λ) l-1 2 F 1 (1, l + r -1; l + 1; λ), (5)
where 2 F 1 (a, b; c; λ) denotes the Gauss hypergeometric function.

In Section 3 we will detail the Markov chain Monte Carlo algorithm for estimating the model based on geometric weights. First, let us look at the conditional distribution for each N i that motivates this choice for q N . If we assume model (3) for a set of observations, {y i } n i=1 , and introduce a latent variable d i that, given N i , indicates from which component y i comes from, then

P(d i = l|N i ) = N -1 i 1 (l ∈ {1, . . . , N i }).
Now, since we have P(N i = l) = q l , then

P(N i = N |d i ) ∝ q N N 1(N ≥ d i ).
Hence, it is convenient that the sequence of probabilities {q N /N } take a form from which is relatively easy to sample truncated versions. As we will see, a special case of the negative binomial distribution, specifically a Neg-Bin(2, λ), leads to a truncated geometric distribution for

P (N i | d i ),
which is clearly simple to simulate from. Furthermore, a beta prior distribution could be taken as a conjugate choice easing even more the implementation of the MCMC algorithm. It is worth mentioning that at the outset our plan was to start with this latter choice for q N and then move to other, perhaps more general, choices but as we will see this appears unnecessary at least for mixture modelling aiming at density estimation.

3. Simulation algorithm. In order to see how to construct a Gibbs sampler for this model and our choice of random sets A, we write it in hierarchical form for a general choice of where the {θ l } are assumed to be i.i.d. from a distribution with density g and a prior is assigned to the parameters of q n , namely π(q).

q N f (y i |d i , N i ) = K(y i ; θ d i ) P(d i = l|N i ) = N -1 i 1(l ∈ {1, . . . , N i }) P(N i = N ) = q N , 4
The full conditional for θ j is then given by

f (θ j | • • • ) ∝ g(θ j ) d i =j K(y i ; θ j )
which in particular is easy to sample when K(y; θ) and g(θ) form a conjugate pair. The full conditional for d i is given by

P(d i = l| • • • ) ∝ K(y i ; θ l ) 1(l ∈ {1, . . . , N i })
which being a discrete distribution with finite support it is easy to sample. The full conditional for N i has already been considered in Section 2, repeated here, as

P(N i = N | • • • ) ∝ q N N 1(N ≥ d i ).
Finally, the full conditional for q is given by

π(q| • • • ) ∝ n i=1 q N i π(q).
As we mentioned in Section 2, in order to simplify the sampling of the full conditional for N i an easy form for q N /N is required. In particular, this is attained by setting q N to take Neg-Bin(2, λ) distribution, i.e. with density

q N = N λ 2 (1 -λ) N -1
which, following (4), results in weights given as

w l = λ(1 -λ) l-1 .
That is, the decreasing weights take a geometric distribution. We then assign a beta hyper-prior distribution for λ.

As we will corroborate in the following section this model, although at first sight simplistic and not flexible enough, will prove to perform well for density estimation purposes. Before going into the numerical illustrations let us adjust and complete the details of the Gibbs sampler for sampling the full conditional distributions of N i and λ. Notice that assuming a Neg-Bin(2, λ) for q N results in

P(N i = N | • • • ) ∝ (1 -λ) N -1 1(N ≥ d i ) 5 F o r P e e r R e v i e w O n l y
which is a truncated geometric distribution and is easy to sample. The full conditional for λ, assuming a Beta(a, b) prior, is given by

π(λ| • • • ) ∝ n i=1 λ 2 (1 -λ) N i -1 λ a-1 (1 -λ) b-1
which is also a beta distribution with parameters a + 2n and b -n + n i=1 N i . Note that with this choice of q N we could see our approach as a Bayesian nonparametric mixture model with a mixing discrete random distribution, of the type (1), with geometric weights.

In fact, weights defined as above can be thought of as the expected value of the weights corresponding to Dirichlet process. That is, if we use the stick breaking representation of the Dirichlet process, i.e. with weights wl = v l k<l (1 -v k ) with the {v l } being iid from Beta(1, c) and c > 0, then

E[ wl ] = 1 c + 1 c c + 1 l-1
, which is a simple re-parametrization of λ (1 -λ) l-1 when λ = (c + 1) -1 . When implementing models based on the Dirichlet process, typically the assignation of a prior distribution on the total mass parameter, c, is needed to achieve good results. Therefore, our approach could be seen as the removal of a hierarchical level from the Dirichlet process model by replacing the random {v l } with their expected values. i=1 , chosen uniformly from the set {1, . . . , 10}, the full conditional distributions are given by ixture of two normal distributions; N(0, 1) and N(6, 1), with corresponding weights 0.3 and 0.7. For the implementation of the method described in Section 3, let us assume that K(y; θ) = N(y; θ, 1),

g(θ) = N(θ; m, 1/v), q N (N ; λ) = N (1 -λ) N -1 λ 2 and λ ∼ Be(a, b). Hence,
for a given set of hyper-parameters (m, v, a, b), starting configurations for the {N i } 200 i=1 and the

π(θ j | • • • ) = N θ j | mv + s j v + n j , 1 v + n j ,
where n j := d i =j 1 and s j := d i =j y i ,

P(d i = l | • • • ) = N(y i | θ l , 1) N i k=1 N(y i | θ k , 1)
1(l ∈ {1, . . . , N i }), N i -n .

P(N i = j | • • • ) = λ (1 -λ) j-1 1(j ≥ d i ) 6
Figure 1 shows the Monte Carlo density estimate,

f (y) = 1 M M k=1 1 n n i=1 1 N k i N k i l=1 N(y | θ k l , 1),
resulting from M = 10, 000 iterations after a 2, 000 burn-in period. The choice of hyper-parameters is given by (m, v, a, b) = (3, 1, 1, 1) and was obtained by inspecting the data, i.e. by preserving the original mean and variance of the model that generated the data. As in any other nonparametric mixture model, changing this values radically would lead to different estimations. However, this could be extended to a more complex model, possibly with further hierarchies as done in the following subsection. In this subsection we keep it simple in order to better understand the role of having an unlimited number of θ's.

Figure 2 shows an estimator of the number of θ's below and above a cutoff point, set at y = 3

where visually we could locate a separation between the 2 cluster locations. The plot could be seen as representing the number of θ's used to capture each mode in the mixture. Hence, the following interpretation follows: for the mode with higher probability (located around y = 6) we observe a tendency to represent it with a small number of θ's, namely the bar plot shows a mode in two θ's.

Whereas for the mode with the smaller probability (located around y = 0) the tendency points towards a higher number, the bar plot shows a mode in four θ's. This effect can be explained by the fact that the weights, w l 's, are decreasing. That is, if a small weight needs to be increased, this is achieved by increasing the number of θ's used to represent the corresponding mode.

We believe that this assignation of θ's to represent a particular cluster location is reinforced in a more ordered fashion than the assignation founded when using non-consecutive sets, as in the Dirichlet process case. This argument is better illustrated in the following subsection.

4.2 Location and scale modeling for simulated data. Here we consider a more complicated data set that allows us to highlight the flexibility of our approach. We generate 240 data points coming from a mean-variance mixture of six normal distributions with weights (0.17, 0.08, 0.125, 0.2, 0.125, 0.21) and mean-variance parameters given by (-18, 2), (-5, 1), (0, 1), (6, 1), (14, 1) and (23,125). Similar to the previous section, for our modeling approach, we assume K(y; θ) = N(m, 1/v), so θ := (m, v), and a conjugate prior distribution given by g(θ) = N(m; µ, τ v -1 ) Ga(v; α, β). The only substantial difference for this example is that the posterior density is given by

π(m j , v j | . . .) = N m j | τ n j ȳj + µ τ n j + 1 ; τ v (τ n j + 1) × Ga v j | n j 2 + α; n j (ȳ j -µ) 2 2(τ n j + 1) + D j 2 + β
where ȳj = s j /n j , s j and n j are as before and D j = d i =j (y i -ȳj ) 2 .

Figures 3 and4 show the dynamics of the density estimator for the first 100 iterations based on our approach, here termed geometric, and on the MDP model respectively. From Figure 3 we note that the availability of an unlimited number of θ j 's to represent a particular cluster location always results in a improvement in subsequent iterations. Whereas in the MDP case, Figure 4, the algorithm might require several iterations to obtain a good candidate for the θ j representing a particular location. This feature is better appreciated in the mode welling around -18, which can be thought as being far from the overall mean of the data. This can be also observed at the tails of the density estimators in Figure 3, where for the initial iterations a bigger mass, than that shown for the MDP, is allocated.

In fact this drawback of the MDP and other mixtures based on more general random distributions, has received considerable attention in the Bayesian nonparametric literature resulting in algorithms that aim to accelerate the identification of good candidates for the θ j 's identifying particular cluster locations. See for instance MacEachern (1998). It is worth emphasizing that, despite these efforts, this issue is not fully resolved.

Figure 5 shows the estimates for both, the Dirichlet process and our geometric approach, at a convergent stage. This figure also compares the true model that generated the observations, as we can see both approaches can be thought as being relatively satisfactory, however our approach appears to be closer to the true model.

It is then clear that the decreasing order of the weights results in a more ordered and faster convergence of the density estimation.

4.3 Galaxy data set. In this section we consider the galaxy data set; see e.g. [START_REF] Roeder | Density estimation with confidence sets exemplified by superclusters and voids in the galaxies[END_REF].

This data set has been widely used as an example in mixture modeling and in particular as a benchmark when proposing or comparing new Bayesian nonparametric mixture models. See for instance Escobar and[START_REF] Escobar | Bayesian density estimation and inference using mixtures[END_REF]Lijoi et. al. (2005). Some discussion on the advantages and drawbacks of using mixtures of Dirichlet processes for density estimation can be found in [START_REF] Green | Modelling heterogeneity with and without the Dirichlet process[END_REF].

The galaxy data are typically captured by relatively complex Bayesian nonparametric mixture models, e.g. with Gaussian kernels and where the mixing parameters are both, mean and variance.

These parameters are then modelled non-parametrically through random distributions where the corresponding mean measure needs further hierarchies in order to improve the density estimation.

For simple choices of random distributions, as in the Dirichlet process case, the total mass parameter also requires a further randomization through the assignation of a prior distribution, as done in [START_REF] Escobar | Bayesian density estimation and inference using mixtures[END_REF]. Further discussions on the galaxy data and its modelling through Bayesian nonparametric mixtures can be found in Lijoi et. al. (2005Lijoi et. al. ( ,2006)).

Our intention here is not to claim a superiority of our approach neither to give an exhaustive comparison of existing models, since this would basically consist of restating arguments already well established in the literature. We rather aim at illustrating the simplicity of our approach and how this performs in the particular case of this widely discussed data set. Having said that, we do compare it with the Dirichlet process.

Hence, with this purpose in mind, we have used the same framework, i.e same model with same parameter and hyper-parameter specifications, used in Section 4.2. We have based the estimations using our approach on 1,000 iterations, and we have used 10,000 iterations plus a 2000 for burning in the sample in the case of the Dirichlet process. For this latter, we have additionally randomized the total mass parameter with a gamma distribution as done in [START_REF] Escobar | Bayesian density estimation and inference using mixtures[END_REF] and make use of the acceleration step suggested by MacEachern (1998). The additional sampling used in this latter approach is needed since otherwise compromised the convergence and therefore the quality of the corresponding density estimation. As we can see in Figure 6, both fits are comparable and satisfactory. Though we emphasize the estimate we have used is obtained with less parameters, less iterations, in less than a tenth of the computational time and with a much simpler implementation.

5. Discussion. The current trend in Bayesian nonparametric mixture modelling focuses on generalizations of the Dirichlet process model. However, in most cases these generalizations result in complex models hard to implement and to apply in real situations, see Lijoi et. al (2005b) for an example of how complex these generalizations can be. In this context, our results are appealing, in that we have proposed a simple approach and yet competent for Bayesian nonparametric density estimation. To some extent we could say that we have gone in the opposite direction of such a trend by proposing a simpler approach when using a random distribution with geometric weights. As stated in Section 3, these weights can be seen as the expected values of those corresponding to the Dirichlet process, hence removing a hierarchy from this latter one, which is apparently unnecessary, at least for density estimation purposes. [START_REF] Blackwell | Ferguson distributions via Pólya urn scheme[END_REF] for the Pólya urn scheme.

One might wonder why an approach based on such a simple construction works, at least as well, as other methods based on more complex models, as those based on Dirichlet or Poisson-Dirichlet processes models where an infinite number of beta variables is needed for the corresponding stickbreaking construction. Our explanation is quite straightforward. While the weights would be practically useless if we could only have one of the θ j 's identifying a particular cluster location, the fact that there are an infinite number of possible θ j 's implies that we can have an unlimited number of them supporting this location. Hence the weights for a particular cluster location are obtained via a combination of the geometric weights and the number of θ j 's supporting that cluster location.

For a more mathematical explanation consider the following: Let

P = ∞ j=1
ρ j δ φ j be a Dirichlet process where the weights have been ordered to be decreasing, so

ρ 1 > ρ 2 > • • • .
The φ j are iid from some density defined on the real line. Now consider our random distribution function

P G = ∞ j=1 w l (λ)δ θ j
where the θ j are also iid from the same density as the {φ j } and the {w j (λ)} are the geometric weights, with λ being assigned a distribution.

We can use our model to arbitrarily approximate the Dirichlet model when for some sequence n 1 , n 2 , . . . we have

|w 1 (λ) + • • • + w n 1 (λ) -ρ 1 |, |w n 1 +1 (λ) + • • • + w n 2 (λ) -ρ 2 |, . . .
are all suitably small and correspondingly

max{|θ 1 -φ 1 |, . . . , |θ n 1 -φ 1 |}, max{|θ n 1 +1 -φ 2 |, . . . , |θ n 2 -φ 2 |}, . . .
are all suitably small. Since there is positive probability on these events we can see that we do not need the weights to be that exotic; such as those obtained via stick-breaking construction. Hence, our conclusion is that the

P G = λ ∞ j=1
(1 -λ) j-1 δ θ j is sufficient for mixture modeling and that the current trend of further elaborating on Dirichlet process mixture models must be compromised with an application that potentially would require more complicated weights specifications. The hyper-parameters are given by (µ, τ, α, β, a, b) = (0, 100, 0.5, 0.5, 0.5, 0.5) and N i = 10 and d i ∈ 1, . . . , 10 for all i = 1, . . . , 240.

  4. Numerical Illustrations. In this section we consider 3 examples; 2 simulated data sets and one real data set; the well known galaxy data set. 4.1 Location modeling for simulated data. Here we generate 200 iid data points, {y i } 200 i=1 , coming from a minitial values for the {d i } 200

  | • • • ) = Be λ; a + 2n, b + n i=1

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 12345 Figure 1: Fitted density (solid line) to simulated data set (histogram) with n = 200. The estimate is based on 10, 000 iterations after a burn in of 2, 000 iterations and hyperparameters (m, v, a, b) = (3, 1, 1, 1), N i = 10 and d i ∈ 1, . . . , 10 for all i = 1, . . . , 200.

Figure 6 :

 6 Figure 6: Density estimators for the galaxy data.

  Gibbs sampler algorithm is available, which results in a simpler alternative to those typically used for Bayesian nonparametric mixtures. It is worth noting that most of these MCMC algorithms are based on the Pólya-urn construction of the Dirichlet process, or its extensions when dealing with other random distributions. In contrast to our algorithm, these algorithms are based on almost sure approximations to the random distribution through exchangeable sequences. See Blackwell

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Communications in Statistics -Simulation and Computation

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

Acknowledgements. The authors are grateful to the Associate Editor and two referees for their valuable comments and suggestions. The second author thanks CONACYT for providing the Grant No. J50160-F. The work was completed during a visit by the first two authors to the University of Kent.


Patricio Gonzalez-Hormazabal

Sara Gutierrez-Enriquez

Daniel Gaete

Jose M Reyes

Octavio Peralta

Enrique Waugh

Fernando Gomez

Sonia Margarit

Teresa Bravo

Rafael Blanco

) ; Orland Diez

Ph. D Lilian Jara
email: ljara@med.uchile.cl

Ph. D Orland Diez
email: odiez@vhebron.net

Spectrum of point mutations and genomic rearrangements in high-risk breast/ovarian cancer Chilean families

Keywords: Breast cancer, BRCA1/2, Chilean population, LGRs, recurrent mutations

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

Breast cancer (BC) is the most common cancer among women worldwide. It has been established that one out of eight women will develop BC during their lives [START_REF] Jemal | Cancer statistics, 2009[END_REF]. In Chile, mortality in women due to BC has risen, from 8.5 deaths per 100,000 women in 1985 to 12.8 per 100,000 women in 1995 [START_REF] Peralta | Cáncer de mama: resultados del programa de pesquisa y tratamiento del Servicio de Salud Central[END_REF]. Currently, it has the second-highest mortality rate among cancers (13.8/100,000 women) [START_REF]Mortalidad en mujeres[END_REF]. Incidence increased from 16.2/100,000 women in 1998 to 26.2/100,000 women in 2002 [START_REF] Prieto | Situación epidemiológica del cáncer de mama en Chile 1994-2003[END_REF].

Hereditary BC accounts for 5-15% of all BC cases [START_REF] Easton | Familial risks of breast cancer[END_REF]. Together, germline mutations in the two major susceptibility genes BRCA1 and BRCA2 (BRCA1/2) account for approximately 20% of familial BC cases [START_REF] Wooster | Breast and ovarian cancer[END_REF]. Carriers of mutations in any of these genes have a 40-85% cumulative lifetime risk of BC by the age of 70 . Studies of BRCA1/2 mutation frequencies have revealed significant differences in populations of different geographic regions and ethnicities. Disease-causing mutations are distributed throughout the entire coding regions of both genes. Since the identification of BRCA1 and BRCA2 as the principal genes responsible for inherited BC [START_REF] Miki | A strong candidate for the breast and ovarian cancer susceptibility gene BRCA1[END_REF][START_REF] Tavtigian | The complete BRCA2 gene and mutations in chromosome 13q-linked kindreds[END_REF], more than 3,400 distinct DNA sequence variants have been described in the BIC database (http://research.nhgri.nih.gov/bic/), of which 1,625 can be classified as pathogenic, including 1,454 truncating mutations (1,075 frameshift and 379 nonsense) and 139 splicing alterations. The remaining mutations, including 1,351 distinct missense changes, are unclassified variants of uncertain clinical consequences. In addition to point mutations that can be detected within a PCR fragment, BRCA1 and BRCA2 are both known to have germline mutations resulting from Large Genomic Rearrangements (LGRs) that result in duplications or deletions of one or more exons, usually producing premature stop codons.

Little is known about the contribution of BRCA1/2 to hereditary BC in South American populations. In the Chilean population there are only two reports of mutation analysis of BRCA1/2, and these included a low number of BC and/or ovarian cancer (OC) patients [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF][START_REF] Gallardo | Incidence of BRCA1 and BRCA2 mutations in 54 Chilean families with breast/ovarian cancer, genotype-phenotype correlations[END_REF]. Moreover, the prevalence of BRCA1/2 genomic rearrangements in Chilean and in other South American populations is unknown. Here we present the mutation-detection data corresponding to a set of 326 high-risk families analyzed by conformation-sensitive gel electrophoresis and heteroduplex analysis. Results of 64 out of these 326 high risk families were previously reported [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF] showing that the BRCA1/2 gene mutation spectrum was heterogeneous and broad.

Our current study, which is the largest conducted to date in a South American population, provides a comprehensive analysis on the type and distribution of BRCA1/2 mutations and allelic variants. To determine the contribution of BRCA1/2 LGRs in Chilean BC patients, we analyzed 56 high-risk subjects with no pathogenic BRCA1/2 point mutations.

METHODS

Families

In this study, 326 high-risk BC/OC Chilean families were selected from the files of the Servicio de Salud del Area Metropolitana de Santiago, Corporación Nacional del Cáncer (CONAC) and other private services in the Metropolitan Area of Santiago. Pedigrees were constructed on the basis of an index case considered to have the highest probability of being a deleterious mutation carrier. None of the families met the strict criteria for other known syndromes involving BC, such as Li-Fraumeni, ataxia-telangiectasia, or Cowden disease. All families participating in the study self reported Chilean ancestry dating several generations, after extensive interviews with several members of each family from different generations.

Table 1 shows the specific characteristic of the families selected according to the inclusion criteria. In the sample of selected families, 15.3% (50/326) had bilateral BC, 9.0% (29/326) had BC and OC, and 2.8% (9/326) presented male BC. From the 326 families which participated in this study, 348 women had only BC, two had both BC and OC, 5 had OC, and 7 had male BC. BC and OC for all cases included in the study were verified using the original pathology report.

This study was approved by the Institutional Review Board of the School of Medicine of the University of Chile.

Informed consent was obtained from all the participants.

BRCA1 and BRCA2 mutation analysis

Genomic DNA was extracted from peripheral blood lymphocytes of 362 index cases belonging to the 326 high-risk selected families. Samples were obtained according to the method described by Chomczynski and Sacchi [START_REF] Chomczynski | The single-step method of RNA isolation by acid guanidinium thiocyanate-phenolchloroform extraction: twenty-something years on[END_REF].

The whole coding sequences and exon-intron boundaries of the BRCA1 and BRCA2 genes were analyzed for sequence variants using conformational-sensitive gel electrophoresis according to described protocols [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF]. Any fragment showing a mobility shift was directly sequenced in both directions. Sequencing was performed in an ABI prism 3100 automated fluorescence-based cycle sequencer (Applied Biosystems, USA) and a rhodamine dye terminator system (Applied Biosystems, USA).

Multiplex Ligation-Dependent probe Assay (MLPA) was performed for screening LGRs in a subgroup of 56 index cases negative for BRCA1/2 point mutations. MLPA analysis was performed according to manufacturer instructions (MRC Holland, Holland) using the SALSA MLPA Kit P002-B1 for BRCA1 and SALSA MLPA Kit P045-B1 for BRCA2. The fragments obtained were analyzed by capillary electrophoresis using an ABI3130-xl Genetic Analyzer (Applied Biosystems, USA) with a 36cm capillary array and POP-7 polymer (Applied Biosystems, USA). GeneMapper 4.0 software (Applied Biosystems, USA) was used for fragment analysis and the results (peak size, height and areas) were exported to an Excel data sheet to calculate the relative peak area. Normalization was achieved by dividing the intra-normalized peak area by the average intra-normalized probe ratio of all analyzed samples in the same round of analysis.

Mutation nomenclature

Mutations are described at the cDNA level according to the Human BRCA1 reference sequence: accession U14680; and the Human BRCA2 reference sequence: accession U43746; from GenBank sequence database (http://www.ncbi.nlm.nih.gov/genbank/). The BRCA1 and BRCA2 numbering for the BIC traditional mutation nomenclature is based on reference sequences as stated above where the A of the ATG translation initiation codon is at position 120 of BRCA1 and position 229 of BRCA2. The Human Genome Organization (HUGO) systematic nomenclature for the description of sequence variants in DNA and protein sequences [START_REF] Den Dunnen | Mutation nomenclature extensions and suggestions to describe complex mutations: a discussion[END_REF] follows the rule in which the A of the ATG translation initiation codon is +1.

RESULTS

The BRCA1 and BRCA2 genes of 362 index cases belonging to 326 high-risk unrelated families were scanned for mutations. We identified a total of fourteen point pathogenic mutations (seven in BRCA1 and seven in BRCA2) (Tables 3 and4). Furthermore, we identified 14 variants of unknown significance (6 in BRCA1 and 8 in BRCA2) (Table 5) and 28 polymorphisms (17 in BRCA1 and 11 in BRCA2) (Table 6). According to the type of mutation, small deletions leading to frameshifts were more frequent (n=11), followed by splicing mutations (n=1), insertions (n=1) and a missense pathogenic mutation. No large deletions or duplications involving BRCA1/2 were identified in a subgroup of 56 index cases negative for BRCA1/2 point mutations.

BRCA1/2 pathogenic point mutations

Germline BRCA1/2 point mutations were found in 23 (7.1%) of the 326 Chilean families (Table 2). Despite the low frequency of pathogenic point mutations detected in this series, the families that had at least 3 BC and/or OC cases showed the highest frequency of mutations (15.9%). The frequency was lower for families with 2 BC cases (6.6%), and two out of the nine families (22.2%) with one BC case and one OC case were carriers of pathogenic mutations. No BRCA1/2 pathogenic mutations were identified in the group of 57 (17.5%) early-onset BC patients (<35 years) reporting no first or second degree relatives affected with BC or OC (Table 2). It is probable that in this group BC is due to moderate or low penetrance genes and not to BRCA1/2 mutations.

In the sample of 326 Chilean families, our group identified 14 point pathogenic mutations. Nine have been previously reported by our group [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF], four by other groups, and one was a new mutation not previously described. Nevertheless, it is important to emphasize that two of the previously reported mutations c.3977_3980delTGAG (BRCA1) and c.8296delGT (BRCA2) have only two and one records in the BIC database, respectively. The frameshift c. 3977_3980delTGAG was identified in a Chilean family (F203), which only presented two cases of female BC diagnosed at age 36 (index case) and at age 40 (bilateral BC). The father of the index case was diagnosed with prostate cancer at age 50 (Table 3). We obtained a DNA sample only from the index case who was carrier of the aforementioned mutation. This mutation has only two records in the BIC database, one of them in an Asian population. The c.8292delGT mutation has only one record in the BIC database. This mutation was found in family F93, a BC/OC cancer family containing two BC cases diagnosed at ages 26 (index case) and 32, and one OC at 60. We only analyzed the index case and four healthy relatives (a sister, a brother and two cousins), and only the index case was a carrier of the c.8296delGT mutation.

Four of the 14 distinct pathogenic mutations found by our group were novel. To our knowledge, these have not been reported in the BIC database or elsewhere. Three of them were reported in our previous study and to date have not been reported in other studies (c.2605_2606delTT [BRCA1]; c.4185_4188delCAAG [BRCA1]; c.5667delT [BRCA2]) [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF], and c.9490delG (BRCA2) is a new novel mutation. The BRCA2 c.9490delG mutation was identified in only one BC/OC family (F211). The family presented three BC cases, two of them diagnosed under the age of 50, and one OC/BC diagnosed at age 42/50. This mutation was found in the index case (OC/BC) and in her sister affected with BC at age 38. This mutation is located in exon 25 and generates a stop at codon 3088, deleting 9% of the protein. The deleted segment includes a DNA binding domain with unique structural features for binding ssDNA and dsDNA.

Three recurrent mutations in BRCA1 (c.187_188delAG, c.2605_2606delTT, and c.3450_3453delCAAG) and three in BRCA2 (c.4969_4970insTG, c.5374_5377delTATG, and c.6503_6504delTT) contributed to 63.6% and 66.7% of all deleterious mutations of each gene, which may reflect the presence of region-specific founder effects. The most frequent mutation of BRCA1 was c.3450_3453delCAAG, found in three BRCA1(+) families (27.3%), whereas c.5374_5377delTATG was the most prevalent alteration in BRCA2 (found in four families, 33.3%). Taken together, BRCA1/2 recurrent point mutations account for 65.2% (15/23) of the BRCA1/2(+) families.

Variants of unknown significance

Six BRCA1 variants of the missense type were detected in five different families (Table 5). Of these, five were described in our previous report [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF]. In BRCA2 we found eight variants of unknown significance. Seven correspond to missense variants, some of which are described in our previous report [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF]. In 12 of the 13 families, the variants of unknown significance were present in the BC cases; in only one family (F14) the variant was detected in a healthy relative. In 9 of the 13 families, we obtained a DNA sample from healthy relatives only. In family F239, the mother with BC was a carrier of variant c.8381T>C, but her daughter who also had BC was not a carrier. The families who were carriers of variants of unknown significance did not present pathogenic mutations in the BRCA1/2 genes. The only exception was F65, which presented the c.IVS17-1G>A mutation (BRCA1). In this family, it is likely that the BC was a result of the pathogenic mutation c.IVS17-1G>A. The most interesting variant is c.4747_4749delATT, which produces the deletion of codon 1583, and corresponds to a novel variant with no BIC records and not described by other authors to date. This variant produces the deletion of isoleucine at position 1583 of the BRCA2 protein, which was found in a BC case diagnosed at age 32 with no family history of BC or OC, and was not detected in her healthy sister. Nevertheless, in her maternal lineage there are relatives with gallbladder cancer, early onset gastric cancer, leukemia and lung cancer cases. We cannot exclude the possibility that this mutation could be a pathogenic point mutation.

DISCUSSION

In the present study we conducted a screening for point mutations in the complete coding sequence of BRCA1 and BRCA2 genes in a group of 326 high risk families. Additionally, we analyzed LGR in both genes in a sample of 56 high-risk BC cases. Although there are some previous studies conducted in Hispanic American populations such as Mexico [START_REF] Ruiz-Flores | BRCA1 and BRCA2 mutation analysis of early-onset and familial breast cancer cases in Mexico[END_REF],

Colombia [START_REF] Torres | High proportion of BRCA1/2 founder mutations in Hispanic breast/ovarian cancer families from Colombia[END_REF], and Chile [START_REF] Gallardo | Incidence of BRCA1 and BRCA2 mutations in 54 Chilean families with breast/ovarian cancer, genotype-phenotype correlations[END_REF], this is the largest study conducted in high risk families in an Hispanic American population.

Evidences from different studies show that 3 -50% of familiar BC cases are accounted for by mutations in BRCA1/2 [START_REF] Fackenthal | Breast cancer risk associated with BRCA1 and BRCA2 in diverse populations[END_REF]. Prevalence of BRCA1/2 mutations among high-risk cancer patients may vary by ethnicity and study inclusion criteria. In this study the frequency of BRCA1/2 point mutations in the high-risk families was low (7.1%). This percentage depends on the number of BC cancer in the family, the presence of OC, and on the presence of male BC. The highest frequency of BRCA1/2 mutations was found in families (n=88) with 3 or more cases of BC or OC (15.9%, 95%CI [8.3 -23.6]), and 22.2% of the families (n=9) with one BC and one OC were carriers of BRCA1/2 mutations. Our results agree with those reported by other groups in Spanish and in Hispanic American populations. Diez et al. [START_REF] Diez | Analysis of BRCA1 and BRCA2 genes in Spanish breast/ovarian cancer patients: a high proportion of mutations unique to Spain and evidence of founder effects[END_REF] reported 17% (95%CI 11.9 -22.1) of BRCA1/2 mutation in the group of families with 3 or more BC cases (n=206). A study conducted in Chilean population by Gallardo et al.

[10] reported a 25% mutation frequency in families with 3 or more BC cases (5/20 [95%CI 6.0 -44.0]) [START_REF] Torres | High proportion of BRCA1/2 founder mutations in Hispanic breast/ovarian cancer families from Colombia[END_REF], and in Colombian population a 22.2% (95%CI 0 -49.4) mutation frequency was found in families with 3 BC cases (n=9). In Mexico, Ruiz-Flores et al. [START_REF] Ruiz-Flores | BRCA1 and BRCA2 mutation analysis of early-onset and familial breast cancer cases in Mexico[END_REF] reported that three of 17 (18% [95%CI 0 -35.8]) site-specific BC families were carriers of BRCA1/2 mutations.

No BRCA1/2 pathogenic mutations were found in the group of early-onset BC patients (<35 years), which suggests that this group of families are likely associated with other susceptibility genes. Previously, our group reported that in Chilean BC cases, the RAD51-135G>C polymorphism and the combined genotypes Thr/Met -E/G (XRCC3-T241M -RAD51D-E233G) were associated with an increased BC risk among women who (a) have a family history of BC, (b) are BRCA1/2negative, and (c) were <50 years at onset. These findings also increased BC risk for BC cases diagnosed before 35 years and with no family history of BC and/or OC [START_REF] Jara | Variants in DNA double-strand break repair genes and risk of familial breast cancer in a South American population[END_REF]. Also, Diez et al. [START_REF] Diez | Analysis of BRCA1 and BRCA2 genes in Spanish breast/ovarian cancer patients: a high proportion of mutations unique to Spain and evidence of founder effects[END_REF] described low frequencies (2.6%) of BRCA1/2 mutation for single women with BC and no family history.

We report four novel pathogenic mutations (two in BRCA1 and two in BRCA2). Three of them were reported in our previous study [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF], and the BRCA2 c.9490delG mutation was described for the first time. The new mutation was found in the BC/OC index case of a family that included other three BC cases and one prostate cancer case. The mutation was found in the index case who presented OC at age 42 and BC at age 50 and in her sister affected with BC at age 38. We considered c.9490delG mutation to be a pathogenic mutation because it generates a truncated protein at codon 3088, deleting 330 aminoacids at its C-terminus. The C-terminal aminoacids are critical because the nuclear localization signals (NLSs) of BRCA2 reside within the final 156 residues of BRCA2 [START_REF] Spain | Truncated BRCA2 is cytoplasmic: implications for cancer-linked mutations[END_REF]. The smallest known cancer-associated deletion of BRCA2 is predicted to remove 224 aminoacids (7% of the coding sequence) from its C-terminus [START_REF] Hakansson | Moderate frequency of BRCA1 and BRCA2 germ-line mutations in Scandinavian familial breast cancer[END_REF]. Previous reports have indicated that all of the known disease linked truncation of BRCA2 are likely to be non-functional because they do not translocate to the nucleus [START_REF] Spain | Truncated BRCA2 is cytoplasmic: implications for cancer-linked mutations[END_REF].

Therefore, the c.9490delG is probably pathogenic and disease associated.

Recurrent mutations

In our first screening of BRCA1/2 mutations in a sample of 64 high-risk BC and/or OC families from Chile we conclude that the BRCA gene mutation spectrum was heterogeneous and broad [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF]. The present study found three recurrent mutations in BRCA1 (c.187_188delAG, c.2605_2606delTT, and c.3450_3453delCAAG) and three in BRCA2 (c.4969_4970insTG, c.5374_5377delTATG, c.6503_6504delTT), which contributed to 63.6% and 66.7% of all deleterious mutations in each gene respectively, that may reflect the presence of region-specific founder effects.

The contemporary Chilean population stems from the admixture of Amerindian peoples (Asians) with the Spanish settlers (European Caucasian) initiated in the 16 th and 17 th centuries. Later migrations (19 th century) of Germans, Italians, Arabs, and Croatians have had only a minor impact on the overall population (not more than 4% of the total population) and are restricted to the specific locations of the country where they settled [START_REF] Cruz-Coke | Origen y evolución étnica de la población chilena[END_REF]. The relationships among ethnicity, Amerindian admixture, genetic markers, and socioeconomic strata has been extensively studied in Chile [START_REF] Valenzuela | Socioeconomic assortative mating in Santiago, Chile: As demonstrated using stochastic matrices of mother-child relationships applied to ABO blood groups[END_REF][START_REF] Valenzuela | Gradiente sociogenético en la población chilena[END_REF][START_REF] Valenzuela | On Sociogenetic Clines[END_REF].

The most prevalent mutation in BRCA1 was c.3450_3453delCAAG. This frameshift mutation deletes the SQ sequences known as SQ-cluster domain (SCDs) that are the preferred sites of ATM phosphorylation. It also deletes the entire C-terminal region that includes two regions known as the BRCT domains. They are involved in DNA repair pathways and bind to many proteins. The c.3450_3453delCAAG mutation was detected in three unrelated families. Two of these families presented five cases of BC and the third family presented only two BC cases but with early age at diagnosis (Table 3).

According to data from BIC database, this mutation has been identified in Norwegian, Australian, British, Spanish, African,-American and Colombian populations. Blesa et al. [START_REF] Blesa | Frequency of germ-line BRCA1 mutations among Spanish families from a Mediterranean area[END_REF] detected this mutation in two (3.9%) out of 51 high-risk families from Eastern Spain (Valencian Community). In Colombia the 3450_3453delCAAG mutation was the most commonly observed mutation in BRCA1, detected in 9.4% of the BC/OC cancer families from this country. The Chilean and Colombian populations have a high percentage of Hispanic admixture, and therefore the presence of the c.3450_3453delCAAG in both countries could be explained by a founder effect of Spanish origin.

The 2605_2606delTT was reported first by our group in the Chilean population as a novel BRCA1 mutation [START_REF] Jara | BRCA1 and BRCA2 mutations in a South American population[END_REF]. To date, we have detected this BRCA1 frameshift mutation in two Chilean families that also included cases with early age at diagnosis (Table 3). No BIC records or other description exist for this mutation. The affected families (F43 and F84) with the c.2605_2606delTT mutation had Chilean ancestry dating to many generations ago. Therefore, this mutation could have been present in the original Amerindian population that inhabited Chile prior to the colonization.

The most prevalent mutation in BRCA2 was c.5374-5377delTATG. It was found in four families. In addition, it was detected in other two Chilean families in a previous report [START_REF] Gallardo | Incidence of BRCA1 and BRCA2 mutations in 54 Chilean families with breast/ovarian cancer, genotype-phenotype correlations[END_REF], for a total of six unrelated carrier families in the Chilean population. This 4-pb deletion is also the third most frequent BRCA2 mutation in Spain [START_REF] Diez | Analysis of BRCA1 and BRCA2 genes in Spanish breast/ovarian cancer patients: a high proportion of mutations unique to Spain and evidence of founder effects[END_REF][START_REF] Diez | Heterogeneous prevalence of recurrent BRCA1 and BRCA2 mutations in Spain according to the geographical area: implications for genetic testing[END_REF][START_REF] Infante | High proportion of novel mutations of BRCA1 and BRCA2 in breast/ovarian cancer patients from Castilla-Leon (central Spain)[END_REF], and it was found in 6 of 59 (10.2%) families from different geographic areas of this country. Three of these Spaniard families are from Castilla-Leon [START_REF] Neuhausen | Haplotype and phenotype analysis of six recurrent BRCA1 mutations in 61 families: results of an international study[END_REF][START_REF] Tonin | Founder BRCA1 and BRCA2 mutations in French Canadian breast and ovarian cancer families[END_REF]. Notably, the Spanish settlers that arrived in Chile in the 16 th century came mainly from Central Spain, specifically from the former kingdom of Castilla-Leon. Therefore, it is possible that the high prevalence of c.5374-5377delTATG in Chilean families may be a consequence of a founder effect of Spanish origin. The BRCA2 c.5374_5377delTATG mutation truncates the BRCA protein at codon 1732, disrupting 3 out of 8 BRC repeats that interact with RAD51, and the entire C-terminal region.

Previous reports have indicated that BRCA2 is associated with an older age of diagnosis of BC [START_REF] Infante | BRCA1 5272-1G>A and BRCA2 5374delTATG are founder mutations of high relevance for genetic counselling in breast/ovarian cancer families of Spanish origin[END_REF]. On the contrary, in the Chilean families carriers of the c.5374_5377delTATG mutation the average age of BC onset is 42 years. Moreover, one of the positive families presents three cases with prostate cancer (Table 4).

The second recurrent mutation in BRCA2 is a 2-bp insertion of TG in nucleotide 4969 in exon 11 (c.4969_4970insTG), and it leads to a premature termination at codon 1617. This frameshift mutation is predicted to result in a protein truncation at codon 1617, deleting 53% of the protein. This mutation was previously described by Gallardo et al. [START_REF] Gallardo | Incidence of BRCA1 and BRCA2 mutations in 54 Chilean families with breast/ovarian cancer, genotype-phenotype correlations[END_REF] in an Italian/Chilean family. We detected this point mutation in two unrelated families. The affected families (F77 and F325, Table 4) had Chilean ancestry dating from many generations ago. Both families had cases with early age at diagnosis (≤ 40 years), indicating a high penetrance of this mutation. Moreover the family F325 presents one case of prostate cancer diagnosed at age 35. To our knowledge this mutation has not been described in other populations.

The spectrum of recurrent mutations identified in Chilean families differed completely from that of Hispanic families of predominantly Mexican origin from Southern California [START_REF] Weitzel | Prevalence of BRCA mutations and founder effect in high-risk Hispanic families[END_REF]. None of the six recurrent mutations identified in Hispanic families of predominantly Mexican origin in the USA were found in the Chilean families or in Hispanic families from Colombia [START_REF] Torres | High proportion of BRCA1/2 founder mutations in Hispanic breast/ovarian cancer families from Colombia[END_REF], implying that the mutation spectra among Hispanic populations in South America and the USA may differ.

Variants of unknown significance

In our screening of the BRCA1/2 genes, we found fourteen variants of unknown significance, six in BRCA1 and eight in BRCA2 (Table 5). In 12 of the 13 families the variants of unknown significance were identified exclusively in healthy relatives, and therefore it was not possible to establish whether they were associated with the cancers present in the families.

Only in family F239 the proband with BC was carrier of variant c.8381T>C, but her daughter who also had BC was not a carrier. In this family it is likely that the variant is not the genetic cause of the BC. The most interesting variant was c.4747_4749delATT in exon 11 of BRCA2, which deletes isoleucine at position 1583 of the BRCA2 protein. The BRCA2 protein directly binds to human RAD51 through its eight BRC repeats located at the 5' region of exon 11. The number, sequence and spacing between these motifs is conserved during vertebrate evolution, suggesting its functional relevance [START_REF] Shivji | DNA recombination, chromosomal stability and carcinogenesis: insights into the role of BRCA2[END_REF].

BRC3 and BRC4 (amino acids 1517 -1551) repeats have the strongest interaction with RAD51 [START_REF] Powell | BRCA2 keeps Rad51 in line. High-fidelity homologous recombination prevents breast and ovarian cancer?[END_REF]. Pellegrini et al. [START_REF] Pellegrini | Insights into DNA recombination from the structure of a RAD51-BRCA2 complex[END_REF] have solved the crystal structure of the BRC4 peptide sequence bound to the RAD51 protein. This structure demonstrates a series of hydrophobic and hydrophilic interactions involving the hairpin structure of BRC4. Contact between BRC4 and RAD51 is maintained from Leu1521 to Glu1548 of the BRC4 sequence. The c.4747_4749delATT mutation deletes a hydrophobic amino acid (isoleucine) at position 1583, near to BRC4. This mutation was found only in a BC case with no family history of BC or OC cancer but with early age at diagnosis. Considering that this mutation does not result in a protein truncation, it is not possible to classify it as pathogenic. Nevertheless, we cannot exclude the possibility that this mutation could be a pathogenic point mutation. Functional assays are necessary to determine how this mutation could affect critical BRC4 interaction sites.

Large genomic rearrangements

To determine the impact of BRCA1/ [START_REF] Peralta | Cáncer de mama: resultados del programa de pesquisa y tratamiento del Servicio de Salud Central[END_REF] LGRs in Chilean population, 56 hereditary BC and/or OC Chilean families negative for small mutations were screened using the MLPA technique. This represents the first study to screen for LGRs in BRCA1/2 in Chile and South America. No LGRs were found in either BRCA1 or BRCA2. In different populations it has been reported that LGRs in BRCA1 account for 0 -27% of all disease-causing mutations, while LGRs in BRCA2 are rare and play a minimal role in BC/OC [START_REF] Hansen | Large BRCA1 and BRCA2 genomic rearrangements in Danish high risk breast-ovarian cancer families[END_REF][START_REF] Sluiter | Large genomic rearrangements of the BRCA1 and BRCA2 genes: review of the literature and report of a novel BRCA1 mutation[END_REF]. The variation in reported percentages may be attributable to ethnicity, inclusion criteria or technique used for LGRs detection. In this study, the mutation analysis for LGRs in BRCA1 and BRCA2 was performed using MLPA, which is the most common technique for LGR detection in the BRCA genes. The literature recommends screening for

LGRs in BRCA1 in families with multiple cases of BC/OC and average age at diagnosis of 50 years or less. It is also recommended to screen for LGRs in BRCA2 in families with at least one case of male BC. In our study only 36 out of the 56 analyzed cases belong to families with at least three BC/OC cases, five of which have OC cases in their families.

With respect to ethnicity, BRCA1/2

LGRs play little or no role in hereditary BC in Afrikaner [START_REF] Sluiter | Large genomic rearrangements of the BRCA1 and BRCA2 genes: review of the literature and report of a novel BRCA1 mutation[END_REF], Finnish [START_REF] Laurila | Search for large genomic alterations of the BRCA1 gene in a Finnish population[END_REF][START_REF] Pylkas | Analysis of large deletions in BRCA1, BRCA2 and PALB2 genes in Finnish breast and ovarian cancer families[END_REF][START_REF] Lahti-Domenici | Exclusion of large deletions and other rearrangements in BRCA1 and BRCA2 in Finnish breast and ovarian cancer families[END_REF],

French-Canadian [START_REF] Moisan | No Evidence of BRCA1/2 genomic rearrangements in high-risk French-Canadian breast/ovarian cancer families[END_REF], and Iranian [START_REF] Pietschmann | Mutation analysis of BRCA1 and BRCA2 genes in Iranian high risk breast cancer families[END_REF] populations. The high proportion of LGRs detected in the Hispanic population of the USA can be explained by a single founder deletion of exons 9-12 [START_REF] Weitzel | Evidence for common ancestral origin of a recurring BRCA1 genomic rearrangement identified in highrisk Hispanic families[END_REF]. In Spain, the frequency of LGRs affecting the BRCA1/2 genes have been estimated at around 2% in BRCA1 and 1.5% in BRCA2 in cases previously testing negative for BRCA1/2 point mutations [START_REF] Valle | Identification and comprehensive characterization of large genomic rearrangements in the BRCA1 and BRCA2 genes[END_REF]. In Asian populations, LGRs account for 3% of case in Singapore [START_REF] Lim | Identification of novel BRCA large genomic rearrangements in Singapore Asian breast and ovarian patients with cancer[END_REF] and 0.8% in Korea [START_REF] Seong | Comprehensive mutational analysis of BRCA1/BRCA2 for Korean breast cancer patients: evidence of a founder mutation[END_REF]. In the Chilean group screened in this study, no LGRs were found (0/56) in either BRCA1 or BRCA2. Is likely that such mutations play no role in BC/OC or have a low frequency in the actual Chilean population.

ACNOWLEDGEMENTS

The authors thank the many families who participated in the research studies described in this article. We acknowledge the Breast Cancer Group of CONAC: Maria Teresa Barrios, Angelica Soto, Rossana Recabbarren, and Leticia Garcia; and Lorena


Dr Michael Bramwell Sprakes
email: michael.sprakes@leedsth.nhs.uk

Alexander C Ford

Nicole C Suares

Lisa Warren

CF Dan Greer

Clare Donnellan

Jason Jennings

Peter Simon Everett

John Hamlin

Jsr Donnellan

S M Jennings

PJ Hamlin Everett

Costs of care for Crohn's disease following institution of infliximab: A single centre UK experience

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.

Infliximab (Remicade®, Pennsylvania, USA) is licensed in the UK to treat severe luminal and perianal fistulising CD. It is a chimeric monoclonal antibody directed against tumour necrosis factor alpha (TNFα) and is given as an intravenous infusion, initially over 2 hours. Recent data from our centre suggest, however, that subsequent infusions can be given safely over 30 minutes. (3) Data from randomised controlled trials (RCT) have confirmed that infliximab is more effective than placebo for the induction of remission of active CD, [START_REF] Targan | A short-term study of chimeric monoclonal antibody cA2 to tumor necrosis factor alpha for Crohn's disease. Crohn's Disease cA2 Study Group[END_REF] healing of fistulising CD, [START_REF] Present | Infliximab for the treatment of fistulas in patients with Crohn's disease[END_REF] and in preventing relapse of disease activity once remission has been achieved. [START_REF] Hanauer | Maintenance infliximab for Crohn's disease: the ACCENT I randomised trial[END_REF] At present, there are few published studies reporting the effect of the use of infliximab in CD on subsequent health service CD-related costs. We have examined this issue in a large cohort of CD patients treated with infliximab at a single tertiary referral centre in the UK. Crohn's disease-related health services resource data were then collected retrospectively from case notes and computer records for all 100 patients for the 12 months prior to commencement of infliximab, and for the 12 months after commencement of therapy. These included inpatient admissions (medical or surgical), day case admissions for infliximab infusions, outpatient visits, surgical procedures (including intestinal resections and examinations under anaesthesia (EUAs)), endoscopic procedures (oesophagogastroduodenoscopy (OGD), enteroscopy, colonoscopy, sigmoidoscopy and capsule endoscopy), radiological investigations (plain X-ray, ultrasound, barium studies, computed tomography (CT), and magnetic resonance imaging (MRI)), blood tests, and costs of all prescribed medications (prednisolone, budesonide, hydrocortisone, 5-aminosalicylate preparations, azathioprine, 6-mercaptopurine, methotrexate, and mycophenolate mofetil).

National Health Service reference costs for 2006 to 2007 were applied to all these data in order to calculate the total CD-related health services costs per patient. The cost of infliximab was excluded from these analyses, but the mean cost of infliximab use over the 12 months of therapy in this cohort of 100 patients was calculated. A paired samples t-test was used to ascertain any statistically significant differences in the costs for each individual in the 12 month period prior to commencement of infliximab therapy and the 12 months after commencement of therapy.

Patients requiring infliximab undergo specific investigations to stage their disease prior to therapy being instituted. They may also have more aggressive disease that requires biological therapy earlier on in the disease course, which will tend to skew the CD-related costs prior to infliximab commencement, because the costs of the investigations that led to the initial diagnosis of CD will be included. We therefore performed pre-planned subgroup analyses with the costs of investigations that may be performed as part of the work-up prior to infliximab commencement, such as EUA, MRI, and colonoscopy, removed. We conducted a further subgroup analysis with the group of patients who had received infliximab in the first year following a diagnosis of CD removed from the analysis, as costs may be higher in these individuals. Finally, we compared total costs post infliximab in those who had received episodic and those who had scheduled maintenance therapy, as well as the total number and costs of infusions in these two groups of patients, and the total costs post infliximab in responders and non-responders to therapy. All statistical analyses were performed using SPSS for Windows version 14.0 (SPSS inc, Chicago, IL, USA).

RESULTS

Demographic data of involved individuals

Demographic data for the 100 patients included in the study are provided in Table 1.

There were 61 female patients, 32 were current smokers, and 53 were receiving corticosteroids (hydrocortisone, prednisolone, or budesonide) at commencement of infliximab. Of these 100 patients, 57 received infliximab as scheduled 8-weekly maintenance therapy, and the remaining 43 received episodic treatment. There were a total of 518 infliximab infusions administered to these 100 patients during the 12 months of the study (mean 5.2 infusions per patient). Sixty of the 100 patients had undergone at least one previous surgical intervention (either intestinal resection or EUA) at some point following their initial diagnosis, and prior to the commencement of infliximab therapy, with 36 (60%) of these having had more than one operation. 15 patients received infliximab in the first year following diagnosis, with 5 of these patients requiring infliximab during their index admission with acute severe CD. The commonest disease phenotype in the cohort, as determined by the Montreal Classification, was A2, L3, B1 (n = 30). This translates as ileocolonic disease of inflammatory nature in the 16-40 age group. Almost 40% of the cohort had fistulising disease as denoted by the P modifier.

Effect of infliximab on total CD-related costs

The mean cost of CD-related care in the 100 patients in the 12 months pre infliximab was £4965. Cost savings were achieved in all areas of patient care, with highly statistically significant reductions observed in the costs of CD-related endoscopic procedures, radiological investigations, outpatient visits, and inpatient admissions (Table 2). The reduction in CD-related total costs was highly significant following infliximab therapy, with When costs of diagnostic tests that may have been performed as part of the work-up of patients prior to the commencement of infliximab were excluded from the analysis there remained a significant cost saving (£3431 pre infliximab compared with £2211 post, P = 0.01) When the 15 patients who commenced infliximab within the first year of diagnosis of CD were considered, the mean costs of care in the year prior to commencement of infliximab were higher, but not statistically significantly different, compared with the other 85 patients (£5797 versus £4825, P = 0.43). Excluding these 15 individuals from the analysis, the mean cost savings per person following commencement of infliximab were £3055. No statistically significant difference in costs post infliximab was detected between the scheduled and episodic groups (£3339 versus £2906, P = 0.44). A total of 357 infusions were given to the scheduled group (mean 6.3 infusions), compared with 161 (mean 3.7) in the episodic group (P < 0.001). The mean difference in costs of infliximab in the two groups of patients was statistically significant (£10 940 in scheduled versus £6514 in episodic, P < 0.001).

There were seven patients who were either primary or secondary non-responders to infliximab at 12 months. In addition, 10 patients had to discontinue therapy due to intolerable adverse events. Costs post infliximab were compared between the 83 patients with a continued response to infliximab and the non-responders, with a mean cost at 12 months post infliximab in responders of £1656 versus £3608 in non-responders (P = 0.02).

Effect of infliximab on CD-related investigations

There were a total of 377 diagnostic tests performed in the 100 included patients in the year prior to infliximab therapy, compared with 75 in the year following commencement of infliximab, a decrease in total CD-related investigations of 80% (Table 3). All 100 patients had a chest X-ray (CXR) prior to commencement of infliximab, to exclude tuberculosis, and 67 plain X-rays were requested for other CD-related indications. A total of 23 plain X-rays were performed in the year post infliximab, a decrease of 66% if the screening CXRs prior to infliximab administration are excluded. There was an 80% reduction in the usage of CT scanning, and a 55% reduction in need for MRI scans.

Effect of infliximab on CD-related inpatient admissions

There were 90 CD-related admissions to acute hospital beds in the 12 months prior to commencement of infliximab, with a mean total length of stay of 14 days per admission for medical admissions, and 7 days per admission for surgical admissions (Table 4). In the 12 months after commencement of infliximab therapy there were 98 admissions. However, only 22 of these were CD-related acute medical or surgical admissions, with 76 of the 98 admissions being for the scheduled administration of infliximab, prior to the set up of the Immune Mediated Inflammatory Diseases centre in 2005. The mean total length of stay post infliximab was 8 days for medical admissions and 9 days for surgical admissions.

Effect of infliximab on CD-related surgery

In the 12 months pre infliximab therapy there were 47 surgical procedures performed, either EUA or intestinal resection, and in the 12 months following commencement of infliximab there were only 13 procedures performed. There were 41 EUAs performed pre infliximab, compared with 9 EUAs in the 12 months post infliximab (P < 0.001). There were

DISCUSSION

This study, conducted in a large single centre cohort of CD patients, has demonstrated a mean total cost saving per patient in excess of £2750 in the 12 months following infliximab therapy. Highly significant savings were observed in inpatient stays, outpatient visits, endoscopic procedures, and radiological tests. The costs of hospitalisations for CD accounted for almost 50% of overall costs of care prior to infliximab therapy, which is of a similar magnitude to a previous cost analysis in inflammatory bowel disease. [START_REF] Bassi | Cost of illness of inflammatory bowel disease in the UK: a single centre retrospective study[END_REF] We also demonstrated a significant cost saving in terms of the need for any surgical intervention, particularly EUAs, in the year following the initiation of infliximab therapy. There are a number of work-up costs involved before initiating infliximab therapy. However, even when we assumed that EUA, MRI, and colonoscopy were necessary work-up investigations, and excluded the cost of these from the total costs prior to commencement of infliximab, there was still a statistically significant cost saving in the first year post therapy. Indeed, there are likely to be similar work-up costs before commencement of any disease modifying agent in CD patients, so these costs are not necessarily unique to patients commencing biological therapy.

These data provide the largest single centre experience of the CD-related costs of care following infliximab therapy. As the Leeds General Infirmary is a tertiary referral centre for inflammatory bowel disease, the dataset includes patients from a relatively large geographical region in the North of England. Strengths of the study include consistent data collection, similar patient work-up prior to therapy, consistent availability of resources for all patients, and the application of National Health Service reference costs to the data. Limitations of the study include the fact that our centre includes a tertiary referral population, which may therefore not be generalisable to a standard secondary care population. In addition, the patients acted as their own controls, meaning that we cannot exclude the possibility that patients who had severely active disease at the time biological therapy was commenced improved spontaneously as a result of regression to the mean. However, approximately onethird of the patients in this study had fistulising or stricturing disease, and it seems unlikely that patients such as these would improve without the institution of either medical or surgical therapy. In fact, when costs in the 12 months after commencement of infliximab were compared between those who maintained a response and continued therapy, with those who discontinued the drug, these were significantly lower in the former group of individuals. In addition, it would be unethical to include a control group of patients with severe disease, who would not be considered for biological therapy, a treatment that we know from rigorously designed and conducted RCTs is efficacious in this situation. Finally, the costs of care for CD patients may vary between centres, depending on local resource availability, for instance MRI enterography versus small bowel barium study.

We did not include the cost of infliximab in the data analysis. Infliximab, like all biological therapies, is an expensive drug. The mean cost of infliximab per year of treatment in our cohort was almost £9000 per person, though vial sharing saves our Immune Mediated Inflammatory Diseases centre approximately £120,000 per year for all CD patients treated.

Due to the high drug cost, it is unlikely that such therapies will ever demonstrate an overall net saving, in terms of costs of care. However, extrapolations made regarding cost per quality-adjusted life year in Markov modelling studies, [START_REF] Lindsay | Health-economic analysis: cost-effectiveness of scheduled maintenance treatment with infliximab for Crohn's disease--modelling outcomes in active luminal and fistulizing disease in adults[END_REF][START_REF] Bodger | Cost-effectiveness of biological therapy for Crohn's disease: Markov cohort analyses incorporating United Kingdom patient-level cost data[END_REF] and health-related quality of life scores, suggest that infliximab is a cost effective treatment strategy for CD in the longer term. Furthermore, recent guidance from the National Institute for Health and Clinical Excellence (NICE), [START_REF]Crohn's disease -infliximab (review) and Adalimumab (review of TA40)[END_REF] allows for equal first line therapy with biologic agents in CD, depending on individual drug costs for the patient. This, coupled with the development of generic biologicals in the future, may contribute to driving down drug costs in the UK. At the present time, there have been few other studies examining CD-related costs of care following infliximab therapy. One previous study demonstrated a reduction in hospitalisations, diagnostic procedures, and EUAs following infliximab therapy, with a reduction in the total costs of care of approximately £130 per patient, though this included the cost of infliximab. (13) However, there are some limitations to this study. The duration of follow up was only 6 months after administration of infliximab, so extrapolating whether this cost saving holds true for long-term therapy is not possible. In addition, the mean number of infusions per patient was only 1.7 during this period, which is not the accepted regimen for induction of remission. ( 6) Most CD patients treated with infliximab in the UK will receive 3 dose induction, followed by scheduled 8-weekly infusions for responders, therefore increasing the drug cost. Analysis of a small cohort of CD patients treated with infliximab 12 months before and after administration of infliximab demonstrated reductions in hospitalisations, surgeries, and diagnostic testing, but an overall increase in expenditure when the cost of infliximab was taken into account. ( 14 but no reference costs were applied to the data in this study. [START_REF] Rubenstein | Infliximab decreases resource use among patients with Crohn's disease[END_REF] Predicting who will respond to therapy remains an elusive goal. Selecting only patients that are likely to do well with infliximab may reduce overall costs to the health service. However, whilst there are some clinical parameters that may help predict a severe disease course, [START_REF] Beaugerie | Predictors of Crohn's Disease[END_REF] and hence who may benefit from early anti-TNFα therapy, at present there are no clinically useful serological or genetic markers to predict response to infliximab, though subgroup analysis of the SONIC data suggests that patients with an elevated CRP at commencement of therapy are more likely to respond. [START_REF] Colombel | Infliximab, azathioprine, or combination therapy for Crohn's disease trial[END_REF] Mucosal healing remains one of the best modalities of assessing the success of therapy and, where achieved, appears to reduce need for hospitalisation or surgery. [START_REF] Schnitzler | Mucosal healing predicts long-term outcome of maintenance therapy with infliximab in Crohn's disease[END_REF] Complete mucosal healing in combination with 19) could be used to determine which patients have achieved deep remission, and who therefore may be able to discontinue anti-TNFα therapy, with a lower risk of subsequent disease relapse. Conversely, lack of mucosal healing may help identify patients in whom infliximab therapy is failing, and in whom escalation in either dose or frequency of infusions, or a switch to an alternative biologic agent should be considered. Using these strategies will optimise the use of infliximab therapy, in line with recent guidelines from NICE, perhaps providing more targeted cost effective health care.

In conclusion, these data demonstrate, in the largest single centre cohort to date, that infliximab therapy reduces CD-related costs of care in a 12 month period following the initiation of therapy, but that these savings are insufficient to render the use of infliximab in CD patients cost-neutral, and a regression to the mean effect cannot be excluded.

Conflicting Interest

  disease (CD) is a chronic relapsing and disabling disease of the gastrointestinal tract. It is often diagnosed in childhood, or early adulthood, and may therefore be associated with significant long-term costs of care. (1) Many patients with aggressive disease require substantial amounts of sickness-related absence from work, increasing the economic, as well as social, burden of the disease. (2) Maintaining disease remission and minimising hospitalisations, surgical interventions, and toxicity of therapy are key treatment aims, in an attempt to maximise quality of life.

  The study was conducted at the Leeds General Infirmary, a large teaching hospital serving a population of approximately 800 000 people in the city of Leeds, West Yorkshire, England. Infliximab has been used as a treatment for luminal and fistulising CD at our centre since 1999. Since 2005, every CD patient receiving infliximab attends the Immune Mediated Inflammatory Diseases centre as a day case visit. The service is coordinated by a specialist nurse and has a number of benefits, including vial sharing of infliximab and administration of the infusion during the visit, rather than admission to an inpatient bed, both of which may reduce the costs of treatment. Data on 100 consecutive patients who commenced infliximab between 1999 and 2008, were collected. These included patient demographics (sex, current age, age at diagnosis of CD, and smoking history) history of previous CD-related surgery, indication for use of infliximab, whether the patient received scheduled 8-weekly infusions or intermittent episodic therapy, baseline C-reactive protein (CRP), Harvey Bradshaw Indices (HBI), (7) any use of steroids or immunomodulators on commencement of infliximab, extraintestinal manifestations of CD, and CD phenotype according to the Montreal classification of disease.[START_REF] Silverberg | Toward an integrated clinical, molecular and serological classification of inflammatory bowel disease: Report of a Working Party of the 2005 Montreal World Congress of Gastroenterology[END_REF]

  cost saving per patient in excess of £2750. This saving excluded the mean cost of infliximab therapy per patient for the 12 months of study inclusion, which was £9037 (range £874 to £36708). The largest cost savings occurred in inpatient admissions in the 12 months following infliximab, which were almost £2000 per patient, a decrease of approximately 75% when compared with the cost of inpatient admissions in the 12 months prior.

  terms of intestinal resections pre or post infliximab (6 operations pre infliximab compared with 4 operations post infliximab).

  ) Rubenstein et al. demonstrated a significant decrease in resource use in a cohort of infliximab-treated CD patients in Chicago;

  parameters, such as normal CRP and faecal calprotectin, (

  Abbot. Support for the Inflammatory Bowel Disease Nurse Specialist at the Leeds General

Table 1 . Demographics of 100 involved individuals Characteristics N=100

 1

	Female

Table 2 . Total CD-related costs in 100 CD patients 12 months pre and post IFX

 2

		Mean cost per	Mean cost per	Mean cost-	95%	P value
		person pre-	person post-	saving per	confidence
		infliximab	infliximab	person post-	interval
				infliximab
	Medications	£598.71	£448.45	£150.26	£54.59 to	0.002
	costs*				£245.93
	Radiology	£315.79	£89.46	£226.33	£170.48 to	< 0.001
	costs				£282.18
	Endoscopy	£397.64	£77.86	£319.78	£227.26 to	< 0.001
	costs				£412.30
	Surgery costs	£536.88	£124.06	£412.82	£116.00 to	0.007
					£709.64
	Outpatient visit	£479.30	£372.67	£106.63	£53.78 to	< 0.001
	costs				£159.48
	Blood test	£48.52	£37.13	£11.39	£2.77 to	0.01
	costs				£20.01
	Inpatient	£2588.36	£670.90	£1917.46	£1219.63 to	< 0.001
	admission				£2615.29
	costs
	Day case	£0	£393.86	-£393.86	-£453.18 to -	< 0.001
	infusion costs				£334.54
	Total costs	£4965.20	£2214.37	£2750.83	£1856.91 to	< 0.001
					£3660.93

Table 3 . Investigations in 100 CD patients 12 months pre and post IFX therapy

 3

		Pre IFX	Post IFX	% Reduction
	Endoscopic investigations:
	Colonoscopy	44	8	81.8
	OGD	13	4	69.2
	Flexible sigmoidoscopy	23	2	91.3
	Capsule endoscopy	2	1	50.0
	Total number	82	15	81.7
	Radiological investigations:
	Plain X-ray	167	23	86.2
	MRI	31	14	54.8
	CT	50	10	80.0
	Barium studies	37	10	73.0
	Total number	285	57	80.0
	Other*	10	3	70.0
	Totals	377	75	80.1
	*Other studies include DEXA scans, Hydrogen urease breath tests, water soluble enemas,
	skin biopsies

Table 4 . Inpatient admissions in 100 CD patients 12 months pre and post IFX

 4

	Pre IFX	Post IFX