André De Palma
email: andre.depalma@ens-cachan.fr

Matthieu De Lapparent
email: matthieu.de-lapparent@ifsttar.fr.

Nathalie Picard
email: nathalie.picard@u-cergy.fr

Modeling real estate investment decisions in households

Introduction

There is substantial literature on modelling individual residential location choices. We restrict here our attention to some key aspects discussed below, which remain overlooked in the litterature.

First, the set of decisions related to residential location in a multiperiod setting typically involve a very large number of alternatives. At a given date, a choice entails several dimensions: where to locate, which dwelling types and which tenure status. A fine tuned demand analysis of housing choices, would consider dozens of small geographical units for potential locations, at least two tenure types (own or rent) and at least two dwelling types (apartment or house).

Another aspect is: who makes residential location related decisions. Recent litterature (see [START_REF] Picard | Couple residential location and spouses' workplaces[END_REF], de Palma et al. ( 2013)) shows that accounting for intra-household negotiation processes provide a new understanding about how residential location choices may result from consensus reached by household members. Most of research work is yet based on unitary household approaches that consider there is a single decision maker in the family.

Another point is about the dynamics of these choices. One may reasonably assume that a household optimises over its lifecycle the path of decisions about labour supply, goods/services and floor space by dwelling type consumptions, tenure statuses [START_REF] Di Salvo | Analysis of the dynamics of housing tenure choice in britain[END_REF], where to locate dwellings, whether housing is used as a financial asset and whether it is left for bequest to heirs [START_REF] Arrondel | Consumption and investment motives in housing wealth accumulation: A french study[END_REF]). All these decisions are subject to per-period financial constraints.

Also, housing markets are segmented but interacting with each other and with other markets such as the labour market, transport activity and land development. Prices are not always sufficient to clear the markets. Most models do not question equilibrium, or consider only partial equilibria. There are relatively few spatial general equilibrium or micro-simulation models with both heterogeneous agents and markets.

Data requirements would be very stringent if one would carry out a complete analysis at a very fine level of analysis. In general, one uses several statistical sources and data merging procedures to prepare samples. The types of model and their focus are often adjusted to available data.

The importance of transportation costs has been pointed out by [START_REF] Weisbrod | Tradeoffs in residential location decisions: transportation vs. other factors[END_REF], [START_REF] Anas | Discrete choice models and the housing price and travel to work elasticities of location demand[END_REF], [START_REF] Waddell | Incorporating land use in metropolitan transportation planning[END_REF], [START_REF] Lee | Residential mobility and location choice: a nested logit model with sampling of alternatives[END_REF], inter alia. They focused on the induced effects of the transportation market on residential location choices. Accessibility to and from a residential location greatly affects households choices. [START_REF] Quigley | Consumer choice of dwelling, neighborhood and public services[END_REF], [START_REF] Nechyba | Community choice and local public services: A discrete choice approach[END_REF], [START_REF] Brueckner | Why is central Paris rich and downtown Detroit poor? An amenity-based theory[END_REF] focus on the effects local amenities and neighbourhood to explain the choice of a specific location. They show how extrinsic attributes of dwellings play a significant role in spatial distribution of housing demand and on the corresponding market prices. [START_REF] Bureau | Evaluation de l'impact des politiques "quartiers verts" et "quartiers tranquilles" sur les prix de l'immobilier à paris[END_REF] find that market prices of owned dwellings are sensitive to their surrounding environment.

de [START_REF] De Palma | Residential change and economic choice behavior[END_REF], [START_REF] Ben-Akiva | Analysis of a dynamic residential location choice model with transaction costs[END_REF] recognized that transaction costs and moving costs may affect the dynamics of location choices since they increase the duration of stay at one location. Any fiscal distorsion that increases market price (either temporarily or permanently) needs to be compensated by either a longer stay period to return on investment or larger streams of income.

Duration of stay at one location is inversely proportional to the levels of transaction prices and moving costs effective in the housing market. As a consequence, households that rent a dwelling are more mobile than households that purchase a dwelling, because of lesser transaction costs.

de [START_REF] De Palma | Discrete choice models with capacity constraints: An empirical analysis of the housing market of the greater paris region[END_REF] recently showed that existence of capacity constraints in housing supply changes considerably location choices.

Analysis of choices of dwelling and tenure types have also been subject to several analysis, e.g. [START_REF] Ioannides | Estimating the consumption and investment demands for housing and their effect on housing tenure status[END_REF], [START_REF] Henderson | A model of housing tenure choice[END_REF], [START_REF] Mills | Housing tenure choice[END_REF], [START_REF] Cho | Joint choice of tenure and dwelling type: a multinomial Logit analysis for the city of Chongju[END_REF], [START_REF] Skaburskis | Modelling the choice of tenure and building type[END_REF]. They discussed the effects on individual demand functions of the dwelling attributes (such as number of rooms, presence of garden/balcony, age of the building, etc..). They mainly discuss the effects of intrinsic characteristics and how they may differ across socioeconomic and demographic groups. [START_REF] Mcfadden | Modelling the choice of residential location[END_REF], [START_REF] Weisbrod | Tradeoffs in residential location decisions: transportation vs. other factors[END_REF], [START_REF] Thisse | Toward a unified theory of economic geography and urban economics[END_REF], Dantan et al. (2010), Dantan & Picard (2010) also discussed in a more general way existing tradeoffs that may have consequence on location choices, including differences across individuals with different socioeconomic characteristics. [START_REF] Linneman | The impacts of borrowing constraints on homeownership[END_REF], [START_REF] Zorn | Mobility-tenure decisions and financial credit : Do mortgage qualification requirements constrain homeownership?[END_REF], [START_REF] Brueckner | Consumption and investment motives and the portfolio choices of homeowners[END_REF], [START_REF] Gobillon | L'impact des contraintes d'emprunt sur la mobilité résidentielle et les choix entre location et propriété[END_REF], discussed the dynamics of housing expenditures of homeowners in presence of credit rationing. He shows how the latter may not only affect the demand for floor space but also the choice of a tenure type (for a given demand of floor space) and less directly the choice of a dwelling type (since, on average, consumed floor space is larger for houses than for apartments).

In this paper, we propose a theoretical microeconomic model to analyze residential choices of households in a dynamic context with perfect information. The decision maker is a household. We do not envisage intra-household negotiation between members. We consider that the household lives two periods. Addressing simultaneously economic choices of residential location, dwelling and tenure and their dynamics, while accounting for interaction with transportation market, with demand for local amenities, and with financial investment constraints represent the main focus of the paper.

At the beginning of each period, household is endowed with a per-period utility function that depends on the level of amenities, the level of floor space, and the level of consumption of a composite good. It is faced with continuous and discrete decisions: choices of optimal quantity of floor space, consumption level of an outside composite good, and the choices of residential location, tenure and dwelling types. Indeed, these choices are subject to budget and technical constraints. In our model, borrowing is allowed in the first period, but not in the second one: no debt can be left when at the beginning of a third period. We also assume that the interest rate is higher when borrowing for a dwelling than when saving/borrowing on the money market (this is a form of credit imperfection). We do not consider any selection mechanism: every household can borrow money for housing purpose. Transaction costs apply to real estate (acts made by notaries or lawyers but also local taxes). We consider existence of moving costs whenever changing home location in the second period. Of course, transportation costs affect the choices of households. Another feature of our model is the introduction of a bequest motive. The household leaves a bequest to heirs at the end of his/her lifecycle for altruistic reasons, which enters in the third period utility. The bequest consists in money and/or in real estate.

The household program is to maximise the sum of discounted flows of utility over its lifecycle subject to an inter-temporal budget constraint. The problem can be solved in two preliminary steps, then by backward induction. First, we compute for each combination of locations, tenure and dwelling types, optimal demands for floor space and consumption of a composite good. Second, we derive the associated indirect utility functions. The household chooses the combination of locations (hence levels of amenities), tenure and dwelling types that maximises its utility. The We detail our theoretical model in Section 2. We discuss the mathematical formulation and related solutions of the household optimisation program. We choose functional forms which lead to analytically tractable theoretical model of intertemporal utility maximization. We study the effects of the most relevant ingredients of residential location choices: demand for local amenities, financial constraints (pay-down requirement, borrowings and savings), housing and goods/services prices, income, transaction costs, transportation and moving costs.

In Section 3, we then turn to an empirical application. We present data in the first subsection. Our main data source is the 2006 French Housing Survey, which comprises a short retrospective survey back to 2002. We focus on the population living in Paris region during these years. Due to lack of statistical information about precise locations of dwellings, we restrict our analysis to the dynamics of tenure and dwelling types choices given location choices. Also, since the survey is based on revealed preferences, we need to buid conterfactuals and impute values of the attributes of unchosen alternatives. To this extent, we use data on credit from the survey and from the Côtes Callon. The latter provides average observed market prices by tenure type for 2002 and 2006. We also address the problem of missing information about precise locations of dwellings: we only have information about the "département" (large French administrative unit) where households live. Therefore we cannot compute any reliable transportation costs. The moving costs are accounted for through a dummy variable indicating whether the household moved between 2002 and 2006. In a second subsection, we propose an econometric specification of the theoretical model accounting for data availability and identification constraints. Our approach is based on random utility maximization. It takes the form of a Nested Logit choice model, see for example [START_REF] Mcfadden | Modelling the choice of residential location[END_REF][START_REF] Train | Discrete Choice Methods with Simulation, number 9780521816960[END_REF]. We discuss estimation results in the third subsection.

We conclude in a last section and argue that our theoretical model can be used as a building block for detailed analysis of residential location choices.

A microeconomic model of residential choices

We consider a household living 2 periods j ∈ {1, 2}. A bequest B is transmitted to heirs at period 3. At the beginning of each period, the household has to choose its dwelling location, its dwelling type, its tenure type, and the levels of consumption of floor space, composite good, and local amenities. The latter are actually not really chosen but instead determined by residential location choices.

Household preferences

At the beginning of every period j ∈ {1, 2}, a household obtains utility u from consumption of floor space Q, local amenities x, and a composite good C (exclud- ing dwelling). We define by u j (x j , C j , Q j ) the household utility in period j. We assume that u j (•) is strictly increasing and quasi-concave in its arguments.

The utility of a household over its lifecycle is measured at the beginning of the first period. It is defined as the discounted sum period-specific utilities plus the level of bequest B left to heirs at period 3 (bequest is transmitted once the household disappears). We denote by β ∈ [0, 1] the discount factor. The resulting intertemporal utility function U (•) is defined as

U (x 1 , C 1 , Q 1 , x 2 , C 2 , Q 2 , B) = u 1 (x 1 , C 1 , Q 1 ) + βu 2 (x 2 , C 2 , Q 2 ) + β 2 γ 2 ln (B) (1)
and we further assume that u j (•) has a Cobb-Douglas mathematical formulation

u j (x j , C j , Q j , B) = ψ j (x j ) + α j ln (C j ) + (1 -α j ) ln (Q j ) , j ∈ {1, 2} . (2)
If the household does not change dwelling in period 2, floor space consumption is determined once for all in period 1, i.e. Q 2 = Q 1 . We assume that the level of consumed amenities may change over time whenever location is the same. The intertemporal utility function simplifies to

U (x 1 , C 1 , Q 1 , x 2 , C 2 , Q 1 , B) = u 1 (x 1 , C 1 , Q 1 ) + βu 2 (x 2 , C 2 , Q 1 ) + β 2 γ 2 ln (B) (3)

Budget constraints

Choices of household are made under finite budget constraints. Before writing explicitly the inter temporal budget constraint of the household, we need first to define further notations. For each period j ∈ {1, 2}, we assume that tenure type (k j ) corresponds to either owning (o j ) or renting (r j ), dwelling type (d j ) corresponds to either house (h j ) or flat (f j ), and location corresponds to a predetermined geographical zone l j in a region that is divided into L mutually exclusive units. Let π k j ,d j ,l j t

x j,l j be the price (per unit of surface) in period t ∈ {1, 2, 3} , t > j, of a dwelling located at l j that is occupied by the household in period j. Whatever d j , k j or l j , the household is faced with additional transaction costs when considering dwelling consumption. These are of two types. The first applies only once to the transaction itself when purchasing or renting a dwelling, often under the form of a proportional tax rather than a lump sum. Let µ k j ,d j ,l j j > 0 be this unit tax level. The second applies to the occupation of the dwelling and is recurrent over time as long as the dwelling is occupied. It mainly models local taxes. Let then κ k j ,d j ,l j j be the unit tax level.

Prices of the composite good are defined as p j , j ∈ {1, 2}1 .

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The household is endowed a strictly positive level of (exogenous) income R j at the beginning of each period j ∈ {1, 2}. As household members have to participate in out-of-home activities, e.g. work or education, D j x j,l j , y j > 0 is a transportation cost in period j for a residential location l and a set of locations to be reached y j , j ∈ {1, 2}2 .

Let also S j model monetary savings at period j ∈ {1, 2}. For j = 2, it corresponds to the level of monetary bequest left to heirs, and we assume that S 2 ≥ 0. When j = 1, it can be either positive or negative. If positive, the return on money savings is r j > 0, j ∈ {1, 2}. We assume that the household can borrow money only during the first period (out of two) of its lifecycle. It is excluded to leave debts to heirs. If money is borrowed in period j = 1, the household contracts a loan that has to be reimbursed during the second period j = 2. The interest rate of the loan is τ 1 . We assume that τ 1 > r 1 . If money is borrowed for housing purpose, as the household must pay down a fraction ρ ∈ [0, 1] of the total dwelling price, only the remaining portion has to be reimbursed in period 2. By convention, ρ = 1 when dwelling is rented in period 1 (no borrowing is allowed for renting), and µ

r j ,d j ,l j j = 0.
There is yet one component to consider. When household makes the choice to change dwelling in period 2, moving costs affecting the budget constraint may occur. We model them by ∆ (x 1,l 1 , x 2,l 2 ) ≥ 0. By convention, these costs are equal to zero when not changing dwelling.

The budget constraint for the first period is then

p 1 C 1 + 1 + µ k 1 ,d 1 ,l 1 1 ρ + κ k 1 ,d 1 ,l 1 1 (x 1 ) π k 1 ,d 1 ,l 1 1 (x 1,l 1 ) Q 1 + S 1 = R 1 -D 1 (x 1,l 1 , y 1 ) (4)
The budget constraint in period 2 is more involved:

p 2 C 2 + (1 + τ 1 ) 1 + µ k 1 ,d 1 ,l 1 1 (1 -ρ) π k 1 ,d 1 ,l 1 1 (x 1,l 1 ) Q 1 + 1 + µ k 2 ,d 2 ,l 2 2 + κ k 2 ,d 2 ,l 2 2 (x 2,l 2 ) π k 2 ,d 2 ,l 2 2 (x 2,l 2 ) Q 2 + S 2 = (1 + r 1 ) S 1 + R 2 -D 2 (x 2,l 2 , y 2 ) -∆ (x 1,l 1 , x 2,l 2 ) +π o 1 ,d 1 ,l 1 2 (x 1,l 1 ) Q 1 I 1 2 , (5)
where I 1 2 is a dummy variable indicating that dwelling bought in period 1 may be sold in period 2. We can combine equations 4 and 5 to obtain the intertemporal budget constraint:

(1 + r 1 ) p 1 C 1 + p 2 C 2 + S 2 +      1 + µ k 1 ,d 1 ,l 1 1 ρ + 1+τ k 1 ,d 1 ,l 1 1 (1-ρ) 1+r 1 +κ k 1 ,d 1 ,l 1 1 (x 1,l 1 )      (1 + r 1 ) π k 1 ,d 1 ,l 1 1 (x 1,l 1 ) Q 1 + 1 + µ k 2 ,d 2 ,l 2 2 + κ k 2 ,d 2 ,l 2 2 (x 2,l 2 ) π k 2 ,d 2 ,l 2 2 (x 2,l 2 ) Q 2 = (1 + r 1 ) (R 1 -D 1 (x 1,l 1 , y 1 )) + R 2 -D 2 (x 2,l 2 , y 2 ) -∆ (x 1,l 1 , x 2,l 2 ) + π o 1 ,d 1 ,l 1 2 (x 1,l 1 ) Q 1 I 1 2
(6) This general constraint further simplifies when considering specific series of discrete residential choices. For instance:

• if k j = r j then ρ = 1, τ 1 = 0, µ r j ,d j ,l j j = 0; • if l 1 = l 2 then d 1 = d 2 , Q 2 = Q 1 , and ∆ (x 1,l 1 , x 2,l 1 ) = 0 by convention.

Bequest function

The dwelling(s) transmitted at the beginning of period 3, if any, were necessarily bought previously. For j = 1, 2, we denote by I j 3 the dummy variable indicating that a dwelling is bought in period j and transmitted to heirs at period 3. The total value of the bequest evaluated in period 3 is therefore:

B = π o 1 ,d 1 ,l 1 3 (x 1,,l 1 ) Q 1 I 1 3 + π o 2 ,d 2 ,l 2 3 (x 2,l 2 ) Q 2 I 2 3 + (1 + r 2 ) S 2 , (7)

Characterization of the solution

Consider now that the household is able to compute optimal demands and derived indirect utility function for each possible trajectory of discrete decisions. It would then compares the levels of utility of every possible series of decisions and it selects the one that maximizes its utility. As modellers, we want to define more precisely these optimal demands and indirect utility functions so as to develop a structural framework.

We proceed in two steps to solve the problem of the household. We consider in a first step that the household chooses one of the possible trajectories of discrete residential choices, i.e. location, tenure and dwelling types. Given prices and budget resources, its problem is then to determine its optimal demands for floor spaces Q 1 and Q 2 and other consumption expenditures C 1 , C 2 plus a potential level of savings S 2 due to bequest behaviour so as to maximize an intertemporal utility function subject to budget constraints.

We however have to account for two key decisions. The first regards whether to move from one dwelling to another in between period 1 and period 2. The second regards whether to leave housing or savings as bequest to heirs. Combination of both does not give the same maximization program. In a second step, once obtained optimal demands and savings, thus the associated indirect utility function, and still considering that the household is maximizing its utility function, the optimal series of discrete choices is the one that corresponds to the conditional (to discrete residential choices) indirect utility function that reaches the largest level.

On bequest composition

As already stated, the solution of the problem depends on the composition of the bequest, which in turn depends on whether markets are perfect. We make some proposition accounting only for tenure type but extension to account simultaneously for tenure and dwelling types would just introduce more complexity without improving understanding of our baseline assumptions.

Definition 1. Full perfection holds if

• r 1 = r 2 = τ 1 ≡ r • µ o 1 1 = µ o 2 2 = 0 • κ o 1 1 (x 1 ) = κ o 2 2 (x 2 ) ≡ κ • π b j (x j ) = π r j (x j ) , j = 1, 2 • (1 + r t ) π b t (x j ) = π b t+1 (x j ) , j = 1, 2, t = 1, 2.
In order to simplify notations, we define implicit prices :

Π 0 Q 1 = 1 + µ l 1 [(1 + r 1 ) ρ + (1 + τ 1 ) (1 -ρ)] + (1 + r 1 ) κ l 1 (x 1 ) π l 1 (x 1 ) Π 0 Q 2 = 1 + µ l 2 + κ l 2 (x 2 ) π l 2 (x 2 ) Π 0 C 1 = (1 + r 1 ) p 1 Π 0 C 2 = p 2 Π 0 S 2 = 1 (8)
Lemma 1. Full perfection implies that the relative implicit prices in the bequest equation are equal to the relative prices in the intertemporal budget constraint:

Π 0 Q 1 π b 3 (x 1 ) = Π 0 Q 2 π b 3 (x 2 ) = 1 (1 + r 2 )
Proof. The result is straightforward by applying the simplifications implied by full perfection in Equations ( 6) and ( 7).

Lemma 2. Under full perfection, and with no budget constraints (S 1 ≷ 0), at the optimal solution, the household is indifferent between renting and buying, and the bequests are transmitted indifferently as real estate or money. The problem reduces to the maximization of a standard Cobb-Douglas function

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under the simplified intertemporal budget constraint:

(1 + r) p 1 C 1 + p 2 C 2 + S 2 + (1 + r) (1 + κ) π l 1 (x 1 ) Q 1 + (1 + κ) π l 2 (x 2 ) Q 2 = (1 + r) [R 1 -D 1 (x 1 , y 1 )] + [R 2 -D 2 (x 2 , y 2 ) -∆ (x 1 , x 2 )] .
Proof. Indifference between renting and buying results from the absence of budget constraints associated with the conditions π b j (x j ) = π r j (x j ) , j = 1, 2 and µ b 1 = µ b 2 = 0. Lemma 1 implies that real estate has exactly the same value whether is is transmitted as real estate or sold at period 2 (or at period 1 when relevant), and the corresponding value is transmitted to heirs as a monetary bequest S 2 . We can therefore assume that dwellings are rented at both periods, and only a monetary bequest is transmitted.

Proposition 1. There exists exactly one form of bequest, entailing either real estate (bought either in first or in second period), or money if and only if the three ratios

Π 0 Q 1 π b 3 (x 1 ) = Π 0 Q 2 π b 3 (x 2 ) = 1
(1+r 2 ) . Proof. According to Lemma 1, when the three ratios are equal, interior solutions with composite bequest (entailing both real estate and money) are optimal. The reciprocical part proceeds by contradiction. Consider an optimal solution denoted by

{C * 1 , Q * 1 , C * 2 , Q * 2 , S * 2 }.
Assume, without loss of generality, that

π b 3 (x 1 ) Π 0 Q 1 > 1 + r 2 Assume further I 1 3 = 1 and S 2 > 0. Consider an infitesimal change ∆ > 0 such that Q * 1 is replaced with Q * 1 -∆ Π 0 Q 1 < Q * 1 and C * 1 is replaced with C * 1 + ∆ ( 1+r
1 )p 1 . The total cost of this infinitesimal change is zero, so intertemporal utility remains unchanged. Consider an additional change such that S * 2 is replaced with

S * 2 + ∆π b 3 (x 1 ) (1+r 2 )Π 0 Q 1
and first period consumption of composite good becomes

C * 1 + ∆ (1+r 1 )p 1 - 1 (1+r 1 )p 1 ∆π b 3 (x 1 ) (1+r 2 )Π 0 Q 1 = C * 1 + 1 - π b 3 (x 1 ) (1 + r 2 ) Π 0 Q 1 <0 since π b 3 (x 1 ) Π 0 Q 1 >1+r 2 ∆ (1+r 1 )p 1 < C * 1 .
The total cost of this additional infinitesimal change is zero, so intertemporal utility remains unchanged. The second change moves the total bequest back to its initial value (here, we use I 1 3 = 1). The combination of these two infinitesimal changes leaves intertemporal utility, total bequest value, and second-period utility unchanged. As a result, it leaves first-period utility unchanged. This is in contradiction with the decrease in both

C 1 and Q 1 , since u 1 (•) is increasing in its arguments. Similarly, considering Q * 2 → Q * 2 -∆ Π 0 Q 1 < Q * 2 and C * 2 → C * 2 + ∆ p 2 proves that π b 3 (x 2 ) Π 0 Q 2 > 1 + r 2 , I 2 3 = 1 and S 2 > 0 cannot hold simultaneously. Finally, a similar infinitesimal change in Q * 1 , C * 1 , Q *
2 and C * 2 leaving both total bequest and total cost unchanged proves that

π b 3 (x 2 ) Π 0 Q 2 = π b 3 (x 1 ) Π 0 Q 1
, I 1 3 = 1 and I 2 3 = 1 cannot hold simultaneously. Proposition 1 implies that, under perfect foresight, the case in which the household owns and transmits to heirs both the dwelling where it lives in period 1 and the dwelling where it lives in period 2 cannot be optimal when the relative (implicit) price of these two assets is not the same in period 2 and in period 3, which constitues a systematic imperfection in real estate markets in Paris region. It happens that, in our dataset, this case represents less than 1% of the sample. This low percentage is consistent with unanticipated changes in personal or professional situation over the life cycle (such unanticipated changes are ignored in lour model).

Optimal series of discrete choices

Another result of our model is that, once solved the intertemporal optimization program, the indirect utility functions for every sequence of tenure and dwelling types write using only two different mathematical formulations:

Vl 1 ,l 2 ,d 1 ,d 2 ,k 1 ,k 2 = Ω l 1 ,l 2 ,d 1 ,d 2 ,k 1 ,k 2 -λ 0 Q 1 ln Π l 1 ,d 1 ,k 1 1 -λ 0 Q 2 ln Π l 2 ,d 2 ,k 2 2 + λ ln (W (x 1 , x 2 ))
for movers and

Vl 1 ,l 1 ,d 1 ,d 1 ,k 1 ,k 2 = Ω l 1 ,l 1 ,d 1 ,d 1 ,k 1 ,k 2 -λ 1 Q 1 ln Π l 1 ,d 1 ,k 1 1 + Π l 1 ,d 1 ,k 2 2 + λ ln (W (x 1 , x 1 ))
for non movers where

• λ 0 Q 1 = (1 -α 1 ) + β 2 γ 2 I 1 3 , • λ 0 Q 2 = β (1 -α 2 ) + β 2 γ 2 I 2 3 , • λ 1 Q 1 = (1 -α 1 ) + β (1 -α 2 ) + β 2 γ 2 I 1 3 • λ = 1 + β + β 2 γ 2
• Ω's are functions of the possible choices, the exogenous variables, and the parameters of U

The optimal series of discrete choices is solution of

max max l 1 ,l 2 ,d 1 ,d 2 ,k 1 ,k 2 Vl 1 ,l 2 ,d 1 ,d 2 ,k 1 ,k 2 , max l 1 ,l 1 ,d 1 ,d 1 ,k 1 ,k 2 Vl 1 ,l 1 ,d 1 ,d 1 ,k 1 ,k 2 (9)
3 Application

We present in this section a probabilistic discrete choice to analyze dynamics of tenure and dwelling types given locations. We focus on the population of inhabitants that lived and may have moved within the Paris region in 2002 and 2006.

Data

Empirical implementation of our theoretical model is data demanding in that we need to have available at least longitudinal disaggregate data but not only.

Our main data source is the 2006 French National Housing Survey (FNHS). It reports observed housing choices of French households during this year and it briefly reports those made in 2002. For these two years, we also observe socioeconomic and demographic characteristics of these decision makers. We however point out that available information is somewhat limited for year 2002.

As the 2006 FNHS is a revealed preference survey, we don't have any information about unchosen alternatives. We therefore need to complement this survey by drawing statistical information from other data sources, especially regarding housing prices. To this extent, we will use 2003 and 2007 Côtes Callon.

Furthermore, it appears that some of the attributes of all the likely alternatives, especially as it regards local amenities, are not described. As it regards our problem, we see mainly two demanding requirements: information about prices by location, dwelling and tenure types, and information about local amenities by location.

Sample formation

We have initially 6988 observations. When we look at combinations of tenue and dwelling types at these dates, we observe that only 5 of them appears enough significant. They are written italics in table 1. served as a residence in 2002 whatever its new tenure type. We also won't the choice situation where a household changes tenure type from owner to renter. Finally, we won't consider the situation where a household may become owner of the dwelling it was renting in the former period: there is an obligation to change dwelling.

We virtually have 5 sequences of tenure types by 4 sequences of dwelling types but, by natural constraint, we have to remove 4 of them. We then have 16 choice situations. We that our 6745 remaining observations greatly favours non moving choices. Only 1419 observations (21.04% ) concern moving households. We also observe that:

• shift in tenure type from rental to ownership if closely related to households that move from an apartment to a house. The reciprocal exists but it is not that much important; • move and ownership at both periods is often associated to a non change in dwelling type; • house renting is not a very usual choice.

Attributes of unchosen alternatives

As already stated, the 2006 FNHS is a revealed preference survey. We only have description of what has been done but not what may have been done. As we want to parametrize and estimated a probabilistic choice model, one important task is to reconstruct pertinent variables that describe attributes of unchosen alternatives. For other reasons, we also have missing data that describe characteristics of some households. We can use some secondary tables of the 2006 FNHS but it is not enough: we need to draw additional information from other data sources. Data imputation is made using standard statistical techniques and developing a series of auxiliary descriptive models. We discuss and present them in this subsubsection.

First of all, we remind the reader that we don't have accurate information about locations of dwellings. We only have locations at the "département" level, a very large administrative geographical unit (there are only 8 département for the region we consider). Even though we stated that we present a model of dwelling and tnure types given locations, we would have prefered to have available these variables at least to be able to compute less roughly housing prices for unchosen alternatives. This is not the case and, as a result:

• we are not able to compute any transportation cost or accessibility indicator;

• housing prices that we will compute for unchosen alternatives will be at the "département" geographical scale.

In order to reconstruct housing prices, we firstly need some external baseline data. We will use 2003 and 2007 Côtes Callon (data collected during years 2002 and 2006), which provide average housing prices for apartments and houses in several locations of the region and for different levels of comfort and quality of the dwellings. We compute weighted average housing prices for apartments and houses at the "département" level". Weights are drawn from the 2006 census of population and consider only age of the building. We also assume that these weights did not change in between 2002 and 2006 so that we use them to obtain our necessary housing prices for year 2002.

Secondly, we also need to convert both purchasing and renting prices to some comparable unit. To this extent, we will convert purchasing prices to "pseudo" renting prices. We will base our analysis on the "mortgage" table of the 2006 FNHS that regards housing loans that were contracted by French inhabitants of the Paris region (disregarding our sample selection) for the dwelling they purchased earlier and currently live in. Using an auxiliary regression model, we then will be able to impute missing information about mortgage level, pay-down fraction and interest rate for household that actually chose to rent.

Another point is about how to deal with non moving households when reconstructing variables of choice alternatives that imply it to move from one location to another. Here again, we have to constrain our approach. A brief look at the data shows that about 71.20% of moving households stay in the same "département". Another look at the 2006 Census of population also shows that many households keep rather conservative in their choices of new residence place. For our model, we will then assume that if a non moving household would have chosen to change dwelling in between 2002 and 2006, it would then have been in the same "département".

We now list what we assumed to reconstruct housing prices for every considered household in our sample:

• non moving households would have chosen the same "département" if they had chosen to change dwelling • for owners, we assume for each dwelling type that the renting price is given by the corresponding average rental price per square metre at the level of "département" computed from Côtes Callon; • for renters, we proceed in 3 steps:

we draw for each dwelling type the average purchasing price per square metre at the level of "département";

we impute how much, how long, and at which interest rate would be a mortgage to buy the dwelling. To impute the values of these variables, we adjust a hierarchical simultaneous equation system by full information likelihood method. We use the "mortgage" table of the 2006 FNHS that regards housing loans that were contracted by French inhabitants of the Paris region for the dwelling they purchased earlier and currently live in. Our specification is rather simple: we assume that the mortgage amount is function of income per capita, age of the household head, and household size. Mortgage duration is function of the ratio between i i "chap_2_2_20141201" -2014/12/1 -19:42 -page 14 -#14

i i i i i i
mortgage amount and total household income. Mortage interest rate is function of mortgage duration and a year-specific variable. Quality of fit is rather good for a such simple system and estimates are along with intuition. We obtain that mortgage amount is an increasing function of income per capita and follows a U-shape with respect to age of household head. It is also an increasing function of household size. we then impute how much would be the monthly reimbursement amount for renters in our sample (as already stated, we need to make comparable housing purchasing and monthly rental prices per square meter). To this extent, we use simple financial mathematics. We assume that household i buy a dwelling of type k in location l by means of a mortgage. An amount equal to (1 -ρ i ) π per square meter is borrowed over a period of T i years at an annual interest rate of τ i . ρ i is the fraction of down payment and π k,l is the purchasing price per square meter. The monthly expenditure in housing per meter square is defined as the fixed monthly reimbursement C i,k,l :

C i,k,l = τ π k,l 1 -(1 + τ ) -T . ( 10
) i i "chap_2_2_20141201" -2014/12/1 -19:42 -page 15 -#15 i i i i i i
We finally merge these imputed values with these related to the revealed choices of households. We now have available a set of housing prices for every observed and likely housing choice of all households.

Income and wealth

We also miss 2002 income levels. Actually, we have 2006 income levels but some observations are also missing. We proceed as it is often done in many applications to impute missing values of this variable for year 2006. We fit a type II Tobit model (also known as generalized Tobit model). The first part of the model consists in explaining non reporting of the income variable by some households. The second part of the model consists in explaining the levels of incomes of households using only the subset of observed income levels and correcting for this sample selection bias. Estimates are reportted in table 3. Here again, we use a simple specification of the model. Goodness-of-fit of the model is not as good as we would expect but we use these results to impute both We finally compute wealth as R 2002 + R 2006 1+r where r is defined as the interest rate of a risk-free monetary asset. In our application, it is defined as a 4 years investment in the french "livret A":

(1 + r) 4 = 2005 t=2002 (1 + i t ) (11)
where i t , t = 2002, • • • , 2005, are drawn from data of "Banque de France".

Transportation and moving costs

We don't have any accurate measurement of these variables in data. We also are limited as it regards locations of dwellings. Furthermore, we don't have any information about automobile ownership and use at the household level. Finally, there is nothing about travel behaviour of households. There is no possibility to compute variables that regard transportation costs or moving costs.

Model specification

We now turn to the econometric specification of our probabilistic discrete choice model.

Choice set

The first step is to elaborate a little bit more on the structure of the choice set we consider. We focus here on dynamics of dwelling and tenure types at two spaced dates. There exists several ways to nests the different dimensions of our choice set. We assume the following. Firstly, dwelling type for year 2002 is chosen. Then, tenure type for year 2002 is chosen. In between 2002 and 2006, the choice to move or not is made. In year 2006 is made again the choice of a tenure type and then a dwelling type. We may have privileged the choice of a dwelling type prior to the choice of a tenure type or even other combination of the sequence of choices. The search of the most relevant combination is left aside for future research work. Figure 1 summarizes the nesting structure of choices we consider for our application.

Indirect utility functions

Because of missing statistical information, proxy variables, measurement errors, and because we only observe choices, we assume that the indirect utility function for household i are continuous random variables

V i,x i,1 ,x i,2 ,d i,1 ,d i,2 ,t i,1 ,t i,2 = Vi,x i,1 ,x i,2 ,d i,1 ,d i,2 ,t i,1 ,t i,2 + i,x i,1 ,x i,2 ,d i,1 ,d i,2 ,t i,1 ,t i,2
V i,x i,1 ,x i,2 ,d i,1 ,d i,1 ,t i,1 ,t i,1 = Vi,x i,1 ,x i,2 ,d i,1 ,d i,1 ,t i,1 ,t i,1 + i,x i,1 ,x i,2 ,d i,1 ,d i,1 ,t i,1 ,t i,1
We also assume that parameters of the utility function (α's and γ) are function of the characteristics of the household (here, household size)

Probabilistic formulation

's enter additively and are independent from observed variables. For each observed household, they are distributed with a GEV distribution, i → F ( i ) = exp (-H ( i ; σ)). The choice probabilities are defined as H is chosen to satisfy the nested structure of choices as presented in figure 1. It takes the form of a 5-level Nested Logit model. There are effects of lower choices in the tree on related upper choices ("logsum", i.e. effect of maximum expected utility of a subsequent choice on current choice). We refer the reader to [START_REF] Mcfadden | Modelling the choice of residential location[END_REF], [START_REF] Ben-Akiva | Discrete choice analysis : theory and application to travel demand / Moshe Ben-Akiva[END_REF], [START_REF] Train | Discrete Choice Methods with Simulation, number 9780521816960[END_REF] for explicit formulation of these choice probabilities.

Pr (x i,1 , x i,2 , d i,1 , d i,2 , t i,1 , t i,2 ) = exp Vi,x i,1 ,x i,2 ,d i,1 ,d i,2 ,t i,1 ,t i,2 ∂H(exp( Vi) ;σ) ∂ exp Vi,x i,1 ,x i,2 ,d i,1 ,d i,2 ,t i,1 ,t i,2 H exp Vi ; σ -1 (12)

Results

The model is estimated by maximum likelihood method. Estimates are reported in tables 4 and 5. We observe several significant effects, all along with theory and common practive.

It is found that household is sensitive to floor space consumption (1 -α's coefficients) and that this sensitivity increases with household size. We also remark that the ratio of periodic sensitivities is larger than 1, as expected, meaning that there exists a strictly positive (and lower thatn 1) discounting factor. There also exists a significant bequest effect as scaled γ is found to be positive. Accumulating assets, whatever they take the form of money or housing, increases household's level of utility. We are however not sure whether it directly regards heirs or future period of the household as we did not control for lifecycle effects. Anyway, data shows that there exists a positive effect in accumulating assets for future periods of life, whichever they regards the household or its heirs.

Results also show that there are different effects of socio-economic and demographic characteristics on dynamics of delling and tenure types. Income has a positive effect on the probability to choose a house instead of an apartment. It also has a positive effect on the probability to move, i.e. to change dwelling, over time. This is not surprising as it the relative contribution of moving costs are then lesser and that the relative larger purchasing power favours consumption of more space and a more private type of dwelling (no direct up and down neighbours).

We also observe that the structure of a household and its evolution affects the sequence of dwelling and tenure types. Actually, it is found that work status of the household head change the way housing is consumed. If he/she retires in the second period then he/she anticipated a lowering of his/her household income and then privileges the choice to own in the first period and then stay in the same dwelling. If he/she is unemployed in the second period, he/she prefers to rent in both period and move to another dwelling. Any choice that involves ownership in either the first or the second period is ranked down. If he/she is unemployed in both period, then renting the same dwelling both periods is favoured. We also observe that if he/she is a student in 2002 and then work in 2006, what is favoured is renting during the first period and then buying in the second period.

When there is a change in workplace or job type of any household member, the probability to move is increasing. Such a result is along with the fact that the household looks at minimizing transportation costs. We also find that a variation of the household size has an asymmetrivcal effect on the probability to move: an increase of the size favours change of dwelling but a decrase of size does not affect significantly the proability to move.

Finally, All the same, there is a "natural" trend in prefering to consume flat rather than houses. with theoretical constraint that ensure that the probabilistic model actually derives from random utility maximization. They all exhibit existence of "within-nest" substitution patterns.

Conlusion

We developed a structural microeconomic framework to analyze simultaneously several aspects of the dynamics of residential choices: location, dwelling, and tenure. We accounted for intertemporal budget constraints while allowing for bequest motives. Our analytical formulation is tractable for empirical matters, and we therefore proposed an econometric formulation of the approach by using a nested-Logit prob-20 abilistic choice models. We discussed demanding and stringent data requirements to implement it.

Our work may however be further extended in several ways. First, the model may be extended to a multi-period maximization program. Second, the assumption about perfect information and perfect foresight of market variables is questionable. The approach may be formulated as a dynamic discrete choice model with forwardlooking economic agents. We also think that using estimated parameters from the econometric model would provide a better basis to perform simulation of an urban system equilibrium.

  (continuous) demands adjust to these optimlal (discrete) choices.

  income R for years 2006 and 2002. The latter is made using part of socio-demographic information we have available at this year in the survey. Of course, we implicitely assume that the relation between the dependent variables and the exogenous variables stays constant over the 2002 -2006 period.

  Figure 1: Sequence of choices

Table 1 :

 1 Matrix of tenure and dwelling types in 2002 and 2006

		Dwelling types (2002, 2006)
	Tenure types (2002, 2006) (h,h) (h,f) (f,h)	(f,f)	Total
	Move, (o,o), keep	23	9	10	16	58
	Move, (o,o), resell	53	14	44	46	157
	Move, (o,r), keep	3	17	1	14	35
	Move, (o,r), resell	7	10	4	17	38
	No move, (o,o)	1440	0	0	967	2407
	No move, (o,r)	33	0	0	19	52
	Move, (r,o)	25	6	133	170	334
	Move, (r,r)	18	41	60	809	928
	No move, (r,o)	25	0	0	35	60
	No move, (r,r)	171	0	0	2748 2919
	Total	1798	97	252 4841 6988
	o: own, r: rent; h: house, f: flat; ( , ) is defined as (type in 2002 , type in 2006)
	Move, No move: change home or not, Keep, resell: keep formerly owned home or resell it
	For the rest of our application, we will not consider choice situations where
	a household moves in between 2002 and 2006 and keep its owned dwelling that

Table 2 :

 2 Duration of a mortgage is and increasing function of the ratio between amount and income. Naturally, interest rate decreases in between 2002 and 2006 and is a decreasing function of the duration. Estimates are reported in table 2. Mortgage-related system of equations

	Log. of amount equation
	Label of variable	Estimate T-stat.
	Intercept	6.66	6.68
	Log. of income per capita	0.62	6.84
	Age of household head	-0.10	-6.67
	Age of household head squared	0.001	5.81
	Log. of household size	0.27	4.03
	Log. of duration equation
	Intercept	2.59	259.80
	Log. of ratio between amount and total income	0.16	24.28
	Log.of interest rate equation
	Intercept	3.57	7.77
	I a : year 2002	0.21	6.27
	Log. of duration	-0.91	-5.23
	Number of observations	1628
	Overal ρ 2	0.78

a : I: dummy variable

Table 3 :

 3 Imputation of income variable

	Selection equation
	Label of variable	Estimate T-stat.
	Intercept	0.84	33.02
	I a : household head is an active worker	0.33	11.94
	I: household head is unemployed	-0.14	-3.99
	I: household head is retired	0.36	12.11
	Log. of 2006 income equation
	Intercept	7.14	148.47
	Log. of age of household head	0.48	39.21
	Log. of household size	0.48	81.34
	I: household head is an active worker	0.91	68.16
	I: household head is unemployed	0.04	2.54
	I: household head is retired	0.54	34.53
	I: household lives in Paris	0.02	1.50
	I: household lives in Seine-et-Marne	0.14	6.93
	I: household lives in Yvelines	0.23	10.63
	I: household lives in Essonnes	0.16	8.71
	I: household lives in Hauts-de-Seine	0.11	6.15
	I: household lives in Seine-Saint-Denis	-0.13	-7.89
	I: household lives in Val de Marne	0.06	3.22
	I: household lives in Val d'Oise	0.07	3.82
	Standard deviation of error term	0.58	272.49
	Correlation of error terms	-0.00	-0.00
	Overall ρ 2	0.58

a : I: dummy variable

Table 4 :

 4 Estimates of the discrete choice model

	Label

Looking now at the inclusive values, i.e. "logsum effects", these are all in line

Table 5 :

 5 Estimates of the discrete choice model, cont'd HH member other than HH head (re)starts working, effect on prob. to move h 0.01 0.14 Change in job and or workplace of any HH member, effect on prob. to move h 0.37 3.21 HH member other than HH head stops working, effect on prob. to move h -0.16 -2.59 Decrease in HH size in between 2002 and 2006, effect on prob. to move i 0.04 0.80 Increase in HH size in between 2002 and 2006, effect on prob. to move i HH head works in 2002 and 2006 and HH rents the same dwelling over both period; b : reference is flat, same dwelling in 2002 and 2006

	Label

a : reference: c : reference is flat in 2002 and move; d : reference is flat in 2006 and move e : reference is flat in 2002; f : reference is flat in 2006; g : reference is stay h : reference is no modification in job or workplace for every HH member; i : reference is no modification of HH structure

Note that it means that prices of the composite good does not differ across zones in the considered region.

Note that yj is a vector when many household members work and/or when considering other locations than workplaces. Note also that x is an argument of the transportation cost function as presence of public transport or any special transport infrastructure may be considered as amenities for location lj and may have effect on the level of transportation costs.


Marie De Tayrac
email: marie.detayrac@univ-rennes1.fr

Marie-Paule Roth

Anne-Marie Jouanolle

Hélène Coppin

Gérald Le Gac

Alberto Piperno

Claude Férec

Sara Pelucchi

Virginie Scotet

Edouard Bardou-Jacquet

Martine Ropert

Régis Bouvet

Emmanuelle Génin

Jean Mosser

Yves Deugnier

Genome-wide association study identifies TF as a significant modifier gene of iron metabolism in HFE hemochromatosis

Keywords: Hereditary hemochromatosis GWAS: genome-wide association study SNP: Single Nucleotide Polymorphism HFE-hemochromatosis, GWAS, transferrin

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Introduction

Genetic hemochromatoses are hereditary disorders proceeding from impairment in the production and/or activity of the key regulator of plasma iron, hepcidin, and resulting in progressive iron loading of parenchymas. HFE-hemochromatosis accounts for more than 95% of genetic hemochromatosis cases in Caucasian populations [START_REF] Liver | EASL clinical practice guidelines for HFE hemochromatosis[END_REF]. It is chiefly related to one major mutation, p.Cys282Tyr (C282Y), whose frequency ranges from 5% to 15% according to an increasing gradient from South/East to North/West but whose penetrance is far from complete [START_REF] Allen | Iron-overload-related disease in HFE hereditary hemochromatosis[END_REF].

Large studies based on systematic genotyping of large populations [START_REF] Allen | Iron-overload-related disease in HFE hereditary hemochromatosis[END_REF][START_REF] Adams | The effect of the metabolic syndrome, hepatic steatosis and steatohepatitis on liver fibrosis in hereditary hemochromatosis[END_REF][START_REF] Beutler | Penetrance of 845G--> A (C282Y) HFE hereditary haemochromatosis mutation in the USA[END_REF][START_REF] Deugnier | Gender-specific phenotypic expression and screening strategies in C282Y-linked haemochromatosis: a study of 9396 French people[END_REF][START_REF] Jackson | HFE mutations, iron deficiency and overload in 10,500 blood donors[END_REF] have consistently found that transferrin saturation and serum ferritin levels, the key biochemical markers of genetic hemochromatosis, were significantly increased in C282Y homozygotes when compared to sex-matched controls with other HFE genotypes. According to studies, the percentage of C282Y homozygous subjects with elevated transferrin saturation ranged from 73 to 84% in males compared to 40 to 73% in females. The same was found for serum ferritin levels with a prevalence of increased values ranging from 70 to 88% in males and 33 to 69% in females. As a whole, the biochemical penetrance of C282Y in homozygotes can be estimated as about 75% in males and 50% in females. However, only a few studies of the clinical expressivity of C282Y homozygotes achieved a sufficient statistical power and referred to a control group to allow for a correct interpretation of the data. [START_REF] Allen | Iron-overload-related disease in HFE hereditary hemochromatosis[END_REF][START_REF] Deugnier | Gender-specific phenotypic expression and screening strategies in C282Y-linked haemochromatosis: a study of 9396 French people[END_REF][START_REF] Adams | Hemochromatosis and iron-overload screening in a racially diverse population[END_REF][START_REF] Andersen | Hemochromatosis mutations in the general population: iron overload progression rate[END_REF][START_REF] Beutler | The significance of the 187G (H63D) mutation in hemochromatosis[END_REF] Based on these studies, it can be concluded that the clinical expressivity of the C282Y homozygous genotype is indisputably much lower than previously admitted, averaging 28% in males and 1% in females when using strict definitions of both iron overload and iron-related organ damage [START_REF] Allen | Iron-overload-related disease in HFE hereditary hemochromatosis[END_REF]. The main manifestations of HFEhemochromatosis are chronic fatigue, arthritis and liver disease. The frequency of heart disease and diabetes are not significantly increased in C282Y homozygotes compared with controls [START_REF] Liver | EASL clinical practice guidelines for HFE hemochromatosis[END_REF]. However fatigue and arthritis are not clearly correlated with the amount of iron burden. With respect to liver disease, serum ferritin levels lower than 1000µg/L allow exclusion of significant fibrosis, as demonstrated by Guyader et al [START_REF] Guyader | Noninvasive prediction of fibrosis in C282Y homozygous hemochromatosis[END_REF] and confirmed by Allen et al [START_REF] Allen | Iron-overload-related disease in HFE hereditary hemochromatosis[END_REF]. Thus C282Y homozygosity appears to be a necessary but not a sufficient condition for the development of HFE-hemochromatosis and the existence of both environmental and genetic modifiers of its penetrance is strongly suggested.

Although familial studies have shown that non-HFE iron-related genes are involved in the modulation of iron burden in C282Y homozygotes, only a few putative genetic modifiers have been identified so far in humans. A mitochondrial polymorphism has been reported as more frequent in iron loading expressing than in non-expressing C282Y homozygotes [START_REF] Livesey | The 16189 variant of mitochondrial DNA occurs more frequently in C282Y homozygotes with haemochromatosis than those without iron loading[END_REF] but this was not confirmed by another study [START_REF] Beutler | The mitochondrial nt 16189 polymorphism and hereditary hemochromatosis[END_REF]. Coinheritance of mutations in the hepcidin gene (HAMP) [START_REF] Jacolot | HAMP as a modifier gene that increases the phenotypic expression of the HFE pC282Y homozygous genotype[END_REF][START_REF] Merryweather-Clarke | Digenic inheritance of mutations in HAMP and HFE results in different types of haemochromatosis[END_REF] or in the hemojuvelin gene (HFE2) [START_REF] Gac | The recently identified type 2A juvenile haemochromatosis gene (HJV), a second candidate modifier of the C282Y homozygous phenotype[END_REF] together with C282Y homozygosity was found to be associated with more severe iron burden of earlier onset in a French cohort of C282Y homozygotes [START_REF] Jacolot | HAMP as a modifier gene that increases the phenotypic expression of the HFE pC282Y homozygous genotype[END_REF][START_REF] Gac | The recently identified type 2A juvenile haemochromatosis gene (HJV), a second candidate modifier of the C282Y homozygous phenotype[END_REF]. However these mutations have a frequency lower than 2‰ among C282Y homozygotes and can thus explain increased disease severity in a few patients only.

Based on these results, the BMP -SMAD pathway regulating hepcidin production was highlighted as an important pathway that was likely including potential modifying genes. This was confirmed by the finding, in a large cohort of C282Y homozygotes, of an association between common variants in the BMP pathway and the level of iron burden [START_REF] Milet | Common variants in the BMP2, BMP4, and HJV genes of the hepcidin regulation pathway modulate HFE hemochromatosis penetrance[END_REF][START_REF] Milet | A common SNP near BMP2 is associated with severity of the iron burden in HFE p.C282Y homozygous patients: a follow-up study[END_REF]. The full expression of HFE-hemochromatosis may thus be linked to abnormal hepatic expression of hepcidin, through both impairment in HFE function and functional modulation in the BMP pathway. Other results support the hypothesis that polymorphisms in different genes regulating iron metabolism may modulate penetrance of HFE-HH. CYBRD1 was shown to be a possible modifier gene of iron phenotype in patients with HFE-HH [START_REF] Constantine | A novel association between a SNP in CYBRD1 and serum ferritin levels in a cohort study of HFE hereditary haemochromatosis[END_REF][START_REF] Pelucchi | CYBRD1 as a modifier gene that modulates iron phenotype in HFE p.C282Y homozygous patients[END_REF] and, recently, the p.Ala736Val TMPRSS6 polymorphism was shown to be likely a modifier of HFE-HH in a highly selected subgroup of male C282Y homozygotes [START_REF] Valenti | Effect of the A736V TMPRSS6 polymorphism on the penetrance and clinical expression of hereditary hemochromatosis[END_REF].

We hypothesized that other common variants located in genes outside this pathway could modulate iron overload in HFE-HH. To identify these variants, we conducted a genome-wide association study in 518 C282Y homozygous HFE-HH patients from the tertiary referral centre of Rennes, France. The association between SNPs and 7 clinical and biochemical outcomes was examined and a replication study of candidate SNPs was conducted in a sample of 748 HFE-HH patients from 4 Italian and French centres. In this paper, we present the results of this GWAS study that is the largest conducted so far in HFE-HH patients. [START_REF] Brissot | Current approach to hemochromatosis[END_REF]. All clinical and biochemical data were recorded at the time of diagnosis before any venesection therapy. Table 1 presents the characteristics of all the samples included in the GWAS and replication studies.

Materials and Methods

Study population and replication sample

Liver fibrosis was assessed using the Metavir scoring system when liver biopsy was available (n=227) [START_REF] Bedossa | An algorithm for the grading of activity in chronic hepatitis C. The METAVIR Cooperative Study Group[END_REF]. Patients were classified as having severe fibrosis when the Metavir score was either F3 or F4. In the absence of liver biopsy, according to Guyader's algorithm, severe liver fibrosis was considered as absent when serum ferritin was < 1000 µg/L. HAS score [START_REF] Brissot | Current approach to hemochromatosis[END_REF] ranged from 0 to 4 according to the absence/presence of increased transferrin saturation (stage 1), elevated serum ferritin levels (stage 2), iron-related functional symptoms (asthenia, distal arthralgia; stage 3) and iron-related organ damage (liver fibrosis, diabetes; stage 4). In addition, the following data, recorded at the time of diagnosis, were available for the Rennes GWAS cohort: alcohol consumption, tobacco smoking, medicinal iron and drug intake, year(s) and number of blood donations, year(s) and number of pregnancies, age at menopause, weight and height, blood pressure, common blood tests including serum cholesterol, triglycerides, ASAT, ALAT, glucose, uric acid, creatinine, and HCV antibody and HBs antigen (negative in all patients).

Laboratory Methods

We determined iron status by measuring the levels of serum iron (mmol/L), transferrin saturation with iron (%) and serum ferritin (µg/L). Amount of iron removed (g) was assessed from the volume of blood extracted during initial depletion therapy until the achievement of low body iron stores (serum ferritin 50), assuming that 500 ml of blood contains 250 mg of elemental iron. For patients that were not subject to phlebotomy because of the absence of significant iron overload, it was assumed to be 0. Genomic DNA was extracted from peripheral blood cells by the phenolchloroform method or by use of the Flexigen DNA kit (Qiagen). Only DNA samples with quality in accordance with Illumina recommendations were kept.

Genome-wide genotyping and quality control procedures

GWAS was performed on the 518 cases with the Illumina™ InfiniumHD technology (Human660W-Quad). A total of 657,366 markers were assessed for quality. Quality control tests were carried out using the GenABEL library [START_REF] Aulchenko | GenABEL: an R library for genome-wide association analysis[END_REF] of the R statistical package (http://www.r-project.org/). The quality control flow diagram is presented in supplementary Fig. 1. Quality control assessments resulted in the exclusion of 95,988 CNV markers and 27,165 SNPs because of at least one of the following criteria: a minor allele frequency less than 1%, a call rate less than 95%, or rejection of Hardy-Weinberg equilibrium (HWE) at p-value equal to 10 -6 . Thirty-one samples were excluded from the analysis due to a call rate <99%, too high autosomal heterozygosity (FDR <1%), an average identity-by-state (IBS) value > 0.2, or misclassification of sex. Iterative principal component analyses (PCA) of a matrix of IBS distances computed from the SNP genotype data excluded 13 patients as heterogeneous in ancestry or outliers. After filtering of SNPs and samples, there were 534,213 SNPs available for analysis in a sample of 474 cases. Genetic population structure was assessed by PCA thanks to the OriginMineR R package. [START_REF] De Tayrac | OriginMiner : show me your genes and I'll tell you where you come from[END_REF] Genotyping and quality control procedures for replication samples Replication for SNPs identified from the GWAS was carried out by custom Fluidigm SNPtype assays based on allele-specific PCR SNP detection chemistry and designed for the BioMark HD System. Each sample was assessed for completeness of data (>90%) and genotype data were assessed for deviation from HWE (p<10 -6 ), minor allele frequency (>5%) and completeness (>99%).

Statistical analyses

Statistical analyses of the GWAS genotype data were carried out using the GenABEL R library for genome-wide association analysis [START_REF] Aulchenko | GenABEL: an R library for genome-wide association analysis[END_REF]. The quantitative iron status outcomes were analysed using linear regression after rank-based inverse normal transformation to avoid inflated type I error resulting from departure from normality.

Genotypes were coded as 0, 1 or 2, indicating the number of copies of the less frequent of the two alleles in the genotype. The regression models for all outcomes included the additive genotype term and the covariates: age, with consideration of age groups of 10 years, and sex. Population stratification was also taken into account by adjusting models for the two principal components obtained from the PCA of the whole genotype data. For liver fibrosis, logistic regression was performed and we used ordered logistic regression (R cran function, polr) to model HAS-score. For the replication phase, a four-level factor indicating the centre where the sample was collected was added to each model instead of the principal components. As we conducted several analyses using different phenotypes and performed 8 * 534,213 tests in our entire GWA analysis, we considered p-values < 10 -8 (0.05/4.3 × 10 6 ) to indicate genome-wide significance in our study.

The 20 SNPs tested in the replication study consisted of (i) SNPs with P<10 -6 from which only two SNPs were selected by LD block (Table 2), and, (ii) SNPs with P<10 -5 and P>10 -6 with one SNP being selected for each LD block to avoid redundancy (Supplementary Table 1).

Genotype imputation

Data were imputed for over 10 million SNPs using data from the 1000 Genomes Project [START_REF]A map of human genome variation from population-scale sequencing[END_REF]. Genotypes were aligned to the positive strand in both imputation and genotyping. SHAPEIT2 [START_REF] Delaneau | The 1000 Genomes Project Consortium (2014) Integrating sequence and array data to create an improved 1000 Genomes Project haplotype reference panel[END_REF] and IMPUTE2 [START_REF] Marchini | A new multipoint method for genome-wide association studies by imputation of genotypes[END_REF] were used for imputation of nongenotyped SNPs in the Illumina Human660W-Quad chips. We removed SNPs with minor allele frequency less than 1% and impute info measure less than 0.8. Genomewide association analyses were conducted using SNPtest [START_REF] Marchini | A new multipoint method for genome-wide association studies by imputation of genotypes[END_REF].

Results

Characteristics of patients

The clinical and biological characteristics of patients belonging to the primary and replication cohorts are reported in Table 1. With respect to primary cohort, additional descriptive data were as follows: BMI (men: 25.15±3.27, women: 24.25± 4.5), excessive alcohol consumption (men: 16%, women: 5%), tobacco consumption (men: 31%, women:15%), blood donation (men: 23%, women: 21%), proportion of pregnancies (none=17%, one or 2: 37%, greater than 3: 24.5%) , number of menopausal women (44%). Link between biological iron data and these putative modifying factors was investigated using both univariate and multivariate Gaussian regression models. Alcohol consumption was strongly associated with body iron (p=0.004) and serum ferritin (p=6x10 -7 ) in univariate analyses. This association remains significant only with serum ferritin in a multivariate analysis including gender and age. In women, pregnancy and menopause were associated with body iron (p=0.04 and p=0.02, respectively), serum ferritin (p=0.04 and p=0.01, respectively) and serum iron (NS and p=0.002, respectively) in univariate analyses only. Thus, GWAS was performed with regression including age and sex as only covariates. For ferritin, an analysis including also alcohol consumption was performed.

Genome-wide Association Study

The sequencing of the HFE gene confirmed that all participants were homozygous for the p.Cys282Tyr mutation and did not carry any other mutation in this gene known to be involved in HH. Following quality control, a total of 534,213 SNP and 474 patients were included in the GWAS (supplementary Fig. 1). All HFE-HH patients were identified as being from European ancestry and particularly from Western Europe (supplementary Fig. 2).

Figure 1 shows the Manhattan plot obtained for GWAS of all the seven clinical and biochemical outcomes. P-values <10 -6 were obtained for ten SNPs on chromosomes 2, 3, 6, 16 and 9 (Table 2) and 41 SNPs were found associated with at least one of the seven outcomes with p-values between 10 -6 and 10 -5 (Supplementary Table 1 and Supplementary Fig. 3). However, GWAS analyses identified only one locus reaching the genome-wide significance threshold of 10 -8 (Figure 2). This locus associated with serum transferrin concentration was located on chromosome 3q22 (TF gene; rs3811647, intron 11, p-value = 7×10 -9 ). This SNP was also associated with serum iron (p-value = 4.9×10 -6 ) but not associated with other phenotypic descriptors. The effect of rs3811647 was additive with each A allele increasing both serum transferrin and serum iron concentration. It explained 7.7% of the variance of serum transferrin concentration and 4.7% of the variance of serum iron levels. Other potential associations were found between serum ferritin and rs3849200 on chromosome 6p16.3 (p-value = 6.2×10 -7 ) and rs4544229 on chromosome 16q21 (pvalue = 8.9×10 -7 ), between the amount of iron removed and rs4371141 (VAV2 gene) on chromosome 9q34 (p-value = 9.4×10 -7 ), and between the HAS-score and rs3900546 located between LOC644013 and MAP4K4 on chromosome 2 (p-value = 2×10 -7 ). Associations between serum ferritin and rs3849200 and rs4544229 were conserved when alcohol consumption was included in the regression model.

Follow-up Association Study

In the second phase, twenty SNPs were selected for validation on an independent sample of 748 patients. Iron parameters distributions for patients included in the replication study are presented Table 1. Data distributions were compared between centres with linear models adjusted by age and gender (Supplementary Fig. 4). Raw iron parameters were found to vary significantly between centres (Supplementary Fig. 4 and5A) but differences between centres were clearly reduced after rank-based inverse normal transformations (Supplementary Fig. 5B). After quality controls, a total of 18 SNPs were retained for replication, rs3849200 and rs2810493 being removed because of no call rate. Among these SNPs, only rs3811647 in the TF gene showed evidence for association with both serum transferrin and serum iron with p-values of 5x10 -13 and 3.6x10 -6 , respectively (Supplementary Table 2).

Association Analysis of Combined GWAS and Follow-up Samples

The GWAS and follow-up study data were combined (n=1220 patients) and were analysed for each outcome in a model that included age, sex, the collection centre variable and a variable to indicate if patients were from the GWAS or the follow-up study. Results are presented in Supplementary Table 3. Genome-wide significance was found for the association of rs3811647 in the TF gene with serum transferrin (p-value = 1×10 -20 ) and serum iron (p-value = 9.24×10 -11 ). Besides these strong associations, no significant direct association with other phenotypic descriptors was found. Four other loci show potential association signals but with low significance (pvalue around 10 -3 ): rs10788066, located between the PPAPDC1A and SEC23IP genes, with serum ferritin, amount of iron removed, severe liver fibrosis, and HASscore; rs2941832, near the gene SALL3, with serum ferritin and amount of iron removed; rs2810473 and rs4406471 in the VAV2 gene with serum ferritin and, to a lesser extent, amount of iron removed, and rs17012214, located within the gene TTC27, with severe liver fibrosis.

As the role of TMPRSS6 has been highly documented in iron metabolism in the last few years [START_REF] Finberg | Mutations in TMPRSS6 cause iron-refractory iron deficiency anemia (IRIDA)[END_REF][START_REF] Du | The serine protease TMPRSS6 is required to sense iron deficiency[END_REF][START_REF] Chambers | Genome-wide association study identifies variants in TMPRSS6 associated with hemoglobin levels[END_REF][START_REF] Benyamin | Common variants in TMPRSS6 are associated with iron status and erythrocyte volume[END_REF][START_REF] Tanaka | A genome-wide association analysis of serum iron concentrations[END_REF], we also assessed, in the combined cohort, the association of the 7 outcomes with two common variants in TMPRSS6 (rs855791 and rs4820268). Using the same models, we found weak signals of association with the HAS-score for both SNPs (rs855791, p-value = 1×10 -4 and rs4820268, p-value = 6×10 -4 ), and with the amount of iron removed for rs4820268 only (p-value = 4×10 -4 ). No association was detected with other parameters of iron status.

rs3811647 genotypes in the general population

We investigate the frequency of rs3811647 alleles from genotyping data obtained in a non-HFE population from Brittany (n=191). We found that A allele has frequency of 0.343 (AA, n=21; AG, n=89; GG, n=81). We compared allele frequency in the population of C282Y homozygous patients against this population of Brittany and against GBR and CEU from 1000 Genomes and did not find any difference (chisquared test).

Clinical, biochemical, and rs3811647 genotype correlations

Clinical and biochemical parameters were investigated in relation with rs3811647 genotypes in patients included in the GWAS study. Except for the additive effect of rs3811647, with each A allele increasing both serum transferrin and serum iron concentration, no significant influence of the rs3811647 genotype on clinical and other biochemical parameters was found (Table 3a). However, significant positive associations were detected between serum transferrin and serum iron levels and between serum iron levels and all phenotypic outcomes studied. Serum transferrin levels were negatively correlated with all other phenotypic markers except fibrosis (Table 3b).

Discussion

In this paper, we report the first study designed at the genome-wide scale to identify SNPs associated with clinical and biochemical expression of HFE-hemochromatosis.

This study was performed in a large sample of well-defined C282Y homozygous patients, totalizing more than 1,200 individuals presenting with a wide range of phenotypic expression. No significant association was found between SNPs and clinical outcomes. With respect to biochemical outcomes, only one chromosomal region including the rs3811647 SNP in the TF gene showed clear evidence for association with serum transferrin in the GWAS (p-value=7×10 -9 ), in the replication study (p-value=5x10 -13 ) and the combined analysis (p-value=1×10 -20 ). Unexpectedly, this SNP was also clearly associated with serum iron, and therefore indirectly linked to biochemical and clinical outcomes.

Notably, in the general population, rs3811647 was reported as associated with serum transferrin but not with serum iron [START_REF] Tanaka | A genome-wide association analysis of serum iron concentrations[END_REF][START_REF] Benyamin | Variants in TF and HFE explain approximately 40% of genetic variation in serum-transferrin levels[END_REF][START_REF] Pichler | Identification of a common variant in the TFR2 gene implicated in the physiological regulation of serum iron levels[END_REF] contrary to what we found in hemochromatosis patients. It is possible that, in the general population, the power of detecting association with serum iron was compromised by the limited range of the values of this parameter. In contrast, our sample of C282Y homozygotes is a combination of biochemically expressing and non-expressing individuals. The necessarily wider range of serum iron in these patients may have allowed us to highlight the role of rs3811647 genotype in modulating not only serum transferrin but also serum iron levels.

However, our study did not find a direct link between the rs3811647 SNP in the TF gene and the phenotypic presentation of HH. Indeed, although this SNP was associated with serum iron, it was not significantly associated with serum ferritin, transferrin saturation, or any of the clinical outcomes tested. Indirect tests of associations are less powered than direct tests and may require much larger sample sizes than the ones used in this study to allow us to demonstrate a possible influence of the genotype at rs3811647 on other parameters of disease severity. However, we cannot exclude that such an association exists in HFE hemochromatosis only through the dysregulation of iron cellular efflux secondary to the impairment of hepcidin expression (Figure 3).

Our study indicates that the association of rs3811647 with serum transferrin concentration is maintained in C282Y homozygous patients and that the lowest serum transferrin levels are observed in those bearing the GG genotype. However, even the patients with the rs3811647 AA genotype have less serum transferrin than normal controls polymorphism (data not shown). This finding fits with the common observation of decreased serum transferrin levels in C282Y homozygotes, which is attributed to the preservation of a physiologic negative feedback of transferrin synthesis by elevated body iron stores. This could contribute to aggravate the iron burden through the increase of transferrin saturation and the consecutive increase of non-transferrin bound iron, which is considered as the main factor of visceral iron loading in hemochromatosis. However, although they had lower serum transferrin levels, patients with the rs3811647 GG genotype had no increased transferrin saturation when compared to other patients. This is in line with the concomitant decrease in serum iron levels, and could suggests that transferrin levels, as determined by rs3811647 polymorphisms, may participate per se in the regulation of systemic iron, possibly through a direct interaction with the molecular cascade involved in hepcidin production. [START_REF] Finberg | Regulation of systemic iron homeostasis[END_REF] We took advantage of this study to investigate putative candidate genes selected from literature and/or coding for molecules involved in iron-related metabolic pathways and previously identified GWAS-significant SNPs (Supplementary Table 4 and Supplementary Table 5). No association, even borderline, was found. Finally, we focused on TMPRSS6, a modifier gene identified by Valenti et al. in a highly selected population of 96 non-alcoholic male C282Y homozygotes [START_REF] Valenti | Effect of the A736V TMPRSS6 polymorphism on the penetrance and clinical expression of hereditary hemochromatosis[END_REF]. In the subset of 230 non-alcoholic male C282Y homozygotes from the GWAS sample, an association was detected with SNPs located in this gene at the 1% nominal level (p-value = 0.006 with AIR), but this association did not resist multiple testing corrections at the genome-wide level. It remains possible that TMPRSS6 acts as a modifier-gene but with a weak effect compared to age and sex. HH is a long-standing disease whose diagnosis is made at adulthood. Along the constitution of iron excess, many factors are able to act, at various periods and in opposite directions, resulting in highly variable iron burden from an individual to another. These factors include, apart blood donation, pregnancies and menopause that are easy to take into account and to quantify, regimen, drugs (including iron auto-medication), menstrual blood loss, alcohol consumption and evolution of metabolic features that are difficult to reliably assess over a long period. This highlights the need for better controlling environmental factors, not only alcohol consumption, which implies to study much larger population than in the present GWAS.

The present study suffered from several limitations. First, the phenotypic description of HH remains difficult and imprecise. Two types of indicators are available: those measuring the iron burden and those assessing organ damage. The degree of iron burden is usually deduced, at the time of diagnosis, from serum ferritin levels, hepatic iron concentration assessed either by biochemical determination or magnetic resonance imaging, histological semi-quantitative evaluation of hepatic iron stores, and, to a lesser extent, transferrin saturation. However, all these indicators have to be interpreted according to age and gender and are subject to frequent limitations.

Conditions that often coexist in hemochromatosis and may result in overestimation of iron burden can modify serum ferritin levels (i.e. excessive alcohol intake, metabolic syndrome, cell necrosis and inflammatory syndrome). Because it requires an invasive approach, histological and biochemical determination of hepatic iron concentration is less and less performed. It also depends on both liver volume and hepatic iron distribution that may be heterogeneous, especially in case of cirrhosis. Hepatic iron concentration measurement by MRI is reliable within the range of 60-300 µmol/g of dry liver only, which precludes correct assessment of iron burden in patients with early and late hemochromatosis. Finally, transferrin saturation is a rough indicator of iron burden because it is usually rapidly complete regardless of excess iron amount.

Then, we chose to select only patients with amount of iron removed (AIR) available, since AIR is considered as the most reliable means to assess iron burden. However, because AIR is retrospective and often difficult to calculate, numerous C282Y homozygotes of the cohort were lost for inclusion. Indicators of organ damage allow for a precise case description, but the non-specificity of most clinical symptoms and high prevalence of co-damaging factors, such as metabolic syndrome and alcohol, may result in overestimating the role of iron in the clinical presentation. Second, the present study may have been underpowered due to the limited number of cases for a GWAS (n = 474 from the 518 eligible cases) and to the few participants with low or normal body iron stores. Because the frequency of HFE C282Y homozygotes is very low, collecting enough sample size for such a study design to detect variants with moderate effect size is a challenge. Alternative strategy might be needed, such as conducting GWAS of iron status in the general population and then test the identified loci in the C282Y homozygous patients. Large genome-wide studies in which the authors looked for loci controlling serum iron, serum transferrin, transferrin saturation and serum ferritin in the general population have been published recently [START_REF] Tanaka | A genome-wide association analysis of serum iron concentrations[END_REF][START_REF] Benyamin | Variants in TF and HFE explain approximately 40% of genetic variation in serum-transferrin levels[END_REF][START_REF] Pichler | Identification of a common variant in the TFR2 gene implicated in the physiological regulation of serum iron levels[END_REF].

Although performed on large sample sizes, these studies did not provide evidence for variants with significant effects on any of the parameters examined, except for variants in the HFE and TMPRSS6 genes that were controlling serum iron, and variants in TF that were controlling serum transferrin. In this study we found that, in addition to being associated with serum transferrin, the same variants in the TF gene were also associated with serum iron in hemochromatosis patients. If we consider less stringent p-values, the variants in TMPRSS6 can also be considered as marginally associated with some of the iron burden parameters in this sample of hemochromatosis patients. The success rate of this strategy is therefore quite good, but there were not many variants segregating with iron burden in the general population. In addition, it is also possible that different variants control iron parameters in the general population and in hemochromatosis patients, which motivated this particular study. Unfortunately, the C282Y mutation is not routinely screened in the general population, and only few participants with low or normal parameters of iron burden are included in our GWAS study. Therefore, the power of this study is probably compromised to some extent by the limited range of expression of these parameters. Although large-scale studies in the general population could help identify such C282Y homozygotes with low or normal iron parameters, it should be remembered that the frequency of this genotype is only 3-5/1000, and obtaining a number of non-penetrant cases from the same area sufficient to increase the power of this study is unrealistic for the moment. The third limitation is the lack of suitable information about environmental factors. For example, data on regimen with respect to daily iron intake and tea consumption were missing in the database. However, data on alcohol consumption, tobacco smoking, blood donation, and, in females, number of pregnancies and menopause status were collected and analyzed. We did not find significant association when taking alcohol consumption into account but samples sizes were probability too small to detect possible gene-environment interactions. Fourth, although a large number of SNPs were tested (n = 534,213), the present study was far from covering all putative genetic variants able to act as modifiers of iron burden and/or organ damage. Using the SNP-chip data, we investigated the possible role of CNV and did not find any association. However, we were not able to investigate low frequency and rare variants that are not targeted nor tagged by the SNP-chip. We thus cannot exclude based on our results the involvement of one or more modifier genes but we can rule out the role of common variants with large effect outside the TF gene.

In conclusion, our results indicate that, in C282Y/C282Y HFE-HH, the rs3811647 polymorphism in the TF gene continues to regulate serum transferrin levels and is unexpectedly associated with serum iron levels. Our study also demonstrates a potential indirect but weak link, through serum iron levels, between the rs3811647 polymorphism and the clinical and biological expression of the disease. Finally it shows, by contrast to candidate gene studies, that, in an unselected and large population of C282Y homozygotes, i.e. in "true life", there is no other common polymorphism exerting a significant phenotypic effect. At this stage, the role of rare and low frequency variants that are not tagged by SNP-chips remains to be investigated. Next-generation sequencing technologies will enable to explore their role and determine if there exist some rare mutations with clinical significance in HFE-HH. In designing exome or whole genome sequencing studies, it will however be important to carefully select patients and to control for environmental factors. Horizontal lines indicate a suggestive p-value threshold of 10 -6 .

Tables

Figure 2 -Regional plots for rs3811647 located within TF gene.

Regional plots for imputed results are presented for rs3811647 identified as the single locus reaching the genome-wide significance threshold of 10 -8 : for A. serum transferrin concentration analysis (p-value = 7 ×10 -9 ), and B. with pleiotropic effect on serum iron (p-value = 4.9 ×10 -6 ). The rs3811647 SNPs is represented as a diamond.

Other SNPs are gray scaled following their r 2 value with the most associated SNP.

The blue line represents variation in recombination rate. Plots were generated by

LocusZoom.

[28]

  Approval for the genome-wide association study was obtained from the local ethical committee (reference 09/10-722 -23/03/2009). All participants gave written informed consent. Samples were collected thanks to the Logifer database comprising all C282Y homozygous probands and relatives referred to the Liver Unit in Rennes, France, and collected retrospectively before 1989 and, then, prospectively. According to French rules, Logifer was declared to the national committee "Informatics and Freedom" (CNIL). Data are recorded from patient's files by data-managers and keyboarded twice. A clinical research assistant provides quality control, and coherence control and statistical analysis are performed by a bio-statistician. Selection criteria included availability of sex, age at diagnosis, serum ferritin level at diagnosis before any venesection therapy, amount of iron removed by phlebotomy and frozen DNA samples stored at -20°C in the Centre of Biological Resources of Rennes. Carriers of the H63D mutation were excluded from this study. Of the 1730 C282Y homozygotes recorded in Logifer at the time of the study, 518 fulfilled these criteria. Replication for SNPs identified from the GWAS was conducted in 748 C282Y homozygous patients with informed consent from four different European Centres: Toulouse in Southern France (n=279), Brest and Rennes in Brittany (n=226 and n=124, respectively), and Monza in Northern Italy (n=119). Seven clinical and biochemical outcomes were examined: serum transferrin concentration, serum iron, serum ferritin, transferrin saturation, amount of iron removed by phlebotomy, liver fibrosis, and mixed biochemical and clinical score referred as the HAS score (Haute Autorité de Santé)

Figure 1 -

 1 Figure 1 -Manhattan plots displaying results from GWAS of quantitative iron burden indices and clinical outcomes of HFE-HH. Genome-wide analyses were performed for quantitative iron burden indices (serum transferrin concentration, serum iron, transferrin saturation, amount of iron removed by phlebotomy, and serum ferritin), and clinical outcomes (severe liver fibrosis, and HAS-score). All the analyses were performed on 534,213 genotyped SNPs.

Figure 3 -

 3 Figure 3 -Regulation of hepcidin transcription through the bone morphogenetic protein (BMP) -Smad pathway.Binding of holotransferrin to transferrin receptor 1 (TfR1) displaces HFE from TfR1 to TfR2. The HFE-TfR2 complex binds to a complex associating BMPs, BMP receptor (BMPR) and hemojuvelin (HJV). Neogenin and transmembrane serine protease 6 (TMPRSS6) modulate hepcidin transcription by cleaving HJV. Hepcidin acts by favoring the internalization and degradation of the transmembrane iron transporter, ferroportin (FRP), which results in decreasing the systemic biodisponiblity of iron. In HFE hemochromatosis, the C282Y mutation impairs the migration of HFE to the cell membrane and thus the activation of the BMP -BMPR-HJV complex. This results in the preservation of FRP at the cell membrane and thus a high iron efflux.[START_REF] Ruchala | The pathophysiology and pharmacology of hepcidin[END_REF]

Table 1 -Main clinical and demographic characteristics of the primary and replication cohorts GWAS sam ple Replication sam ples

 1

			Rennes	Toulouse	Brest	Monza
	Sample size	474	124	279	224	119
	Gender (female) (male)	(200)(274)	(67)(57)	(108)(171)	(93)(133)	(26)(93)
	Age at diagnosis (years)	45±12	44±14.2	47±12	46.0±13	45±12.2
	Serum iron (mmol/l)	34.5 (29 -39.3)	34.00 (29.34 -38.90) 35.6 (30.4 -40.8)	36.0 (31.0 -41.0)	36.43(33.48 -39.55)
	NA's	26	11	44	16	0
	Serum Transferrin (g/L)	1.80 (1.60-2.00)	1.88 (1.60-2.01)	1.78 (1.60-2.03)	1.77 (1.60-2.00)	1.83 (1.58-2.06)
	NA's	38	14	55	16	0
	Transferrin saturation
	(%)	80 (65 -89)	78 (66.5 -85.85)	84 (67 -92)	83 (73 -92)	84 (72 -90)
	NA's	28	10	35	0	33
	AIR (g)	4.7 (2.1 -8.2)	3.8 (1.7 -7.8)	6.1 (3.5 -11.2)	4.1 (2.12 -6.8)	6(4 -10.75)
	NA's	0	0	197	0	0
	Serum ferritin (µg/L)	776 (446 -1565)	570 (318 -1136)	1118 (634 -2315)	688 (370 -995)	1120 (719-2374)
	NA's	11	5	0	0	0
	Fibrosis (grading)
	no	367	100	128	161	81
	severe	72	14	30	41	25
	NA's	35	10	121	22	13
	HAS (grading)
	0	13	3	3	0	1
	1	44	12	10	0	3
	2	131	45	89	0	48
	3	164	32	141	0	39
	4	76	18	36	0	28
	NA's	46	14	0	224	0
	a Median value ± sd.
	b Median value (25th-75th percentile).
	* Amount of Iron Removed (weekly or bimonthly venesections until serum ferritin < 50; 1 L of blood = 0,5 g of iron)
	NA = non available

Table 2 . GWA Analyses results with P-values <10 -6 SNP Trait Chr Position Closest gene Location A1 A2 maf N effB Pvalue Geno1.freq Geno2.freq Geno3.freq Replication

 2 Abbreviations: sTF=serum transferrin concentration, sFRT= serum ferritin concentration, AIR= amount of iron removed, HAS= HAS score, A1= reference allele, A2: non-reference allele, m af=minor allele frequency, effB= Effect of the non-reference allele in allelic test.

	rs2692695 sTF	3	134968144 TF	intron	G	A	0.41 437 -0.35	1.85E-07	A/A: 78	G/A:230	G/G:166	NA
	rs3811647 sTF	3	134966719 TF	intron	G	A	0.33 437 0.41	7.00E-09	A/A: 46	G/A:217	G/G:211	X
	rs6794945 sTF	3	135001153 SRPRB	flanking_5UTR G	A	0.3	437 0.38	6.03E-07	A/A: 33	G/A:219	G/G:222	NA
	rs3849200 sFRT	6	101765612 GRIK2	flanking_5UTR G	A	0.1	463 0.44	6.19E-07	A/A: 5	G/A: 88	G/G:381	X
	rs4371141 sFRT	16	57773110 GOT2	flanking_5UTR G	A	0.19 463 0.34	9.43E-07	A/A: 18	G/A:144	G/G:312	X
	rs4544229 sFRT	16	57786093 GOT2	flanking_5UTR G	A	0.19 463 0.34	8.91E-07	A/A: 18	G/A:143	G/G:313	X
	rs2810472 AIR	9	135750460 VAV2	intron	A	G	0.25 472 -0.31	9.79E-07	A/A:271	A/G:170	G/G: 33	NA
	rs2810473 AIR	9	135750672 VAV2	intron	G	A	0.25 472 -0.31	9.79E-07	A/A: 33	G/A:170	G/G:271	X
	rs2810493 AIR	9	135756956 VAV2	intron	G	A	0.27 472 -0.3	9.44E-07	A/A: 36	G/A:181	G/G:257	X
	rs3900546 HAS	2	101560458 FLJ42986 flanking_5UTR A	C	0.26 474 -0.75	2.00E-07	A/A:265	A/C:170	C/C: 39	X

Acknowledgements

The authors are indebted to the medical doctors and the nurse staff of the Liver Unit and to the Centre de Ressources Biologiques of the Rennes University Hospital.

They acknowledge all the patients for accepting to participate in the study. The authors would also like to acknowledge Michelle Perrin (Inserm CIC 0203) and Jeff Morcet (Inserm CIC 0203) for managing quality control and statistical analysis of the Rennes Logifer database, Laura Pages (Inserm U1043) for collecting clinical data on the patients, Céline Besson-Fournier (Inserm U1043) for preparing the DNA samples, Frédéric Martins and Jean-José Maoret (GeT Platform, Genotoul) for running the SNPtype assays, and Pr. Jean-Pierre Vinel (Hepatogastroenterology Unit, CHU Purpan, Toulouse) for his support. We thank Pr. W. Bodmer and the People of the British Isles project for the genotyping of controls from Brittany.

The study was granted by the Programme Hospitalier de Recherche Clinique (PHRC National 2008), the Agence Nationale de la Recherche (ANR-08-GENO-034), and the Fonds d'Aide à la Recherche (FAR) en Hépato-Gastroentérologie de la Société Nationale Française de Gastro-Entérologie (2011). It was also supported by the Association Fer et Foie. responsible for study design. M.D.