domain: shs shs.eco shs.envir math sde stat

text:
Julien Chevallier
email: julien.chevallier@ipag.fr

Stéphane Goutte
email: stephane.goutte@univ-paris8.fr

Khaled Guesmi
email: khaled.guesmi@ipag.fr

Climate finance and the restructuring of the oil-gas-coal business model under carbon asset stranding constraints *

Keywords: Stranded asset, Stochastic process, Monte-Carlo simulations, Climate finance JEL Codes: F36, G12, Q57

Oil-gas-coal companies are particularly concerned by the notion of stranded assets, i.e., the fact that known fossil reserves cannot be burnt should limitations on greenhouse gas emissions become more stringent. Those assets can suffer from unanticipated or premature write-downs, devaluations or conversion to liabilities. This paper simulates the impacts of carbon stranded assets for 17 major oil-gas-coal firms' value until the horizon 2050. The core of the paper is a stochastic model with stopping times that determines by initial conditions (reserves and extraction rates) which companies are left with 'stranded assets.' In the business-as-usual scenario, one-quarter of the Earth's capacity for absorbing emissions will be depleted by 2050. With stringent emissions-curbing policies, an environmental gain of 80% can be achieved. Without a restructuring of their business model, many oil-gas-coal companies stand out from our simulations as being particularly vulnerable to the financial risks of bankruptcies and default events.

Introduction

If we burn all current reserves of fossil fuels, we will emit enough CO 2 to create a prehistoric climate, with Earth's temperature elevated to levels not experienced for millions of years. Such a world would be radically different from today.

-Nicholas Stern (LSE, 2013) In 2018, William D. Nordhaus was named co-recipient (alongside Paul M. Romer) of the Nobel prize in economics for integrating climate change into the long-run macroeconomic analysis (Nobel [START_REF] Media | The Prize in Economic Sciences[END_REF]. This recognition of the need to incorporate climate-related topics into economic analysis recalls us that, at current levels, the consumption of fossil energy appears strongly unsustainable. In its 2018 report, the Intergovernmental Panel on Climate Change (IPCC, 2018) stresses -with a high confidence level -that global warming is likely to reach +1.5°C between 2030 and 2052 if it continues to increase at the current rate. As a matter of hope, regional initiatives are at stake, as revealed by the World Bank's (2018) effort to map carbon pricing around the world. As of September 1, 2018: 46 national jurisdictions and 25 subnational jurisdictions are putting a price on carbon; whereas 53 carbon pricing initiatives are implemented or scheduled for implementation.

Unfortunately, the fight against climate change is unlikely to be adequately addressed without a restructuring of the fossil fuel industrial complex. Article 2 of the December 2015 Paris Agreements calls for 'making finance flows consistent with a pathway towards low greenhouse gas emissions and climate resilient development.' Climate policy, therefore, brings the need that carbon will be priced much more vigorously than nowadays [START_REF] Bredin | A microstructure analysis of the carbon finance market[END_REF][START_REF] Philip | Impact of allowance submissions in European carbon emission markets[END_REF]; [START_REF] Kalaitzoglou | Liquidity and resolution of uncertainty in the European carbon futures market[END_REF]. Against this background, many of today's carbon assets would become stranded. For financial investors, these assets are thus at risk. This paper argues that especially oil-gas-coal companies face the risk of stranded assets with ensuing unanticipated and premature write-downs, devaluations and conversions to liabilities.

Global warming proposes to restrict the use of resources for carrying capacities reasons (both biological and ecological), rather than because of fossil fuel depletion. Confronted with the exponential discoveries of new fossil fuel reserves, carbon stranded assets impose a new mode of regulation of resources that are compatible with the objective to reduce carbon dioxide emissions. [START_REF] Caldecott | Stranded Assets and Scenarios[END_REF] elaborate that stranded assets are assets that have suffered from unanticipated or premature write-downs, devaluations or conversion to liabilities, and there is a range of environment-related risks that can cause them to occur. Further on this definition, [START_REF] Mcglade | The geographical distribution of fossil fuels unused when limiting global warming to 2°C[END_REF] discuss the geographical distribution of fossil fuels unused using an integrated assessment model. Many investors and pension funds are thinking of taking action to hedge themselves against the risk of stranded assets.

Based on IPCC (2007a,b) documentation, the Carbon Tracker Initiative (2015) has evaluated that, in order to have an 80% chance of keeping global warming below 2°C, only 565 GtCO 2 can be emitted between 2010 and 2050. [START_REF] Morrissey | Assumption and Calculations Note[END_REF] provides an updated calculation that this carbon budget is now equal to 525 GtCO 2 between 2013 and 2050. Besides, the International Energy Agency (IEA) stated in its 2012 World Energy Outlook that two-thirds of fossil fuel reserves cannot be burnt if the world is to have a 50% chance of limiting global warming to 2°C. Several international initiatives are underway to fight climate change, such as the COP/MOP meetings, the EU emissions trading scheme, China's provincial and citylevel pilot trading schemes, South Africa's carbon tax, Australia's emissions reduction fund, the Mexican carbon platform or sub-national schemes in the USA. If governments live up to their commitments to keep global warming below 2°C, Bloomberg (2013) documents that climate change policy could induce the stranding of company's earnings and share price, particularly those in extractive industries under carbon pollution constraints. MSCI (2015) assesses that companies are exploring the potential impact on their assets of the increase in the Earth's temperature of 2.6-4.8°C based on the current trajectory.

Carbon stranded assets apply mainly to companies that own fossil fuel reserves and companies whose business activities are highly carbon-intensive. That is why this paper focuses mainly on the oil and gas industry, which is deeply concerned about changes in (i) the prices of oil and gas, (ii) companies' cost of exploring new oil and gas reserves, and (iii) the revenues and costs from extracting fossil fuels. If costs are greater than the revenues from fossil fuel extraction, then the company will not extract. These events lead to 'wasted capital' if the price drop of the underlying asset is seen as permanent (LSE (2013)). Changes in CO 2 emissions, carbonintensity levels, and carbon prices could impact financial returns. The market capitalization of oil and gas companies can, therefore, be strongly impacted by the advent of low emissions policies.

The article provides empirical estimates of the loss in market value to be suffered among a sample of 17 fossil companies in the event of (i) a proportion of reserves becoming 'unburnable';

(ii) a reduction in the price of fossil fuels. The original contribution of this paper is to value carbon stranded assets of oil, gas, and coal companies with a stochastic model. Methodologically, this paper uses the techniques of stochastic modeling with stopping times including Monte Carlo simulations with a horizon up to 2050. The theoretical framework hinges on Hotelling's rule translated by [START_REF] Miller | A test of the Hotelling valuation principle[END_REF] into an empirical specification for oil, gas and coal companies. The link with companies' extraction rates and reserves builds on the relationship established by [START_REF] Pickering | The oil reserves production relationship[END_REF]. The data feeding the simulation range from 2005 to 2015.

Inspired by the IEA's World Energy Outlook (IEA, 2012) statistics, we elaborate several scenarios (regarding the stock of oil and gas reserves that may become unburnable and the profile of the cut in fossil fuels prices). The simulations establish that the extent of the losses in the value of the firms (computed as the share price times the number of shares) varies depending on the stringency of the scenario. The more the default intensity rises (i.e., the probability that a carbon asset stranding scenario impacts the company), the more the oil-gas-coal company loses value.

Regarding the core message of the paper, in the benchmark scenario, the firms gathered in our sample will have emitted nearly 150Gt CO 2 -equivalent by 2050, i.e., approximately onequarter of the IEA global target in their 450ppm world. This situation can be avoided by resorting to stringent climate policies, such as the ones simulated in our paper, with a decrease up to 80% of that figure. The carrying capacity of the Earth would, therefore, be preserved. The results feature decreasing values of oil-gas-coal companies in all scenarios, with rapid convergence towards bankruptcy. Therefore, carbon asset stranding seems to threaten the very existence of these firms, unless there are changes in their business model or technology (such as renewables deployment for instance).

The paper is structured as follows. Section 2 details the conceptual framework. Section 3 documents the data and the scenario. Section 4 develops the empirical results. Section 5 develops policy implications for policy-makers and investors. Section 5 concludes.

Model

Until 2050, we create several scenarios of asset stranding, depending on the severity of the carbon constraint at that date.

Our modeling strategy unfolds in three steps:

1. The value of the oil-gas-coal company is determined by resorting to Hotelling's exhaustible resource theory as formulated by [START_REF] Miller | A test of the Hotelling valuation principle[END_REF].

2. Remaining oil reserves are significantly linked with extraction rates as shown by [START_REF] Pickering | The oil reserves production relationship[END_REF]. This second step is required for the calibration of the simulation model.

3. Stochastic processes with stopping times are fitted to each company in order to simulate the impact of carbon stranded assets for a given scenario. Intuitively, the model allocates the unburnable carbon randomly to companies across the scenarios, based on the probability of occurrence of stopping times and their intensity.

2.1

Step #1: Hotelling's exhaustible resource theory for oil, gas & coal companies Following Hotelling's Principle, [START_REF] Miller | A test of the Hotelling valuation principle[END_REF] have created an empirical framework to test that the value of the reserves in any currently operating, optimally managed oil-gas-coal company depends mainly on current period prices and extraction costs. The 'Hotelling Valuation Principle' establishes that the net price explains a large proportion of reserves' market value.

To do so, the authors propose to regress the market values of the reserves of a sample of oil-gascoal companies on their estimated Hotelling values at several points in time during the sample period. Formally, the conceptual framework can be stated by the following equation:

V R = α + β(p -c) + t (1)
with V the value of the firm (share price × number of shares), R the total reserves in tonnes

Step #2: Linking oil, gas & coal companies' extraction rates and reserves

Digging further into this conceptual framework, we need another equation to link extraction rates and reserves. According to [START_REF] Pickering | The oil reserves production relationship[END_REF], the relationship between extraction and remaining reserves is found to reduce to a simple representation: at any point in time, optimal extraction depends on an idiosyncratic constant and the product of a slope parameter and remaining reserves. Therefore, or each company contained in our sample, the linear extractionreserves relationship writes:

q t = δ + θR t + t (2)
with q t extraction at time t, and R t reserves at the start of the current period. Simulations feed on these oil extraction-reserves estimates. As detailed in Section 3, the data consists of proven reserves as of the end-of-year, and average daily extraction rates.

2.3

Step #3: Stochastic processes with stopping times to simulate carbon stranded assets' trajectories by 2050 Now, we implement the trajectories that would occur in the presence of vigorous climate policies by 2050. Carbon stranded assets are assets that may lose economic value before the end of their expected life. To reproduce this behavior, we resort to stochastic processes with random stopping times.

Stochastic model

Consider a probability space (Ω, G, P) equipped with a Brownian motion W = (W t ) t∈[0,T ] over a finite horizon T < ∞. In our study, T equals 2050.

We are given a non-negative and finite random variable τ , representing the default time, on

(Ω, G, P). remark 1

• The default time τ models default events which can occur during the time to maturity 2050. This default time can depend on several energy, environmental, technological or financial factors.

• The Brownian motion W = (W t ) t∈[0,T ] represents the stochastic evolution of the future financial asset such as volatility, or jumps.

We consider a risky asset subject to environmental default risk, which is the price process S = V R given by:

S t = S 1 t 1 t<τ + S 2 t (τ )1 t≥τ , 0 ≤ t ≤ T, (3)
where S 1 represents the dynamic of the asset before the possible environmental default event at time τ ∈ [0, T ]. This process evolves according to following stochastic differential equation:

dS 1 t = S 1 t µ 1 dt + σ 1 dW t , S 1 0 = S 0-, 0 ≤ t ≤ T, (4)
and

{S 2 t (τ ), θ ≤ t ≤ T, τ ∈ [0, T ]
} is a family of processes representing the dynamics of the asset after the environmental default event occurrence at time τ ∈ [0, T ], and governed for all τ < t ≤ T by:

dS 2 t (τ ) = S 2 t (τ ) µ 2 (τ )dt + σ 2 (τ )dW t and S 2 θ (τ ) = S 2 τ -(1 + γ τ ) (5)
Here, we denote by S 0-the initial value of the environmental asset, and γ is a stochastic process valued in [-1, ∞) representing the jump of the asset S at the environmental default time τ .

remark 2 The special case of a death of the asset S after the default event τ is modeled with γ τ = -1 (and µ 2 t (τ ) = σ 2 t (τ ) ≡ 0). Indeed, when the possible default time occurs, after the default the asset price S 2 t will be equal at the time τ to:

S 2 θ (τ ) = S 2 τ -(1 + γ τ ) = S 2 θ-(1 -1) = 0
And so for all τ < t ≤ T S 2 t (τ ) ≡ 0

The interpretation of the default risk model for the asset price S is the following. The process S 1 represents the environmental asset price before the default. There is a jump on the asset price at the default time, represented by the process γ, which may take positive or negative values (corresponding to proportional loss or gain on the asset price). After the default at time τ , S 2 (τ ) represents the asset price process. There is a change of regimes in the coefficients depending on the default time. One typical situation can be as follows: in case of downward (respectively, upward) jump in the asset price at default time τ ∈ [0, T ], the rate of return µ 2 (τ ) should be smaller (respectively, greater) than the rate of return µ 1 before the default. This gap should increase when the default occurs early, i.e. µ 2 (τ ) is increasing (respectively, decreasing) in τ with µ 2 (τ ) < (resp. >) µ 1 .

remark 3 In our setting, there are several sources of randomness of the asset price. Indeed, there can be financial market risks modeled with the Brownian motion W . There are the possible default events modeled with the stopping time τ . There are the stochastic jumps at the default time τ modeled by γ τ . Finally, the regime switching shifts of the parameters before and after the possible default events are modeled by the shifting parameters µ 1 to µ 2 (τ ) and σ 1 to σ 2 (τ ).

Notice that the new parameters values (µ 2 and σ 2 ) and the jump factor γ depend on the time of default τ . This means that the intensity can depend on the time-to-maturity when the default occurs (i.e., T -τ ). This allows us to deal with the case where an earlier default could have a lesser impact on the asset price S than a later one.

Default event

In our framework, we assume that the default event τ is due to exogenous factors (e.g., any shock related to energy, environmental, financial or technological variables) in the stochastic dynamics of the asset price S. The random variable τ is independent of the Brownian motion W . Thus, there exists a deterministic function α(τ ) of τ ∈ R + such that the survival probability is given by:

G(t) = P [τ > t|G t ] = P [τ > t] = ∞ t α(θ)dθ (6)
We assume that the survival probability follows an exponential distribution with constant default intensity λ. There exists a constant λ > 0 such that G(t) = e -λt . The density function is α(θ) = λe -λθ . The higher the value of the default intensity λ, the higher the possibility of a default event in the dynamic of S.

3 Data and Scenarios

Oil-gas-coal companies' share prices and earnings data

By focusing on the oil-gas-coal industry, we select a subset of 17 companies that are particularly concerned about carbon stranded risks. These companies were selected based on their market capitalization in international financial markets, i.e., we are mainly concerned with oil-gas-coal giants.

Principal Component Analysis

To illustrate our database, we run a Principal Component Analysis (PCA) on the variables V R for each company given by [START_REF] Basher | Oil price risk and emerging stock markets[END_REF], where V denotes the value of the firm (share price × number of shares) and R the total reserves in ton / CO2-equivalent. This methodology allows us to represent by clusters the segmentation companies concerning their principal activities: oil, gas, and coal.

The PCA results are given in Figure 1.

*** Insert Figure 1 about here ***

1 For brevity, descriptive statistics of the raw data are not reported, but they can be accessed upon request. 2 Accessible at http://www.eia.gov/beta/international/data/browser/

We can broadly identify six sub-groups among the 17 companies selected in our sample. On the lower left corner, Huaneng and Datang reflect the firm value characteristics of power production companies (in China). Second, from the left, Exxon and Chevron belong to the same category of oil giants. This group is followed by Shell, BP, and Total towards the middle of the plot, reflecting that global oil companies share the same data characteristics concerning firm value. On the right side of the graph, we notice a fourth group composed of PetroChina and CNOOC, i.e., Chinese oil companies. Next, the fifth group is composed of Peabody (coal), Petrobras (oil), China Resources (power) and China Shenhua (coal) which are highlighted by the PCA to share similar characteristics concerning firm value. The last group on the lower right corner is composed of Engie (gas), RWE, EON, and NTPC (power). Unlike the previous companies belonging to the oil and gas sector, the final group reflects mostly the characteristics of power plants. These latter companies do not own resources -presumably, they are affected by carbon budgets because they cannot use their power plants which burn fossil fuels. Interestingly, this is a very different kind of asset-stranding to leaving reserves in the ground.

The total variance explained by each factor of the PCA are given in Figure 2.

*** Insert Figure 2 about here ***

With the first two principal components, we capture a total of 75% of the total variance, which is regarded as extremely satisfactory by all standards in the factor modeling literature (see [START_REF] Stock | Forecasting using principal components from a large number of predictors[END_REF]).

Scenarios

To build our scenarios, we consider as a building block the IEA '450' scenario, whereby GHGs are limited to 450 parts per million, resulting in a 50% chance of limiting global warming to 2°C (IEA, 2012). Our time-frame goes to 2050, i.e., it features both short-term and long-term decision-making without being too distant in the future. Most policy discussions focus on GHG reductions by 2050 (for a review, see Caldecott Cuts in fossil fuels prices are relevant for asset stranding in the sense that they adversely affect the financial health of the company.

Empirical Results

Steps #1 and #2

Eqs. ( 1) and (2) feed-in the existing 2005-2015 data to calibrate the 2050 simulations. 3 Results are reproduced Tables 3 and4.

*** Insert Tables 3 to 4 about here ***

The interested reader can track the significance of the β for each company (Step #1) or fuel (Step #2) feeding the subsequent stochastic simulations.

Simulations of V R losses concerning benchmark and scenario

We run M C = 10, 000 Monte-Carlo simulations of our stochastic model (Step #3 ) with an intensity default event defined in [START_REF] Cummins | Price discovery analysis of green equity indices using robust asymmetric vector autoregression[END_REF]. This value has been fitted regarding the empirical standard deviation fluctuation of all historical data values.

We begin by regarding the loss of values of each firm per unit of the reserve concerning the forecasting values with different values of the random default. We run forecasting simulations with the impact of default equal to 5%, 10%, 20% and 50% on the dynamic components.

The results for the different scenarios are given in Tables 5,6, 7, 8 and 9.4 *** Insert Tables 5 to 9 about here ***

If we look at the scenario where 20% of oil & gas reserves become unburnable, we observe that each company will lose firms' values per unit of reserve at maturity 2050. Total SA will lose 84, 21% of its value per unit of reserve and EON will lose 99, 80% per unit of reserve so goes to bankruptcy. 5We observe that, if we increase the impact of the default event, each loss increases and so each company will lose a higher share of its values.

Regarding the scenario where oil-gas-coal reserves are unburnable (Tables 2 to 5), we can notice that with the weakest scenario (20% of reserves are unburnable, and only 5% of intensity of default), there are already 9/17 firms that go into bankruptcy before the maturity of 2050 with a probability higher than 80%. In the worst case, 67.92% of the firms will bankrupt before 2050 and 87.49%. If we take an intensity of environmental default event of 50% moreover, there are in this case 14/17 firms that go into bankruptcy. 11 of the 14 firms have a probability to go into bankruptcy higher than 95%.

Moving to the scenario dedicated to a 50% cut in fossil fuels price, most firms go into bankruptcy before the maturity of 2050. For a price cut of 25% and an intensity of default of 10%, there are still 9/17 firms which go into bankruptcy with a probability higher than 90%. This figure grows to 12/17 with an intensity of 50%, and 13/17 with the same intensity but with a price cut equals to 50%.

We demonstrate that if there is a cut in fossil fuels price, the firms' values per unit of reserve go down extremely quickly. It means that the solvency and the capital of this firms are very correlated to the fuel price. This means that their income comes for the most critical part of the change in the price of the fuel.

This could explain that with a scenario of a cut of 50% and a very low intensity of default, there are still 13/17 firms which go into bankruptcy with a probability higher than 80%, and 7 with a probability higher than 95%. When we look the worst case, we obtain a global probability of bankruptcy before 2050 of 91.92% of the studied firms, and in details 13/17 with a probability higher than 95% and 6 with one higher than 99%.

Economically speaking: firms are relying too much on incomes from fuel sales, and are adversely impacted by a downward trend in the fuel price. We may advance the following policy recommendation: develop alternative income sources that are not correlated with fuel prices; gear towards an energy model based on the consumption of renewables.

Trajectories for each company, depending on the carbon asset stranding scenario, are displayed in Figures 3 to 7. • The loss increases when the asset stranding scenario is more stringent.

• Firms seem more dependent on fossil fuel price cuts than to their reserves becoming unburnable. Indeed, the scenario of a cut in fossil fuels price is more damaging for the firms' values per unit of reserve. This means that the number of firms which go into bankruptcy is higher in these scenarios than with scenarios where a percentage of oil-gascoal reserves are unburnable.

• The probability of bankruptcy of firms increases with the intensity of default. The higher the probability of a shock in the value of the firm per unit of reserve, the worse the cash-flow of companies.

Link to the Earth's absorbing capacity: horizon 2050

We compute the contents in CO 2 -equivalent of each firms' values regarding equation [START_REF] Basher | Oil price risk and emerging stock markets[END_REF]. Indeed V R corresponds to the value of the firm V (share price × number of shares) divided by R the total reserves in tonnes CO 2 -equivalent. We go back to the amount of CO 2 -equivalent in 2050 of the total reserves in ton with the straightforward calculus:

CO 2 -Equivalent 2050 = V /R share price × number of shares -1
Regarding the previous results we display the more optimistic scenario with an intensity default of 5%. 6 *** Insert Table 10 about here *** R t returns the sum of the column for the subset of 17 companies. Without carbon asset stranding, the benchmark scenario (whereby available reserves are burnt on a business-as-usual fashion, without changes in the business model of companies) results suggest the Earth's absorptive capacity is negatively impacted by 147.77GtCO 2 (Table 8, R t row, first column), i.e., approximately one-quarter of the IEA 565GtCO 2 scenario to meet the 2°C target.

On the other side of the spectrum, the most stringent carbon asset stranding scenario (e.g., 60% of oil-gas-coal reserves are unburnable), the Earth's absorptive capacity is only reduced by 55.56GtCO 2 (Table 8, R t row, fourth column), i.e. a welcome 60% reduction of the GHG emitted for a path towards a sustainable future.

To complete the picture with respect to our theoretical framework, the last line of Table 10 reflects the actual extraction q t computed according to the coefficient estimates of Eq.( 2) for each type of oil-gas-coal company: Notice the coefficients on oil, gas, and coal depletion rates are positively related to oil, gas and coal reserves, respectively, as documented previously by [START_REF] Pickering | The oil reserves production relationship[END_REF]. This corroborates the validity of our empirical results.

Breaking down extraction by fossil fuel type reveals the same information as for reserves: departing from the standard scenario (145.77GtCO 2 ), carbon asset stranding can dramatically dampen the impact of oil-gas-coal companies the Earth's absorptive capacity up to 80% reduction for the most CO 2 -intensive fuel (coal equals 23.42GtCO 2 ) in the most stringent stranding scenario.

Recall that our simulation exercises are only focused on a subset of 17 oil-gas-coal companies, henceforth the goal stated in the Paris COP 21 agreements of keeping global temperature rise to below 2 degrees Celsius need strict CO 2 emissions reductions. The World Bank (2016), in its latest State and Trends of Carbon Pricing report, describes a sense of urgency, with each passing day, the climate challenge grows.

Policy implications

Of all the recent ideas climate change campaigners have come up with to convince the world to do more to curb global warming; none has been as potent as the concept of stranded fossil fuel assets.

-The Financial Times (2015)

CO 2 emissions cuts rank very high in policy makers' agenda, as illustrated by the Paris COP-MOP 21 agreements in December 2015, and the subsequent ratification by China in 2016. The EU announced on October 7, 2016 that more than 50 states representing more than half of GHG had ratified the Paris agreements, only ten months after signature, thereby announcing the entry into force of the new international climate treaty7 .

Indeed, when dealing effectively with climate change, authorities attempt to regulate the consumption of carbon assets. The goal is to manage the expectation of investors, and avoid that the market misinterprets the energy transition. Taken together, limitations on future GHG emissions, substitution with other energy sources, and decreases in the overall demand for energy can financially affect the functioning of the energy sector.

Fixed assets that are locked into burning fossil fuels can become stranded in a carbonconstrained world (MSCI (2015)). For instance, consider the case of a coal-fired power plant, that is at risk of being stranded due to its high carbon-intensive content. If carbon emissions are constrained, the power plant is at risk of drastically losing value. The impact of asset stranding varies depending on the carbon exposure of the companies, and across portfolios. For a given company, its carbon exposure varies on two levels: (i) current emissions, and (ii) fossil fuel reserves representing potential future emissions. Various stakeholders are concerned about climate change and can exert pressure on the company to manage carbon stranded asset risks.

Potentially unburnable carbon is listed on stock exchanges, which is indicative of carbon risk mis-pricing. Companies listed on the London Stock Exchange ought to disclose mandatory carbon reporting. Germany has mostly shifted to renewable energy in 2014, causing hefty write-downs on coal-and gas-fired power plants: EUR 3.3 billion and EUR 4.5 billion for RWE and EON, respectively, whereas the French company GDF-Suez (now re-branded Engie) took a write-down of EUR 14.9 billion on its conventional power plants.

Institutional investors are also concerned about managing carbon risks in their portfolios. Divestment strategies are indeed visible from the investors' perspective. The Norwegian-Swedish pension fund Storebrand ($74bn of asset under management) excluded coal companies from its portfolios in early July 2013. In May 2014, Stanford University announced that its endowment fund would sell off its holdings in coal mining companies. In Sweden alone, the Fourth National Pension Fund, the Church of Sweden, AP3 as well as internationally the French Pension Fund FRR, KPA, APG in the Netherlands, GEPF in South Africa and the United Nations Joint Staff Pension Fund have taken similar steps towards low-carbon asset allocation (Worldbank (2014), Mercer (2014)). UNEP Finance Initiative and UN Secretary-General Ban Ki-Moon support the Portfolio Decarbonization Coalition that aims at reducing the carbon intensity of institutional investors' portfolio up to $100 billion by December 2015. Rebalancing stock holdings based on a higher allocation to carbon-efficient companies relative to their competitors is also gaining momentum among asset managers such as Amundi and MSCI. By construction, such carbontilted strategies offer less exposure to carbon risk.

The strong point of this paper is that it attempts to more formally model the risk of stranded assets rather than the previous policy-based studies. Therefore, our simulation results are particularly relevant to asset owners, banks, other financial intermediaries, businesses and governments. Investment strategies that are compatible with these simulations involve divesting from fossil fuels and moving towards a greener energy mix, for instance through investments in green indices [START_REF] Cummins | Price discovery analysis of green equity indices using robust asymmetric vector autoregression[END_REF].

Conclusion

Carbon stranded assets can be defined as 'blocked assets' that have suffered from unanticipated or premature write-downs, devaluations for oil-gas-coal producing companies. Stranded assets are assets that become obsolete before their complete damping by business cycle or some factors (e.g., regulation, innovation). It results in losses of their market value because of market evolution, or risk to become unusable. For example, it can be the case of coal and hydrocarbon resources.

In the burgeoning field of climate finance, it makes sense to control as well the level of CO 2 emissions using asset stranding in order to alleviate the Earth's absorptive capacities. Carbon stranded assets strongly impact oil & gas companies' earnings and share price, thereby altering asset values and introducing significant investment planning discontinuities. In this paper, we show that the concept of carbon stranded assets leads to redefining risk for a sample of oil, gas and coal companies.

Concerning several carbon asset stranding scenarios, this paper develops a partial-equilibrium stochastic model with stopping times to display the firms' value (defined as the share price times the number of shares) of 17 major oil-gas-coal companies. The theoretical framework hinges on empirical specifications of the Hotelling rule from data retrieved from 2005 to 2015, extended by our simulations until the 2050 horizon. First, the valuation of oil, gas and coal companies is following [START_REF] Miller | A test of the Hotelling valuation principle[END_REF] based on Hotelling's rule. Second, the oil reserves production relationship is established regarding previous work by [START_REF] Pickering | The oil reserves production relationship[END_REF]. The third step is to have a stochastic model with random stopping times and stochastic Poisson jumps in the environmental asset prices. The shocks to prices are exogenous.

The empirical calculations for 17 oil, gas and coal companies require extractions costs from the companies' accounts. As a preliminary analysis, principal components explain about 75% of the variation of the dataset. The scenarios considered are that, respectively, 20%, 40% and 80% of oil and gas reserves are unburnable and that, respectively, there is a 25% or 50% cut in fossil fuel prices.

In the absence of ambitious climate policies, the benchmark scenario implies that the Earth's absorptive capacity will be reduced by nearly 150 Gt-CO 2 -equivalent by 2050, which represents about one-quarter of the IEA's 450ppm target for a subset of only 17 oil-gas-coal companies. With carbon asset stranding, the value of these firms is adversely affected, and in many cases ends up in bankruptcy (without a shift to clean energy, behavioral changes or innovation). 80% of CO 2 -equivalent emissions can be avoided by restricting the use of coal and hydrocarbon resources.

CO 2 -

 2 equivalent, p the fuel price, c the marginal extraction cost computed as ∆C ∆q with C the total extraction cost and q the rate of extraction, and the error term. The market values are based on stock market prices for the firms' shares. The Hotelling values are based on estimates of extraction costs and estimated reserves recovered from various data sources, as detailed in Section 3.

Figure 8

 8 Figure8displays a summary of losses. We remark that:

T6TT

  = 123 R2 = 0, 9944 F (1, 121) = 21795, σ = 0, 00076399 (standard deviation in parentheses) Further results are available upon request, but they are even more pessimistic = 123 R2 = 0, 9823 F (1, 121) = 6791, 1 σ = 0, 0037159 (standard deviation in parentheses) = 123 R2 = 0, 9596 F (1, 121) = 2898, 7 σ = 0, 0032833 (standard deviation in parentheses)

Figure 1 :Figure 2 :

 12 Figure 1: Principal Component Analysis on V R

Figure 3 :

 3 Figure 3: Scenario: 20% of oil & gas reserves are unburnable.

  The training sample of our simulations is restricted to the 2005-2015 period due to data availability.For each company, we collect from Bloomberg daily share prices (period: July 21, 2005, to October 19, 2015), as well as annual earnings (EBIT).1 3.2 Oil-gas-coal extraction and reserves dataOil, gas, and coal total reserves and extraction figures are taken from the U.S. Energy Information Administration (EIA), from their 'International Energy Statistics ' database.2 .To transform U.S. EIA oil, gas & coal reserves, and extraction figures into CO 2 -equivalent quantities, we have used engineer's conversion rates reproduced in Table2.Besides, for each company selected in our sample, we have extracted extraction costs (in USD) manually from the Consolidated Financial Statements as reported individually in each company's annual reports available from the company website.

*** Insert Table 1 about here *** *** Insert Table 2 about here ***

  et al. (2014)). To meet 2°C, there can be minimal additional emissions beyond 2050. According to the IEA (2012), current oil & gas reserves amount to 762 GtCO 2 by 2050, which go far away from the 2°C mark (565 GtCO 2 can be emitted between 2010 and 2050, similar calculations have been performed by the Carbon Tracker Initiative (2015) based on IPCC documentation for instance). Additional exploitation of oil & gas reserves could inflate the potential CO 2 emissions listed on stock exchanges up to 1,541 GtCO 2 .Since there is more fossil fuel listed on the world's capital markets that can be burned, we simulate the following scenario:

	Planet environmental ecosystem preservation
	1. 20% of oil & gas reserves are unburnable;
	2. 40% of oil & gas reserves are unburnable;
	3. 60% of oil & gas reserves are unburnable;
	Financial crisis and technology improvements
	4. 25% cut in fossil fuels price.
	5. 50% cut in fossil fuels price.

Table 1 :

 1 List of Selected Oil, Gas & Coal Companies

		Company	Market Cap (USD Billion)	EBIT in USD thousands
				Dec 31, 2014 Dec 31, 2013 Dec 31, 2012
	1	Exxon Mobil Corp	339,06	51,916,000?	57,720,000?	79,053,000
	2	Petrochina	151,74	29,026,000?	33,226,000?	29,689,000
	3	Chevron Corp	168,49	31,202,000?	35,905,000?	46,332,000
	4	Royal Dutch Shell PLC	204,17	23,026,000?	27,769,000?	37,879,000
	5	BP PLC	106,8	9,555,000?	15,255,000?	11,901,000
	6	Total SA	115,96	16,579,000?	25,249,000?	30,596,000
	7 Petrobras Brasileiro SA	32,55	(4,901,000)	16,083,000	16,509,000
	8	CNOOC Ltd	52,65	14,070,000	13,926,000	14,730,000
	9	Engie (GDF-Suez)	41,98	6,567,000	7,515,000	9,315,000
	10	RWE	7,62	2,936,000	2,923,000	4,973,000
	11	EON	18,44	4,562,000	4,835,000	5,180,000
	12	China Shenhua	274,48	63,665,000	70,979,000	70,544,000
	13	PEABODY	456	(119,700)	(309,100)	197,000
	14	Huaneng Power	17,38	4,330,060??	4,164,284??	2,852,813
	15	Datang	41,53	14,537,000??	15,887,000??	13,036,000
	16	NTPC	1053,77	151,003,000??	144,433,000??	120,330,000?
	17 China Resources Power	36,64	(1,038,000)	2,676,000??	2,507,000??
	Note: EBIT stands for Earnings Before Interest And Taxes.

Table 2 :

 2 CO 2 -equivalent conversion rates for oil-gas-coal reserves and extraction figures from U.S. EIA

	CO 2 content of the original unit	695,13700 millions of tonnes per billions of short tons	0,69514 millions of tonnes per millions of short tons	15,79814 millions of tonnes for 1 000 bcf	0,01580 millions of tonnes for 1 bcf	116,20000 millions of tonnes per billions of barrels	0,11620 millions of tonnes per millions of barrels	0,11620 millions of tonnes per millions of barrels	0,11620 millions of tonnes per millions of barrels
	CO 2 content of the tep	1,123 tonne per tep	1,123 tonne per tep	0,651 tonne per tep	0,651 tonne per tep	0,83 tonne par tep	0,83 tonne per tep	0,83 tonne per tep	0,83 tonne par tep
	Conversion rate in tep	0,619 tep per tonne	0,619 tep per tonne	0,0242675 tep for 1000 cf	0,0242675 tep for 1000 cf	0,14 tep per barrel	0,14 tep per barrel	0,14 tep per barrel	0,14 tep per barrel
	U.S. EIA original unit	Coal Reserves billions of short tons	Coal Extraction millions of short tons	Gas Reserves 1000 bcf	Gas Extraction bcf	Oil Reserves billions of barrels	Oil Extraction Power millions of barrels	Oil Extraction Industrial millions of barrels	Oil Extraction Commercial millions of barrels	Note: tep stands for tonne equivalent petrol.

Table 3 :

 3 Calibration:Step #1

	Company	Beta	Sign of	Significance
			the Beta	level
	EXXON	2,88E-09	+	-
	PETROCHINA	2,50E-08	+	-
	CHEVRON	4,16E-09	+	-
	SHELL	6,31E-09	+	-
	BP	7,83E-09	+	-
	TOTAL	4,05E-09	+	-
	PETROBRAS	1,00E+00	+	1%
	CNOOC	3,14E-08	+	-
	ENGIE	2,21E-08	+	1%
	RWE	8,10E-09	+	-
	EON	2,06E-08	+	10%
	CHINASHENHUA 2,14E-09	+	10%
	PEABODY	-8,90E-08	-	-
	HUANENG	2,00E-08	+	-
	DATANG	1,27E-09	+	-
	NTPC	2,19E-08	+	1%
	CHINARES	4,39E-09	+	-

Table 4 :

 4 Calibration: Step #2

	Commodity Beta	Sign	of	Significance
			Beta		Level
	COAL	-1,79E-04	-		1%
	GAS	-1,41E-04	-		1%
	OIL	-9,01E-03	-		1%

Table 5 :

 5 Scenario: 20% of oil & gas reserves are unburnable.

		Company	20% of oil & gas reserves are unburnable.
			5%	10%	20%	50%
	1	Exxon Mobil Corp	0,2600 0,2535 0,2406	0,2028
	2	Petrochina	0,7203 0,7805 0,8618	0,9562
	3	Chevron Corp	0,1428 0,2742 0,4752	0,7832
	4	Royal Dutch Shell PLC 0,1077 0,1089 0,1113	0,1186
	5	BP PLC	0,6001 0,6530 0,7370	0,8777
	6	Total SA	0,8421 0,8846 0,9356	0,9804
	7 Petrobras Brasileiro SA 0,9926 0,9935 0,9950	0,9976
	8	CNOOC Ltd	0,8469 0,9004 0,9537	0,9863
	9	Engie (GDF-Suez)	0,6571 0,7203 0,8112	0,9325
	10	RWE	0,8824 0,9001 0,9270	0,9678
	11	EON	0,9980 0,9989 0,9996	0,9999
	12	China Shenhua	0,8699 0,9155 0,9620	0,9921
	13	PEABODY	0,9939 0,9959 0,9977	0,9984
	14	Huaneng Power	0,9517 0,9677 0,9843	0,9957
	15	Datang	0,9314 0,9373 0,9475	0,9687
	16	NTPC	0,5301 0,5787 0,6598	0,8139
	17 China Resources Power 0,7397 0,7949 0,8705	0,9607
		Average	0,6792 0,7148 0,7640	0,8310

Table 6 :

 6 Scenario: 40% of oil & gas reserves are unburnable.

		Company	40% of oil & gas reserves are unburnable.
			5%	10%	20%	50%
	1	Exxon Mobil Corp	0,1397 0,1427 0,1486	0,1662
	2	Petrochina	0,7911 0,8226 0,8707	0,9437
	3	Chevron Corp	0,4061 0,4690 0,5739	0,7715
	4	Royal Dutch Shell PLC 0,3996 0,4001 0,4012	0,4044
	5	BP PLC	0,6851 0,7132 0,7613	0,8578
	6	Total SA	0,8634 0,8897 0,9266	0,9724
	7 Petrobras Brasileiro SA 0,9958 0,9962 0,9968	0,9980
	8	CNOOC Ltd	0,9098 0,9317 0,9589	0,9846
	9	Engie (GDF-Suez)	0,7703 0,8000 0,8473	0,9264
	10	RWE	0,8915 0,9035 0,9235	0,9602
	11	EON	0,9982 0,9988 0,9993	0,9996
	12	China Shenhua	0,9164 0,9370 0,9625	0,9884
	13	PEABODY	0,9965 0,9976 0,9987	0,9990
	14	Huaneng Power	0,9674 0,9756 0,9854	0,9940
	15	Datang	0,9449 0,9474 0,9518	0,9623
	16	NTPC	0,6837 0,7056 0,7446	0,8298
	17 China Resources Power 0,7912 0,8213 0,8680	0,9416
		Average	0,7736 0,7913 0,8188	0,8647

Table 7 :

 7 Scenario: 60% of oil & gas reserves are unburnable.

		Company	60% of oil & gas reserves are unburnable.
			5%	10%	20%	50%
	1	Exxon Mobil Corp	0,3648 0,3660 0,3682	0,3748
	2	Petrochina	0,8286 0,8424 0,8667	0,9189
	3	Chevron Corp	0,5089 0,5360 0,5855	0,7014
	4	Royal Dutch Shell PLC 0,5571 0,5573 0,5577	0,5589
	5	BP PLC	0,7559 0,7662 0,7852	0,8317
	6	Total SA	0,8971 0,9072 0,9242	0,9569
	7 Petrobras Brasileiro SA 0,9932 0,9935 0,9940	0,9953
	8	CNOOC Ltd	0,9218 0,9316 0,9472	0,9738
	9	Engie (GDF-Suez)	0,8285 0,8404 0,8616	0,9088
	10	RWE	0,9372 0,9403 0,9459	0,9586
	11	EON	0,9982 0,9984 0,9987	0,9992
	12	China Shenhua	0,9263 0,9362 0,9521	0,9809
	13	PEABODY	0,9967 0,9972 0,9979	0,9987
	14	Huaneng Power	0,9675 0,9717 0,9782	0,9886
	15	Datang	0,9635 0,9646 0,9667	0,9723
	16	NTPC	0,7632 0,7717 0,7878	0,8289
	17 China Resources Power 0,8492 0,8611 0,8819	0,9258
		Average	0,8269 0,8342 0,8470	0,8749

Table 8 :

 8 Scenario: 25% cut in fossil fuels price.

		Company	25% cut in fossil fuels price.
			5%	10%	20%	50%
	1	Exxon Mobil Corp	0,4776 0,4786 0,4804 0,4859
	2

Table 10 :

 10 Earth absorbing capacity for each firms and scenarios at the horizon 2050 (in Giga-Tonne of CO 2 )

		Company				Scenarios
			Benchmark Oil-Gas-Coal reserves are unburnable Cut in fossil fuels price
				20%	40%	60%	25%	50%
	1	Exxon Mobil Corp	15.74	9.28	12.49	6.12	15.63	15.50
	2	Petrochina	8.41	4.95	6.66	3.27	8.30	8.23
	3	Chevron Corp	10.49	6.17	8.32	4.08	10.38	10.30
	4 Royal Dutch Shell PLC	10.50	6.18	8.32	4.09	10.39	10.29
	5	BP PLC	8.38	4.95	6.65	3.27	8.32	8.25
	6	Total SA	9.47	5.56	7.49	3.68	9.37	9.28
	7 Petrobras Brasileiro SA	3.15	1.86	2.50	1.23	3.13	3.09
	8	CNOOC Ltd	10.51	6.18	8.31	4.08	10.41	10.29
	9	Engie (GDF-Suez)	5.47	3.05	4.13	1.98	5.30	5.13
	10	RWE	5.53	3.02	4.25	1.98	5.24	5.10
	11	EON	2.11	1.18	1.62	0.76	2.02	1.95
	12	China Shenhua	15.21	8.62	11.80	5.46	14.86	14.36
	13	PEABODY	15.13	8.51	11.89	5.49	14.80	14.09
	14	Huaneng Power	2.51	1.43	1.95	0.92	2.44	2.35
	15	Datang	5.00	2.82	3.88	1.79	4.81	4.63
	16	NTPC	15.15	8.54	11.83	5.56	14.78	14.25
	17 China Resources Power	5.00	2.79	3.80	1.81	4.82	4.62
		R t	147.77	85.08	115.89	55.56	145.01	141.72
		q t,oil	-145.78	-83.93 -114.33	-54.81	-143.06	-139.81
		q t,gas	-69.29	-39.90 -54.35	-26.05	-68.00	-66.46
		q t,coal	-62.28	-35.86 -48.85	-23.42	-61.12	-59.74

  Scenario: 40% of oil & gas reserves are unburnable. Scenario: 60% of oil & gas reserves are unburnable.

	Pourcentage loss vs standard case Pourcentage loss vs standard case	Exxon Mobil Corp Petrochina Chevron Corp Royal Dutch Shell PLC BP PLC Total SA Petrobras Brasileiro SA CNOOC Ltd Engie (GDF-Suez) RWE EON China Shenhua PEABODY Huaneng Power Datang NTPC China Resources Power Figure 4: 5% 10% 10 20 30 40 50 60 70 80 90 100 Exxon Mobil Corp Petrochina Chevron Corp Royal Dutch Shell PLC BP PLC Total SA Petrobras Brasileiro SA CNOOC Ltd Engie (GDF-Suez) RWE EON China Shenhua PEABODY Huaneng Power Datang NTPC China Resources Power 10% 30 40 50 60 70 80 90 100 Exxon Mobil Corp Petrochina Chevron Corp Royal Dutch Shell PLC BP PLC Total SA Petrobras Brasileiro SA CNOOC Ltd Engie (GDF-Suez) RWE EON China Shenhua PEABODY Huaneng Power Datang NTPC Figure 5: 5% China Resources Power	20% 20%	50% 50%
		Values of the defaut impact Values of the defaut impact
		34 35

These preliminary steps have been executed in Gretl and stored in Excel spreadsheets. They are available for viewing in the data and codes attached to the article.

Recall these numbers are projections of Step #3 up to the 2050 horizon based on 2005-2015 calibration occurring in Steps #1 and #2.

Bankruptcy is defined merely as the value of the firm (share price × number of shares) going to zero.

Although, the situation evolved somewhat unexpectedly with the intention of 45th President of the U.S., Donald Trump, to withdraw from the Paris agreements on climate change and to repeal the US Clean Power Act.


Roger Erivan

Thibault Chaput

Guillaume Villatte

Matthieu Ollivier

Stephane Descamps

Stephane Boisgard

Stéphane Descamps

Stéphane Boisgard

Ten-year epidemiological study in an orthopaedic and trauma surgery centre: Are there risks involved in increasing scheduled arthroplasty volume without increasing resources?

Keywords:

± • ± ± • - - - - ± ±

Introduction

Changes in medical management over time are resulting in ever shorter hospital stays. In addition, the population is ageing and life expectancy is increasing both at birth and at 65 years of age [START_REF] Chevreul | France: health system review[END_REF]. However, disease-free life expectancy is shorter (62.6 years in males and 64.4 years in females) and, consequently, many patients have multiple co-morbidities that produce an increasingly heavy management burden [START_REF] Capone | Periprosthetic fractures: epidemiology and current treatment[END_REF].

Our university orthopaedic and trauma surgery department performs scheduled orthopaedic procedures and also manages a large proportion of the trauma patients in the district and of patients with complex trauma-related conditions in the region. The district has a population of 638,092 and the region a population of 1,359,000. The emergency department of our hospital has 51,697 visits per year, of which 15,768 resulted in hospital admission in 2016. The steadily increasing volume of trauma surgery is resulting in overcrowding and in an excessive number of emergency operations. As a result, scheduled surgical procedures have increasingly long waiting times that have a potential for leading to litigation by the patients [START_REF] Mouton | Litigation in orthopedic surgery: What can we do to prevent it? Systematic analysis of 126 legal actions involving four university hospitals in France[END_REF].

A shortening of hospital stays in university hospitals has been documented over the last decade. However, to our knowledge, no study has assessed possible relationships linking shorter stays to staffing level or complication rate. The objectives of this study were

• to assess changes in case volume in a university orthopaedics and trauma surgery department between 2006 and 2016; • and to look for correlations linking these changes to staffing levels and the rates of significant complications, including the number of hip dislocations after total hip arthroplasty (THA) and the number of infections and complications resulting in malpractice litigation after hip, knee, or shoulder arthroplasty. Only arthroplasty procedures performed in the department were considered for this part of the study. The working hypothesis was that the case volume increased during the study period, whereas resources remained unchanged or decreased.

Materials and methods

Data collection

Our orthopaedics and trauma surgery department performs scheduled orthopaedic surgical procedures, chiefly at the hip and knee and less often at the foot. Upper limb surgery is under development. No spinal surgery or emergency hand surgery is performed. For this study, we searched the hospital database for the codes for healthcare interventions performed at our department in 2006 and 2016. We compiled a list of all codes of healthcare interventions performed and of primary and secondary diagnoses in the inpatient surgery ward, outpatient surgery unit, and operating rooms. We also collected the human and material resources available for the healthcare interventions performed. Data on infections were retrieved from the infection-control department and data on malpractice litigation from the legal department. For the analysis of complications, including infections, and of malpractice suits, only arthroplasty procedures performed at our department were considered. We recorded infections after hip, knee, or shoulder arthroplasty; dislocations after THA; and malpractice complaints about hip, knee, or shoulder arthroplasty procedures (which included requests for out-of-court settlement submitted to the hospital, complaints submitted to the arbitration and compensation commission (Commission de conciliation et d'indemnisation), and complaints filed with the administrative tribunal of our city (Clermont-Ferrand).

Classification of healthcare interventions and adverse events

Healthcare interventions were categorised as scheduled or performed on an emergency basis. Subgroups were then created within each category to distinguish the upper limb from the lower limb then to separate individual joints. The number of dislocations after THA and the number of infections after hip, knee, or shoulder arthroplasties were collected. We also collected the number of complaints related to arthroplasty procedures.

Statistical analyses

Quantitative variables are described as mean standard deviation (range) and compared between 2006 and 2016 using Student's t test. The statistical analyses were performed using Excel TM (Microsoft, Redmond, WA, USA). There were no missing data, and all healthcare interventions were analysed.

Results

Overall time trends

Table 1 reports the results. Mean hospital stay duration per patient was 8.7 10.8 days (range, 0-141) in 2006 and 7 9.4 days (range, 0-150 days) in 2016 (p = 1.5 10 -10 ) (Fig. 1). Mean age increased from 54.4 21.2 years (range, 11.7-100.9 years) in 2006 to 59.3 20.9 years (range, 13.6-103.1 years) in 2016 (p = 4.69 10 -18 ). Case volume increased in the department between 2006 and 2016 (Fig. 2). Thus, the total number of healthcare interventions increased from 2158 to 3100 per year, an overall 43.6% increase for orthopaedic surgery and trauma surgery pooled.

Time trends for scheduled surgery

The number of scheduled orthopaedic surgery procedures increased by 21.8%, from 1447 in 2006 to 1763 in 2016. Our department predominantly performed lower limb arthroplasty procedures. The number of THA procedures per year rose by 16.2%, from 284 in 2006 to 330 in 2016, whereas the number of bipolar hemiarthroplasties of the hip decreased from 80 to 55 ( 31.2%). The number of THA revisions per year increased from 46 to 67 (+45.6%) (Fig. 3). The annual number of total knee arthroplasties (TKAs) increased from 155 to 305 (+96.8%) and the annual number of unicompartmental knee arthroplasties from 14 to 40 (+185%). The annual number of TKA revisions rose from 14 to 16 (+14.3%) (Fig. 4). Ligament reconstruction procedures at the knee diminished from 97 to 83 ( 14.4%) and procedures for meniscal lesions from 125 to 104 ( 14.9%). The number of total ankle arthroplasties remained unchanged at 3 per year, whereas the number of ankle arthrodesis procedures increased from 12 to 17 (+41.7%). Finally, surgical procedures for hallux valgus decreased from 70 to 54 ( 22.8%).

Our upper limb surgical activity grew significantly during the study period. As a result, the annual number of shoulder arthroplasties increased from 0 in 2006 to 22 in 2016. Similarly, procedures to treat shoulder instability increased from 2 to 14 per year (+600%) and procedures for rotator cuff abnormalities from 10 to 25 (+150%) (Table 1).

The annual number of procedures for hardware removal at any site increased from 312 to 408 (+30.8%) between 2006 and 2016. In tandem with the increase in arthroplasty volume, when both patients who underwent arthroplasty in our department and those referred to us from other institutions were considered, the number of arthroplasty complications increased. Thus, the annual number of dislocations after THA increased from 8 to 14 (+75%) and 2).

Time trends for trauma surgery

Overall, the annual number of surgical procedures for trauma increased from 711 in 2006 to 1135 in 2016 (+59.6%). Among traumatic fractures of the lower limb (Fig. 5), most involved the femur in 2006, with a total of 225 and the following distribution by site: proximal femur (other than the femoral neck), n = 81; In 2006, there were 116 fractures of the tibia and ankle. In this group, the most common fractures involved the tibial pilon (n = 43). In 2016, the number of tibial fractures was 219 (+88.8%), including 52 tibial pilon fractures (+20.9%). Bimalleolar and similar fractures increased from 31 in 2006 to 112 in 2016 (+261.3%). Overall, fractures of the foot remained unchanged (18 in 2006 and 16 in 2016, 11.1%). The number of pelvic fractures managed by internal fixation remained low and stable (6 to 10 symphyseal fractures, +66.7%) and the number of acetabular fractures managed by internal fixation was 6 in both 2006 and 2016.

At the upper limb (Fig. 6), the same analysis showed that the number of clavicular fractures managed by internal fixation increased from 1 in 2006 to 18 in 2016. Closed gleno-humeral joint reduction under general anaesthesia decreased from 40 to 15 ( 62.5%). Humeral fractures increased from 58 to 118 (+103.4%) overall. Fractures of the distal humerus, which predominated in 2006, decreased from 19 to 15 ( 21%), whereas fractures of the proximal humerus increased from 17 to 52 (+205.9%). Plate fixation of humeral shaft fractures was performed in 8 patients in both 2006 and 2016. Intra-medullary nailing of the humerus increased over the decade from 14 to 43 (+207.1%). Finally, fractures of the forearm also increased, from 86 to 118 (+37.2%). Fractures of the distal radius increased from 59 to 79 (+33.9%), whereas radial shaft fractures remained stable at 19 during both 2006 and 2016. Finally, proximal fractures of the radius or ulna managed by internal fixation increased from 8 to 20 (+122.2%).

The number of wounds requiring treatment in the operating theatre increased from 46 to 140 (+204.3%). Tendon repair by suturing in the operating theatre increased from 15 to 36 (+140%). Number of patients who complained after being managed at our department 1 8

THA: total hip arthroplasty; TKA: total knee arthroplasty; TSA: total shoulder arthroplasty. As our department does not provide emergency care to hand trauma patients, most wounds either involved the lower limb or involved the hand but occurred concomitantly with more serious injuries and in polytrauma patients.

Outpatient surgery

In 2006, our department had no dedicated outpatient surgical unit. However, some patients were admitted only for 1 day for procedures performed according to an outpatient care pathway. Thus, in 2006, 266 patients had a hospital stay length of a single day (266/2158, 12.3%). An outpatient surgical unit was opened in March 2016. In 2016, i.e., during the first year, 466 patients were managed in this unit. In addition, in 2016, 351 patients were admitted to the conventional ward but had a hospital stay length of a single day, yielding a total of 817 patients managed on a day-care basis. These 817 patients represented 26.4% of the 3100 patients managed in 2016. Thus, over the decade, the number of day-care procedures increased by 243.8%.

Changes in resources over time

The healthcare staff comprised 7 surgeons, 4 anaesthesiologists, and 8.4 operating theatre nurses. During the day, three operating theatres were available, including two for 8 hours each and one for 12 hours. For night-time trauma surgery, we had access to two operating theatres, which were shared among various specialities (orthopaedics, vascular surgery, visceral surgery, neurosurgery, ENT surgery, and ophthalmological surgery). These resources remained unchanged between 2006 and 2016. In contrast, in the wards, the number of beds available for conventional hospital admission decreased from 70 in 2006 to 55 in 2016; a ward nurse and a nursing assistant were lost. On the other hand, an outpatient surgical unit was created.

Discussion

The study results confirm our working hypothesis. Overall, the surgical volume increased substantially over a decade in our department. Further increases can be expected as the population continues to age. Furthermore, our trauma volume is likely to increase, as private community hospitals in our district are becoming less involved with trauma surgery. Among large hospital centres, our university hospital is the only one in the district where orthopaedic surgeons are on call around the clock and manage all trauma emergencies. Among the community hospitals in the district, one manages only hand injuries and the other only simple traumatic injuries (the patients are triaged and no operating theatre is available outside standard working hours).

According to the French national institute for demographic data (Institut national d'études démographiques [INED]), life expectancy at birth increased between 2006 and 2016 from 76.9 to 79.4 years in males and from 84 to 85.4 years in females. A corollary of this increased life expectancy is growth in the numbers of traumatic injuries in elderly individuals and of traumatic and infectious complications of arthroplasty related both to normal ageing and to older age at the time of arthroplasty [START_REF] Capone | Periprosthetic fractures: epidemiology and current treatment[END_REF]. Our data illustrate this fact. Complications related to arthroplasty procedures performed at our department did not increase. However, there was an increase in the number of patients managed for complications, which was due to the fact that other centres in our district did not always provide emergency care for complications in their patients. The number of complaints made by patients who underwent arthroplasty at our centre increased substantially, from 1 in 2006 to 8 in 2016. In general, most complaints are motivated by infection or by deterioration of the patient-surgeon relationship [START_REF] Mouton | Litigation in orthopedic surgery: What can we do to prevent it? Systematic analysis of 126 legal actions involving four university hospitals in France[END_REF]. Infections were not a major source of complaints in our study. Consequently, closer scrutiny of patient-surgeon rapport and, more specifically, of the information supplied by surgeons to patients in our department is warranted.

A Swedish study estimated that the number of TKAs per 10,000 population will increase from 330 in 2020 to 382 in 2030 [START_REF] Nemes | Historical view and future demand for knee arthroplasty in Sweden[END_REF]. Similar estimates have been made for the US and Germany [START_REF] Inacio | Projected increase in total knee arthroplasty in the United States -an alternative projection model[END_REF][START_REF] Jain | Total knee arthroplasty: supply and demand[END_REF][START_REF] Kim | Epidemiology of primary hip and knee arthroplasties in Germany: 2004 to 2008[END_REF]. Our results support these estimates. French health authorities are encouraging surgeons to discharge patients as early as possible, as hospital stay length is a key factor in patient management and costeffectiveness of surgery departments. Thus, hospital stay length has become a highly controversial issue, and healthcare staff are being asked to shorten stays as much as possible. This policy should be viewed within the framework of the medical information system introduced in France in 1991 (Programme de médicalisation du système d'information), which requires healthcare facilities to supply the authorities and statutory health insurance system with information on their caseloads. This information is supplied using a coding system that assigns standardised codes to healthcare interventions and defines homogeneous groups of patients [START_REF] Baron | Orthopedics coding and funding[END_REF][START_REF] Laccourreye | SIGAPS & IF: highly linked French financial medical acronyms[END_REF]. The authorities use this information to determine costs to the healthcare facility and, therefore the amount of funds they assign to each healthcare facility. Thus, funding is based on case volume during the past year. However, costs per code or patient group are considered fixed over time, whereas in reality they increase. Consequently, healthcare facilities must increase their case volume to remain economically viable. An obstacle to decreasing hospital stay durations is the dearth of beds in rehabilitation and convalescence facilities, which increases bed occupancy in surgical wards. This situation constitutes an incentive to the development of outpatient surgery. In our department, a dedicated outpatient surgical outpatient unit was created in March 2016, with the objective of managing 50% of all healthcare interventions performed in the operating theatre on an outpatient basis. In 2016, 15.03% of operations were in outpatient surgical unit patients.

Importantly, global data rather than individual data should be the main focus of attention. Individual data are often influenced by local factors such as the activity of the various practitioners and centres in the area. Globally, surgical volume is increasing. Thus, healthcare staff are working more (managing a higher number of patients) but also perhaps better (due to advances in techniques and practices and to the institution of rest periods after night and weekend duties) and more rationally (informatisation, management of down times in the operating theatre, elimination of unnecessary procedures, and enhanced recovery). It is extremely difficult to prove, using reliable indicators, that the workload has increased commensurately with the surgical volume. Our centre became a referral centre for complex osteo-articular infections during the study period, and we therefore now admit more patients with severe infections. This fact explains the substantial increase in infection case volume. On the other hand, the decrease in femoral neck fractures over time is ascribable to the creation of a geriatric trauma surgery unit in a nearby hospital in our district. In France, healthcare available in public centres has changed, and private centres now focus chiefly on profitable activities such as scheduled surgery, simple emergencies, and hand injuries. A scheduled THA is more profitable than internal fixation of an acetabular fracture, although both procedures are considered by the French authorities to have similar costs. This selection of activities by private facilities is possible due both to technical advances and to the increase in scheduled orthopaedic procedures associated with ageing of the population. Selection is an adverse effect of funding based on prior case volume in a setting where case volume is increasing. At the same time, patients requiring less profitable procedures are increasingly numerous and are usually managed in public hospital centres. Providing patients with appropriate information remains of the utmost importance [START_REF] Gleyze | Patient information in orthopedic and trauma surgery. Fundamental knowledge, legal aspects and practical recommendations[END_REF]. During the study period, the numbers of complaints and of medical errors increased in orthopaedic and trauma surgery [START_REF] Agout | Epidemiology of malpractice claims in the orthopedic and trauma surgery department of a French teaching hospital: a 10-year retrospective study[END_REF]. Consequently, care is in order to ensure that the increase in case volume does not result in poorer patient information or patient-surgeon rapport.

This study has several limitations. First, coding errors may have occurred. A given healthcare intervention or diagnosis can be coded in several ways. However, the predominance of healthcare interventions used for the most common problems probably limited the risk of bias due to faulty coding. Second, failure to code some interventions or diagnoses may have occurred. It should be noted, however, that the use and quality of coding have been optimised in recent years. This fact may explain the dramatic increase in some diagnoses. Third, we compared only 2006 and 2016. Nonetheless, this comparison allowed us to objectively document changes without having to report a large amount of numerical data. We believe that the 10-year interval between the two measurement periods provides a fairly reliable picture.

Conclusion

This study demonstrated an overall increase in case volume in an orthopaedics and trauma surgery department over a decade. During the study, the human and material resources remained unchanged or decreased. The same applies to many healthcare facilities in France. Optimisation of the patient care pathway is therefore a key issue. It is unclear to what extent case volume will be able to continue to increase. Furthermore, the increase in case volume impacts both research and teaching activities in teaching hospitals, with human resources being increasingly used for patient care. Hospital authorities prefer to emphasise patient care, as a means of remaining financially viable. However, university hospitals must retain sufficient human resources for research and teaching if they are to meet their goals of providing high quality care, training future physicians, conducting clinical research to improve practices, and conducting basic research to improve treatments. Any imbalance among these activities will adversely affect hospital departments -which may therefore lose their university status -and the population they serve.

Disclosure of interest

The authors declare that they have no competing interest. A single author has financial relationships unrelated to this study: SB is a consultant for Zimmer-Biomet. The other authors have no financial relationships unrelated to this study to declare.

Fig. 1 .

 1 Fig. 1. Changes in mean hospital stay length and number of healthcare interventions per patient.

Fig. 2 .

 2 Fig. 2. Changes in numbers of the main healthcare procedures; total numbers and numbers for scheduled orthopaedic surgery and trauma surgery are shown.

Fig. 3 .

 3 Fig. 3. Change in the number of hip arthroplasties.

Fig. 4 .

 4 Fig. 4. Change in the number of scheduled procedures on the knee.

Fig. 5 .

 5 Fig. 5. Change in lower limb trauma surgery.

Fig. 6 .

 6 Fig. 6. Change in upper limb trauma surgery.

Table 1

 1 Changes in surgical volume between 2006 and 2016.

			2006	2016	Change (%)
	Overall data
		Mean hospital stay length, days *	8.78	7.04	-19.80
		Mean age, years **	54.4	59.3	9.00
		Number of scheduled orthopaedic procedures	1447	1763	21.80
		Number of procedures for trauma	711	1135	59.60
		Number of patients	2273	2807	23.50
		Total number of procedures	2158	3100	43.70
		Number of outpatient procedures (1-day admission)	266	817	243.8
	Lower limb trauma
	Pelvis	Symphysis	6	10	66.70
		Acetabulum	6	6	0.00
	Femur	Distal	15	10	-33.30
		Proximal	81	164	102.50
		Shaft	49	84	71.40
		Bipolar hemi-arthroplasty	80	55	-31.30
	Patella	Fracture	10	7	-30.00
	Tibia	Tibial plateau	23	31	34.80
		Shaft	10	5	-50.00
		Distal	43	52	20.90
		Medial malleolus only	2	6	200.00
	Fibula	Isolated	7	13	85.70
	Bimalleolar fractures	Or equivalent	31	112	261.30
	Foot	Fractures	18	16	-11.10
	Amputation		18	20	11.10
	Flaps		14	15	7.10
	Autologous skin graft		14	13	-7.10
	Soft tissue irrigation		38	33	-13.20
	Wound care	Soft tissues only	46	140	204.30
		Tendon repair by suturing	15	36	140.00
	Scheduled lower limb procedures
	Hip	Total arthroplasty	284	330	16.20
		Bipolar hemi-arthroplasty	80	55	-31.30
		Hip arthroplasty revision	46	67	45.70
		Acetabular augmentation	6	1	-83.30
		Proximal femoral osteotomy	7	0	-100.0
	Knee	Total arthroplasty	155	305	96.80
		Knee arthroplasty revision	14	16	14.30
		Unicompartmental knee arthroplasty	14	40	185.70
		Valgus tibial osteotomy	39	9	-76.90
		Ligament reconstruction	97	83	-14.40
		Meniscus	125	104	-16.80
		Synovectomy	12	4	-66.70
		Other arthroscopic procedure	8	4	-50.00
		Medial patello-femoral ligament reconstruction	8	8	0.00
		Anterior tibial tuberosity transfer	5	3	-40.00
		Manipulation under general anaesthesia	6	14	133.30
	Foot/Ankle	Total arthroplasty	3	3	0.00
		Hallux valgus	70	54	-22.90
		Ankle arthrodesis	12	17	41.70
		Claw toe deformity	21	8	-61.90
		Joint release	3	2	-33.30
		Non-union	3	8	166.70
	Removal of fixation material		312	408	30.80
	Complications of arthroplasty	THA dislocation	8	14	75.00
		TKA lavage	13	39	200.00
		Knee lavage	30	46	53.30
		Lavage of other joints	4	4	0.00
	Upper limb trauma
	Internal fixation of clavicle fracture		1	18	1700.0
	Internal fixation of humeral fracture	Proximal humerus	17	52	205.90
		Distal humerus	19	15	-21.10
		Plate fixation of shaft fracture	8	8	0.00
		Nailing of shaft fracture	14	43	207.10
	Internal fixation of forearm fracture	Proximal	8	20	150.00
		Shaft	19	19	0.00
		Distal	59	79	33.90
	Shoulder/elbow	Closed reduction of shoulder	40	15	-62.50
		Reverse shoulder arthroplasty	2	18	800.00
		Closed reduction of elbow	12	6	-50.00
	Scheduled upper limb procedures
	Shoulder	Cuff	10	25	150.00
		Total arthroplasty	0	22
		Bone block	2	14	600.00
		Bankart	3	9	200.00
	Hand	Carpal tunnel	11	58	427.30
		Synovial cyst at the wrist	7	7	0.00
		Trigger finger	19	30	57.90

THA: total hip arthroplasty; TKA: total knee arthroplasty.

* p = 1.50E-10.

** p = 4.69E-18.

Table 2

 2 Changes in complication rates in patients who underwent scheduled arthroplasty procedures.

	Year
	2006	2016

Funding

None.

Author contributions

Roger Erivan: designed the study, wrote the article, handled the statistical analyses, validated the final version of the article, and performed surgical procedures.

Thibault Chaput: designed the study, wrote the article, and validated the final version of the article.

Guillaume Villlate: designed the study, wrote the article, validated the final version of the article, and performed surgical procedures.

Matthieu Ollivier: handled the statistical analyses and validated the final version of the article.

Stéphane Descamps: designed the study, validated the final version of the article, and performed surgical procedures.

Stéphane Boisgard: designed the study, validated the final version of the article, and performed surgical procedures.


S Cohen

Xavier Flecher
email: xavier.flecher@gmail.com

S Parratte

M Ollivier

J.-N Argenson

Keywords: Periprosthetic Femoral Fracture, Total Hip Arthroplasty, Implant Revision, Internal Fixation, Morbidity, Mortality. Level of evidence: III, case-control study

Introduction

The incidence of periprosthetic femoral fracture is constantly increasing, with high associated morbidity and mortality. Surgical treatment is guided by the Vancouver classification, but the influence of type of treatment on morbidity and mortality has been Page 2 of 20 little analyzed. The theoretic advantage of implant revision over internal fixation is that it should allow earlier weight-bearing, although the impact of this on morbidity and mortality and autonomy has not been demonstrated. We conducted a case-control study, to assess the influence of type of treatment (implant revision or internal fixation) 1) on mobility and autonomy and 2) on morbidity and mortality.

Hypothesis

The study hypothesis was that clinical results and morbidity and mortality do not differ between these two types of treatment. Mean follow-up was 43±27 months (range, 0.75 -107 months).

Methods

Results

Autonomy on

Introduction

The incidence of periprosthetic hip fracture is constantly increasing, ranging from 0.1% to 6% depending on the report [START_REF] Duncan | Fractures of the femur after hip replacement[END_REF][START_REF] Lindahl | Epidemiology of periprosthetic femur fracture around a total hip arthroplasty[END_REF][START_REF] Lewallen | Periprosthetic fracture of the femur after total hip arthroplasty: treatment and results to date[END_REF]. It is the third most frequent cause of revision of total hip arthroplasty, after aseptic loosening and dislocation [START_REF] Lindahl | Periprosthetic femoral fractures classification and demographics of 1049 periprosthetic femoral fractures from the Swedish National Hip Arthroplasty Register[END_REF]. Treatment is complicated in an elderly population with numerous comorbidities, leading to high intra-and post-operative complications rates of 10% to 50% depending on the report [START_REF] Lindahl | Risk factors for failure after treatment of a periprosthetic fracture of the femur[END_REF][START_REF] Tower | Fractures of the femur after hip replacement: the Oregon experience[END_REF] and high perioperative mortality, varying according to length of follow-up and type of treatment [START_REF] Lindahl | Risk factors for failure after treatment of a periprosthetic fracture of the femur[END_REF][START_REF] Streubel | Mortality after periprosthetic femur fractures[END_REF][START_REF] Bhattacharyya | Mortality after Periprosthetic Fracture of the Femur[END_REF][START_REF] Langenhan | Aggressive surgical treatment of periprosthetic femur fractures can reduce mortality: comparison of open reduction and internal fixation versus a modular prosthesis nail[END_REF]. Surgical treatment is guided by the Vancouver classification [START_REF] Brady | Classification of the hip[END_REF][START_REF] Rayan | European validation of the Vancouver classification of periprosthetic proximal femoral fractures[END_REF],

which recommends open reduction and internal fixation (ORIF) for fractures with stable and well-fixed implants, and stem replacement in case of loosening [START_REF] Parvizi | Treatment protocol for proximal femoral periprosthetic fractures[END_REF][START_REF] Learmonth | The management of periprosthetic fractures around the femoral stem[END_REF]. While ORIF might seem to be less aggressive than implant revision, the impact of type of treatment on mobility and mortality/morbidity has been little studied. We conducted a casecontrol study, to assess: the influence of type of treatment (implant revision or internal fixation) 1) on mobility and autonomy and 2) on morbidity and mortality. The study hypothesis was that clinical results and morbidity and mortality do not differ between these two types of treatment.

Material and Methods

Patients

A retrospective study included 70 patients with 71 periprosthetic femoral fractures managed between January 1 st , 2007 and December 31 st , 2014. Fractures were classified on the Vancouver system [START_REF] Brady | Classification of the hip[END_REF][START_REF] Rayan | European validation of the Vancouver classification of periprosthetic proximal femoral fractures[END_REF], and those with loose implants underwent revision and those with well-fixed implants underwent ORIF. These two groups of patients were comparable for age, gender, side, and ASA [START_REF] Sankar | Reliability of the American Society of Anesthesiologists physical status scale in clinical practice[END_REF] and Parker-Palmer scores [START_REF] Parker | A new mobility score for predicting mortality after hip fracture[END_REF] (Table 1). Only mean body-mass index (BMI) differed significantly between groups, due to one obese patient (BMI, 40) in the ORIF group (Table 1). Primary implant data are shown in Table 2. Fracture was mainly due to minor trauma, with only 1 case of high-energy trauma. Thirty-five fractures were fixed by locking plate (ORIF group), with weight-bearing delayed to the 3 rd month. Thirty-six fractures were treated by implant revision via a posterolateral approach, using a revision stem with or without cement (REVISION group); full immediate postoperative weight-bearing was authorized. Mean follow-up was 43 months (i.e., 3.5 years).

Methods

Thirteen surgeons were involved in treatment: 36 patients (51.4%) were operated on by senior surgeons and 34 (48.6%) by senior registrars, all working in a orthopedicstraumatology department with yearly turnover of more than 1,000 hip or knee replacements in orthopedics and more than 350 in traumatology.

Assessment

Functional status was assessed on Parker-Palmer score [START_REF] Parker | A new mobility score for predicting mortality after hip fracture[END_REF], preoperatively and at 1 year. Overall autonomy was assessed in terms of changes in home conditions.

Complications were inventoried: death, reoperation, implant change, infection, dislocation, new fracture, non-union, cement-related shock.

Statistics.

Patient characteristics, functional scores, mortality and complications rates were reported as mean ± standard deviation for continuous variables and as percentage for categoric variables. Normal distribution of quantitative variables was tested on the Kolmogorov-Smirnov test; normally distributed variables were compared on Student t test and non-normally distributed variables on Wilcoxon test. Qualitative variables were compared on chi² test. All analyses were 2-tailed. The significance threshold was set at p <0.05. Two Kaplan-Meier survival analyses with 95% confidence intervals were performed at last follow-up, and compared between groups on log-rank test; the two endpoints were death from all causes and implant revision for all causes. A post-hoc power test was performed for the principal study endpoint. The study had an 80% chance of detecting a clinically significant difference (2±1.6 points) in Parker mobility score, despite 7 patients (10%) lost to follow-up [START_REF] Morice | Proximal femoral fractures in centenarians. A retrospective analysis of 39 patients[END_REF]. Clinical and radiological data were collected in consultation with an independent investigator for 55 patients and by telephone (with patient, care-giver or family doctor, X-rays being sent by mail) for 9 patients.

Results

Parker mobility scores fell by more than 2 points at 1 year's follow-up 2).

The complications rate was 11/36 (30.5%) in the REVISION group, and 12/35 (34%) in the ORIF group (p=0.9) (Table 3). In the REVISION group, there were no cement-related complications, whereas 9 of the 11 complications (82%) occurred in the cementless stem subgroup (p=0.3).

Discussion

Periprosthetic femoral fracture is the third most frequent reason for revision of total hip arthroplasty, following aseptic loosening and dislocation [START_REF] Lindahl | Periprosthetic femoral fractures classification and demographics of 1049 periprosthetic femoral fractures from the Swedish National Hip Arthroplasty Register[END_REF][START_REF] Füchtmeier | Mid-Term Results of 121 Periprosthetic Femoral Fractures: Increased Failure and Mortality Within but not After One Postoperative Year[END_REF] The Vancouver classification is most widely used to describe these fractures and guide surgery [START_REF] Duncan | Fractures of the femur after hip replacement[END_REF][START_REF] Brady | Classification of the hip[END_REF].

Internal fixation in type-B periprosthetic fracture is more controversial, as the complications rate is high [START_REF] Buttaro | Locking compression plate fixation of Vancouver type-B1 periprosthetic femoral fractures[END_REF], related to the difficulty of distinguishing types B1 and B2.

Lindhal et al. [START_REF] Lindahl | Risk factors for failure after treatment of a periprosthetic fracture of the femur[END_REF] reported type B1 as a risk factor for failure, and Corten et al. [START_REF] Corten | An algorithm for the surgical treatment of periprosthetic fractures of the femur around a well-fixed femoral component[END_REF] reported a 20% risk of misinterpretation of type B1 revealed on ultimate intraoperatuive testing. The present case-control study compared patients managed for type B fracture by implant revision versus internal fixation retaining all implants.

Autonomy in terms of Parker mobility score fell by 2 points at 1 year postoperatively, without significant difference between treatment groups, in agreement with Joetsl et al. [START_REF] Joestl | Locking compression plate versus revision-prosthesis for Vancouver type B2 periprosthetic femoral fractures after total hip arthroplasty[END_REF]. In the present study, almost half the patients were obliged to make changes at home or change place of residence, in agreement with Moreta et al. [START_REF] Moreta | Functional and radiological outcome of periprosthetic femoral fractures after hip arthroplasty[END_REF], who reported that 48% of patients recovered their former level of life, only 10% being able to walk unaided and 80% requiring 1 or 2 canes. In the present study, type of treatment did not impact morbidity: there were no significant differences in walking ability, institutionalization, or complications; mortality, on the other hand, was lower after implant revision, with 88% survival, versus 51% in the ORIF group (p=0.02).

Many studies of periprosthetic fracture reported radiologic and clinical results, but rarely mortality [START_REF] Buttaro | Locking compression plate fixation of Vancouver type-B1 periprosthetic femoral fractures[END_REF][START_REF] Tsiridis | Impaction femoral allografting and cemented revision for periprosthetic femoral fractures[END_REF][START_REF] Ebraheim | Fixation of periprosthetic femoral shaft fractures adjacent to a well-fixed femoral stem with reversed distal femoral locking plate[END_REF][START_REF] Fink | Hip revision arthroplasty in periprosthetic fractures of Vancouver type B2 and B3[END_REF][START_REF] Ricci | Indirect reduction and plate fixation, without grafting, for periprosthetic femoral shaft fractures about a stable intramedullary implant[END_REF]. It ranges from 11% to 20%, depending on the series [START_REF] Bhattacharyya | Mortality after Periprosthetic Fracture of the Femur[END_REF][START_REF] Lindahl | Three hundred and twentyone periprosthetic femoral fractures[END_REF][START_REF] Mclauchlan | Results of an operative policy in the treatment of periprosthetic femoral fracture[END_REF], which is higher than for primary arthroplasty [START_REF] Lindahl | The excess mortality due to periprosthetic femur fracture. A study from the Swedish national hip arthroplasty register[END_REF], but lower than for femoral neck fracture [START_REF] Moran | Early mortality after hip fracture: is delay before surgery important?[END_REF]. The impact of type of treatment on mortality has been little analyzed [START_REF] Langenhan | Aggressive surgical treatment of periprosthetic femur fractures can reduce mortality: comparison of open reduction and internal fixation versus a modular prosthesis nail[END_REF], with only 1 comparative study to our knowledge [START_REF] Langenhan | Aggressive surgical treatment of periprosthetic femur fractures can reduce mortality: comparison of open reduction and internal fixation versus a modular prosthesis nail[END_REF]; in this retrospective study, however, choice of treatment was determined not by implant loosening but by an arbitrary change in strategy for periprosthetic fracture: internal fixation before 2001, and revision after [START_REF] Langenhan | Aggressive surgical treatment of periprosthetic femur fractures can reduce mortality: comparison of open reduction and internal fixation versus a modular prosthesis nail[END_REF]. In the present study, survival was significantly better in the REVISION group, at a mean 43 months and at last follow-up, in agreement with other reports [START_REF] Bhattacharyya | Mortality after Periprosthetic Fracture of the Femur[END_REF][START_REF] Langenhan | Aggressive surgical treatment of periprosthetic femur fractures can reduce mortality: comparison of open reduction and internal fixation versus a modular prosthesis nail[END_REF]. Mortality in the ORIF group was also earlier, in agreement with Langenhan et al. [START_REF] Langenhan | Aggressive surgical treatment of periprosthetic femur fractures can reduce mortality: comparison of open reduction and internal fixation versus a modular prosthesis nail[END_REF], who reported significantly lower overall mortality at 6 months and at last follow-up after revision than after ORIF.

We believe that early resumption of weight-bearing after implant revision improves morbidity and mortality following periprosthetic fracture. Although locking plates improve fixation in porous bone [START_REF] Kregor | Treatment of distal femur fractures using the less invasive stabilization system: surgical experience and early clinical in 103 fractures[END_REF][START_REF] Kregor | Fixation of distal femoral fractures above total knee arthroplasty utilizing the Less Invasive Stabilization System (L.I.S.S.)[END_REF][START_REF] Perren | Evolution of the internal fixation of long bone fractures. The scientific basis of biological internal fixation: choosing a new balance between stability and biology[END_REF] and several biomechanical studies showed their superiority in allowing theoretic immediate resumption of weight-bearing [START_REF] Wähnert | Double plating in Vancouver type B1 periprosthetic proximal femur fractures: A biomechanical study[END_REF][START_REF] Fulkerson | Fixation of periprosthetic femoral shaft fractures associated with cemented femoral stems: a biomechanical comparison of locked plating and conventional cable plates[END_REF][START_REF] Zlowodzki | Biomechanical evaluation of the less invasive stabilization system and the 95-degree angled blade plate for the internal fixation of distal femur Fractures in human cadaveric bones with high bone mineral density[END_REF][START_REF] Zlowodzki | Biomechanical evaluation of the less invasive stabilization system, angled blade plate, and retrograde intramedullary nail for the internal fixation of distal femur fractures[END_REF], this is in fact difficult to achieve in practice, and few studies have assessed immediate resumption of weight-bearing after internal fixation by locking plate [START_REF] Ehlinger | Treatment of femoral fracture on previous implants with minimally-invasive surgery and total weight-bearing: benefit of locking plate. Preliminary report[END_REF]. In the literature, complications rates range between 10% and >50% [START_REF] Lindahl | Periprosthetic femoral fractures classification and demographics of 1049 periprosthetic femoral fractures from the Swedish National Hip Arthroplasty Register[END_REF][START_REF] Lindahl | Risk factors for failure after treatment of a periprosthetic fracture of the femur[END_REF][START_REF] Tower | Fractures of the femur after hip replacement: the Oregon experience[END_REF][START_REF] Füchtmeier | Mid-Term Results of 121 Periprosthetic Femoral Fractures: Increased Failure and Mortality Within but not After One Postoperative Year[END_REF][START_REF] Springer | Treatment of periprosthetic femoral fractures following total hip arthroplasty with femoral component revision[END_REF]. In the present series, they were 37.5% in the ORIF group and 34% in the REVISION group; that the difference was non-significant was probably due to lack of power. At last follow-up, the revision rate in the 2 groups taken together was 13±5%, in agreement with the literature, which reports rates of 10% to 17% [START_REF] Lindahl | Risk factors for failure after treatment of a periprosthetic fracture of the femur[END_REF][START_REF] Langenhan | Aggressive surgical treatment of periprosthetic femur fractures can reduce mortality: comparison of open reduction and internal fixation versus a modular prosthesis nail[END_REF][START_REF] Springer | Treatment of periprosthetic femoral fractures following total hip arthroplasty with femoral component revision[END_REF].

Some reports favor cementless revision [START_REF] Beals | Periprosthetic fractures of the femur. An analysis of 93 fractures[END_REF][START_REF] Incavo | One-stage revision of periprosthetic fractures around loose cemented total hip arthroplasty[END_REF], while others favor cement, especially in elderly patients with diminished bone quality [START_REF] Duncan | Fractures of the femur after hip replacement[END_REF][START_REF] Lewallen | Periprosthetic fracture of the femur after total hip arthroplasty: treatment and results to date[END_REF][START_REF] Buttaro | Locking compression plate fixation of Vancouver type-B1 periprosthetic femoral fractures[END_REF][START_REF] Cooke | Fractures of the femur in relation to cemented hip prostheses[END_REF]. The present results suggest a higher risk of complications with uncemented stems: 36 % versus 18% (although p=0.3: non-significant). There were no new fractures after revision with a cemented stem and no cases of cement-related shock. Functional recovery and autonomy were similar in both cases.

The study had several limitations. 1) It was retrospective, with small sample size.

The sample did, however, comprise all analyzable patient records for a department with high volumes of traumatology and arthroplasty. The sample was large enough, and thus power great enough, to analyze autonomy as an endpoint, but insufficient for precise analysis of morbidity and mortality. Recovery of walking capacity could not be assessed in a standardized manner. Postoperative protocols, however, were identical for all patients, with immediate resumption of weight-bearing after femoral implant revision, whereas at least 3 months' non-weight-bearing was required after ORIF by locking plate.

2) In the REVISION group, fixation was cemented or cementless, which might introduce bias; however, this factor did not affect the rehabilitation protocol. 3) At 3.5 years, mean

Page 10 of 20 follow-up was short for assessing implant results, but seemed to us to be sufficient for assessing morbidity and mortality. The study also had several strong points.

Conclusion

Implant revision in periprosthetic femoral fracture was associated with significantly lower overall mortality than ORIF, without difference in the rates of failure or complications requiring revision surgery. These results contradict the idea that implant revision is heavier and more risky than internal fixation. 0.9 Figure 2: Kaplan-Meier survival analysis with endpoint defined as revision of ≥1 implant for all causes. At a mean 3.5 years' follow-up, overall survival was 86±13%. At last follow-up, the revision rate in the 2 groups taken together was 13±5% (p=0.82).

Accept ed

  Influence of treatment modality on morbidity and mortality in periprosthetic femoral fracture. A comparative study of 71 fractures treated by internal fixation or femoral implant revision S. Cohen, X. Flecher, S. Parratte, M. Ollivier, Jean-Noël Argenson To cite this version: S. Cohen, X. Flecher, S. Parratte, M. Ollivier, Jean-Noël Argenson. Influence of treatment modality on morbidity and mortality in periprosthetic femoral fracture. A comparative study of 71 fractures treated by internal fixation or femoral implant revision. Orthopaedics & Traumatology: Surgery & Research, 2018, 104 (3), pp.363-367. 10.1016/j.otsr.2017.12.018. hal-01960509

A

  retrospective study included 70 patients with a total of 71 femoral periprosthetic fractures treated between 2007 and 2014. Two treatment groups, comparable for mean age, gender and ASA and Parker scores, were studied. Mean age was 78±13.5 years (range, 23-95 years). Thirty-six fractures (50.7%) were treated by implant revision via a posterolateral approach, using a revision stem with (n = 11) or without cement (n = 25) (REVISION group); immediate postoperative weight-bearing was authorized. Thirtyfive fractures (49.3%) were treated by open reduction and internal fixation, using a locking plate (ORIF group); weight-bearing was authorized only in the third month.

  Parker score was reduced by 2 points at 1 year's follow-up. Mean preoperative scores were 7.32 ±1.79 (range, 3-9) and 7.43 ±1.79 (range, 4-9) in the REVISION and ORIF group, respectively, (p=0.8), falling to 5.06 ±2.6 (range, 0-9) and 4.5 ±2.01 (range, 0-9) respectively at follow-up (p=0.349). Sixteen patients in the REVISION group versus 13 in the ORIF group had made adaptations in their home or changed place of residence (p=0.2).

Figure 1 :

 1 Figure 1: Kaplan-Meier survival analysis with death as endpoint. At a mean 3.5 years'

  [START_REF] Corten | An algorithm for the surgical treatment of periprosthetic fractures of the femur around a well-fixed femoral component[END_REF], and 5 late deaths ≥2 years post-fracture, at respectively 29, 31, 46, 54 and 89 months postoperatively. Two patients died of stroke and 2 were admitted to nursing homes for loss of autonomy. The 12 deaths in the ORIF group occurred at13, 17,

	18, 21, 23 26, 29, 33, 37, 41, 43 and 91 months postoperatively. Nine were related to
	decubitus complications in bed-ridden patients; 2 of these showed delayed
	consolidation, preventing resumption of weight-bearing at 3 months. One patient died of
	generalized cancer, 1 of unexplained convulsions, and 1 for no known major cause.
	There were 3 implant replacements in each group (3/32: 9.4%). At a mean 3.5
	years' follow-up, mean overall survival was 86±13%. The revision rate at last follow-up
	in the 2 groups taken together was 13±5% (p=0.82) (figure
	5.06 ±2.6 (range, 0-9) and 4.5 ±2.01 (range 0-9) (p=0.349). Sixteen patients in the
	REVISION group versus 13 in the ORIF group reported changes in home conditions
	(p=0.2).
	Three patients were lost to follow-up (failure to return to consultation and
	unreachable by telephone) in the ORIF group and 4 in the REVISION group, and were
	excluded from mortality analysis. Eighteen of the 63 patients (28.5%) died before last
	follow-up: 6/32 (19.3%) in the REVISION group and 12/32 (37.5%) in the ORIF group
	(p=0.04). Survival in terms of mortality at a mean 3.5 years' follow-up was 88±6% in the
	REVISION group and 51±11% in the ORIF group (p=0.0219). At last follow-up (107
	months in the REVISION group and 89 months in the ORIF group), survival in terms of

. Mean preoperative scores were 7.32 ±1.79 (range, 3-9) in the REVISION group, and 7.43 ±1.79 (range, 4-9) in the ORIF group (p=0.8, non-significant); 1-year scores were respectively mortality was respectively 62±11% and 29±11% (p=0.0219) (figure

1

). The 6 deaths in the REVISION group comprised 1 early death from pulmonary embolism on postoperative day

Table 1 :

 1 Patient characteristics

	p=0.99
	p=0.35