domain: shs qfin

text:
Edouard A Ribes

Navigating the labor market as a salaried knowledge worker -a systematic view

Keywords: Labor economics, Occupational choices, Job mobility, Turnover

This article offers a series of views (backed by quantitative toy models) around the best course of actions individuals can follow when seeking career advancement. It shows that leveraging a firm internal labor market does not yield significant promotion opportunities (i.e. less than an average 2% chance on a year on year basis) unless the firm is growing fast. On the other hand, if high growth firms present significant chances (up to 50%) of getting a promotion up to a director or vice president level over a 3 to 5 years time span, their number is limited. The best course of action thus consists in continuously networking to access opportunities. This strategy is shown here to yield a 5 to 8% chance of landing a promotion on a year on year basis. This in turns open up questions for managers and human resources professionals around the best way to structure a firm in a robust fashion...

Introduction:

Over the past decades, there has been a substantial amount of knowledge accumulated in the field of labor economics and career management. From an economic standpoint, the main questions of the gradual increase in compensation illustrating one's career progression, as well as the underlying performance evaluations have been addressed. From a compensation standpoint, a holistic summary can be found in the seminal research of [START_REF] Lazear | Compensation and incentives in the workplace[END_REF]. On this front, the current remaining areas of debates are mainly associated to the optimal structure of non monetary incentives as well as the specific structure of executive pay (see [START_REF] Gabaix | Why has ceo pay increased so much?[END_REF][START_REF] Gabaix | Ceo pay and firm size: An update after the crisis[END_REF] for an open discussion on the exponential nature of their comp based on firm size). According to the economic doxa, the tenets of one's career are rooted in the idea of differentiating individuals based on their productive capabilities. Interesting this puts productivity appraisal at the heart of one's career and labor journey. For blue collar workers, productivity is easily measured and compensated in a differentiated manner, notably through piece wise schemes [START_REF] Lazear | Salaries and piece rates[END_REF]. This in turns clearly structures the career of blue collars individuals alongside the notion of progression against a productivity curve (see [START_REF] Anzanello | Learning curve models and applications: Literature review and research directions[END_REF] for review). But the situation is quite different for white collar workers. Here performance appraisal is extremely complex [START_REF] Ramírez | Measuring knowledge worker productivity: A taxonomy[END_REF]. Performance in this case is assessed via the proxy of qualitative reviews and ranking. As a result careers are structured as permanent tournaments [START_REF] Lazear | Rank-order tournaments as optimum labor contracts[END_REF] fueled by the feedback of others. But those tournaments are highly sensitive to a firm context (incl. its incumbent) [START_REF] Lazear | Introduction: Firms and the distribution of income: The roles of productivity and luck[END_REF]. To the extent that Email address: edouard.augustin.ribes@gmail.com (Edouard A. Ribes) luck ultimately plays a very large role in one's overall success [START_REF] Pluchino | Talent versus luck: The role of randomness in success and failure[END_REF]). An other interesting trait of white collars workers, is that their jobs are in permanent evolution. Jobs are indeed made of a set of tasks [START_REF] Grossman | Trading tasks: A simple theory of offshoring[END_REF] which gets commoditized over time because of technological replacement and displacement off-nearshore (see [START_REF] Ribes | What is the effect of labor displacement on management consultants[END_REF] for a discussion on professional services (consultants, lawyers etc..)). As a result, certain white collar jobs tend to become highly scripted to the point where their performance can be defined and measured [START_REF] Ramírez | Measuring knowledge worker productivity: A taxonomy[END_REF]. So while some job completely change over time, some other almost become blue collar type of roles... This leaves an open question for white collar workers: if their role is ever evolving and performance is not easily measured, how can one drive his/her career?

If the question is still open on the economic front, there are some interesting teachings in the management literature, which can be used to address this question. Management scholars have indeed built upon topics related to career development and mobility for decades. On this front, they have first noted, as depicted in the review of [START_REF] Sullivan | Advances in career theory and research: A critical review and agenda for future exploration[END_REF], that the initial views of traditional linear career paths, where workers progress hierarchically within an organization, have been gradually replaced by more dynamic and non-linear models where employees jump between employers and roles. If the idea of hierarchical progression is here still prevalent, it is the employer mobility which has starkly increased over the past decades [START_REF] Lyons | How have careers changed? an investigation of changing career patterns across four generations[END_REF]. This has come with two consequences. Transition between roles have set an emphasis on lifelong learning and skill development. Meanwhile transition between employers have increased the importance of networking (de Janasz and [START_REF] De Janasz | Learning the art of networking: A critical skill for enhancing social capital and career success[END_REF][START_REF] Wolff | Do specific types of networking predict specific mobility outcomes? a two-year prospective study[END_REF]. But, the fact that career are now "protean" in nature (i.e. self driven by individuals in a labor market and no longer bounded to the confide of a single corporation) have also resulted in a transfer of responsibil-ity pertaining to training and networking from the firms to the individual worker [START_REF] Baruch | Career issues[END_REF][START_REF] Hirschi | Contemporary career orientations and career selfmanagement: A review and integration[END_REF]. At more granular level, management scholars have even mapped factors influencing career mobility and have found that beyond pure economic questions of compensation and internal advancements (which can already explain 80%+ of the observed mobility as seen for instance in [START_REF] Ribes | Employee turnover prediction and retention policies design: a case study[END_REF]), additional macro (resp. micro) level contextual elements (e.g. industry growth, organization staffing policy... [resp. personality, career interest...]] have proven to further help predict mobility down at the individual level [START_REF] Ng | Determinants of job mobility: A theoretical integration and extension[END_REF][START_REF] Hom | One hundred years of employee turnover theory and research[END_REF]. When it comes to networking, which is one of the core determinant of job search [START_REF] Sullivan | Making sense of different perspectives on career transitions: A review and agenda for future research[END_REF], the tenets revolve around consistently engaging in external professional and/or community activities, while maintaining an increasing internal visibility (Forret andDougherty, 2001, 2004). On this front, success relies on building the maximum numbers of contacts [START_REF] Baruffaldi | Determinants of phd holders' use of social networking sites: An analysis based on linkedin[END_REF] that one can consistently sustain [START_REF] Davis | Networking via linkedin: An examination of usage and career benefits[END_REF].

But the management literature still lacks, to my knowledge (see the review of [START_REF] Sullivan | Making sense of different perspectives on career transitions: A review and agenda for future research[END_REF]), a macro level and quantitative perspective on how can one systematically drive his/her career. There is thus still a gap which may benefit some discussion. The literature has indeed looked at the notion of careers mainly from the point of views of markets, whether those markets are at firm, industrial sector or geographical levels. But very little has been done, to my knowledge, to articulate what a career is for an individual or a household and how to play it efficiently (from an economic standpoint).1 This is something that this article intend to bridge by providing a quantitative review of the options individuals (and especially white collar/knowledge workers) have to structure their career and by discussing how to best leverage them. To do so, this paper first offers a view of the mechanics at stake within firms and a perspective on the rhythm of individuals careers based on enterprises' growth in section (2). It then provides additional insights on what can be expected by individuals when they position themselves on the labor market in section (3). A discussion finally follows (section (4)) to highlight potential shortcomings in the modeling exercises proposed throughout the article and to suggest potential areas of future research. A crisp conclusion is then used as a wrap-up.

Banking on being a company's (wo)man:

The concept of organizational careers (some times referred to as "being a company's (wo)man") have been less prevalent over the past decades [START_REF] Hall | Protean careers of the 21st century[END_REF][START_REF] Hall | The protean career: A quarter-century journey[END_REF]. However, little has been done, to my knowledge, to model and quantify the efficiency of such careers. This is something this section will address and discussed depending in the growth pattern of the firm the incumbent find him/herself. From experience, there are broadly two types of firms: the 'surviving' ones and the 'growing' ones, and depending of the main business dynamic, the impact on individual career is drastically different. This is something which will get illustrated here.

2.1. Being a 'surviving' company's (wo)man:

A surviving company is one that grows at an average rate α. This rate is more or less aligned with the rate at which the economy is evolving. In essence, this means that the revenue of the firm is increasing in the range of 1 to 5% a year depending in various factors such as geographical and economic sector. Now, every year, employees go through their performance review and in this case, I would argue that only two main outcomes are possible. The first scenario is one where the employee will be told that (s)he had a good year and that his/her expertise is valued. And somehow, perhaps with some argument related to having build firm specific human capital, the individual salary will be reviewed and increased at a rate not to dissimilar with the grow rate of the company α. Calling ω t the wage yielded by a role at time t, this means that next's year wage will follow something like: ω t+1 = (1 + α).ω t . In short,the employee will get a 1 to 5% raise a year... The second option is one where a succession opportunity occurs and where the employee can get promoted. For succession to be possible, his/her manager has to leave. This occurs with a probability µ. A good proxy here can be found in the level of turnover occurring within the labor market. And although there are a lot of specificities at a firm level (one can retire, a firm can reorganize etc...), it turns out that, in general, the chance of a succession scheme to occur (i.e.µ) are in the 5 to 15% range. Now, what's interesting here are the gains of the succession game and its underlying mechanisms. Succession is a form of promotion, which comes with a wage increase δ > α. But if gains are straight forward, the underlying mechanics are not so simple. The first thing to ponder is that for a succession scheme to get activated, someone will have to deem the employee worthy. And here, there are ample evidences that this judgement is poorly correlated to the employee's ability [START_REF] Buckingham | Nine lies about work: A freethinking leader's guide to the real world[END_REF]. So in essence, the employee will have a random chance θ to be considered eligible to the succession. And given that there are in general n individuals who could be considered in the process (usually the n direct reports to the "empty seat"), the probability p of one getting promoted through a succession scheme can be depicted as:

p = µ.θ. N-1 k=0 ( (N -1)! (k!.(N -1 -k)!.(N -k) .θ k .(1 -θ) N-1-k ) (1)
Given that we are poor judge of one's potential in a work environment, it could easily be assumed that the probability of being deemed 'worthy' is more or the same as the probability of getting heads when flipping a coin (i.e. θ ≈ 0.5). Besides, since spans of control N are nowadays in the 5 to 7 range, the probability of getting promoted thanks to a succession mechanisms is of about p ≈ 1.9%. The company being more in "survival" mode than in growth mode, it is however very unlikely that a promotion opportunity will occur outside of the succession scheme. Therefore:

Proposition 1. The return r of being a company's (wo)man (i.e. the average year on year rate at which the salary increases ) in a 'surviving' firm follows:

r = α + p.(δ -α) (2)
As a result, being a company's (wo)man means that with a 98%+ chance, one will get a return similar to the rate at which the economy performs and that with a 1.9% chance, a promotion which usually comes with a return of δ ≈ 10%. So a 3 year tenure in the role, comes with a chance of promotion of 5 to 6% and one would have to wait about 40 years to get promoted with 50% chance ... In summary, for the company's (wo)man to ripe the benefits of his/her commitment in the firm in the form a significant increase in living standards, (s)he will have to wait his/her entire career if not more... Since the scheme pretty much equates (on average) stagnation, the question arises: why should someone commit his/herself here?

2.2. Being a 'growing' company's (wo)man:

When companies grow, they naturally offer promotion opportunities as they require more structure. So, to showcase how being a 'growing' company (wo)man can yield interesting results at an individual level, a first depiction of firms' classical managerial structure will be proposed in sub-section (2.2.1). This will then be used in sub-section (2.2.2) to understand how firm growth drives promotion chances.

Management layers & firm size:

It is easy to get a rough approximation of the number of positions in a certain management layer based on the company's size (expressed in terms of number of employees). Assuming the span of control N = 5 of a manager is constant and considering the standard2 size segments [s j , s j+1] ], where j ∈ 0....J = 6, showcased in table (1) the number of management positions n j,l at a level l3 in a firm which size is in the jth segment is more or less worth n j,l ≈ n j,l-1 N (with the norm l≤L j n j j, l = s j+1 ). The associated estimates are shown in tables ( 1) and (2).

Firm growth & promotion chances:

Being promoted as a firm grows can occur in two main set-ups. First, a reorganization happens even though the firm has not added enough employee to justify the introduction of new managerial layers. This is however not so frequent and comes with a number of hurdles, both administrative and human in nature. Because this is rather infrequent, this will not be discussed in this article. Second, the firm changes size to an extent such that managerial roles need to evolve and new managerial layers are added. This actually happening when a firms jumps from one size segment j to another and will be the focus of this discussion. Now, in order to yield some quantitative estimates, let us assume growth follows an independent Poisson process of parameter λ (constant over time). In practice, this means that a firm add λ employees per year, on average, to its rooster. A first order approximation of this parameter could be drafted by looking at how a firm has grown over the past year from an employee standpoint (or even average it over the past couple of years) and use this as a proxy for λ. Since promotions can occur when a firm of size E t reaches at least the next size threshold over a time horizon τ, it is interesting to consider the associated probability:

Firm size (FTEs) [s j , s j+1 ] l = 0 l = 1 l = 2 l = 3 [0,1] 1 [2 ; 6] 5 1 [7;31]
P(E t+τ ≥ s t+1 |E t ) = k≥(s t+1 -st) (λ.τ) k .e -λ.τ k! (3)
Should growth be sufficient, employees will naturally have the possibility to be selected for a promotion which will have a positive outcome with a chance θ (if the employee is deemed worthy -see section (2.1) for a discussion). The chance of being promoted over a period τ because of firm's growth thus equates:

θ.P(E t+τ ≥ s t+1 |E t ).
The chances of being promoted over a 3 or 5 year tenure can then be easily assessed depending in the company growth pace λ and original size. Results are highlighted in figures (??) & (??). This comes with a number of interesting interpretations. First, joining a growing small to medium firm (i.e. less than 150 employees) with a growth rate above 20% yields significant chances of promotion over 3 to 5 years (superior to 10 % up to 50%). However, joining a medium size company (i.e. 150 to 700 employees) does only yield returns over potentially 5 years (and is only interesting for promotion up to director (l = 3) or VP (l = 4) level). Meanwhile, joining a large size company does not come with promotion opportunities outside of a succession pipeline over a relatively reasonable time span (i.e. < 5 years).

In summary, this section has quantified (through small toy models) why organizational careers may not be so interesting. They indeed come with very little perspective in non growing companies and their appeal in the context of growing firms is limited to small to medium enterprises.

Banking on the labor market:

The previous section has shown that, in general, if promotion chances in surviving companies are very low, being in a growing company can yield interesting results. However, growing companies are rare... This section will therefore discuss the extent to which promotions and professional growth can be accessed by leveraging the labor market. To understand how competition is structured, it is important to first depict the general market structure which exist when it comes to labor. Let us consider an economy where there are M = 4 millions firms4 . Stylized economic facts [START_REF] Axtell | Zipf distribution of us firm sizes[END_REF] highlight that firms are distributed according to their size following a Zipf law. Considering the size segments [s j , s j+1] ], where j ∈ 0....J = 6, showcased in table (??) , the number of firms in the market in size segment j can be approximately given as m j = M s j+1 .( i s i ) . Quantitative results are displayed in Combining the standard structure of a firm (see section (2.2.1)) with the distribution of the companies in a given market finally enables us to get a first order estimation of the number of positions in the labor market according to their management level (i.e. n l, j * m j ). Results shown in table (4) represent an overall economy where l j n l, j * m j = 28 millions individuals are employed across M = 4 millions of firms.

Results in a perfectly competitive environment:

Now, to get an understanding of the pool of jobs opened to external incumbents, some additional assumptions are necessary. First, we will consider that the number of firms and the associated distribution is at an equilibrium. Looking back at section ( 2), what this means is that the influx of jobs generated by growing firms compensate the labor market compression related firms that are actually shutting down, while 'surviving' firms stagnate. Second, we will consider that potential reorganization are a second order phenomenon at a market level and that the number of opened positions at a certain management level (i.e. l > 1) are primarily positions where a manager left and where a succession scheme failed. For each position, this occurs with a probability µ.(1 -θ) N ≈ 0.3%. Given the labor market structure depicted in the previous subsection, this also translates into j n l, j * m j * µ.(1 -θ) N ≈ 0.3% of all the managerial position to be vacant in a given year, representing a total of 17-18k openings per year.

If competition were to be perfect, those opportunities/ openings would be known and accessible to everyone. Besides from a pure economic standpoint, openings at a level l would only be interesting for incumbent at a level l ′ < l so that they could yield a revenue increase. Since managerial career track are generally progressive, for an individual to access a role at a level l, this means that they would have to come from the pool of incumbents at level l -1. This translates into promotion probabilities that are below the 0.1% rate, which means that if external promotions mechanisms were to be subjected to a perfect competition, they would be far less interesting that firms' internal succession pipeline. Details are showcased in table (5).

Management level l Promotion chances (%) 2 0.06% 3 to 6 0.05% 7 0.04% However, in real life, job matching for management roles is mainly done through networks. This comes with significant differences which will discussed in the following sub-section.

Playing the shadow market through networking:

The vast majority of managerial roles opened to external incumbents are not advertised on job boards, a phenomenon often dubbed as the "shadow labor market". One of the reason is that publicly promoting such an opening could, for instance, prove detrimental to team motivation as it would officially signal that no team member is deemed worthy of succeeding to the manager. Another possible reason pertains to the signal such a promotion could send to shareholders... From a job seeker perspective, this creates significant hurdles to access opportunities but, at the same time, limits the competition for roles. Those effects will thus be modeled and illustrated in the next two subsections. This will enable a comparison between internal succession schemes and the labor market in terms of outcomes for managers seeking a promotion.

Access the opportunities:

To access an opportunity, individuals must rely on their own professional network. Those networks are by essence small. As discussed in the seminal work of [START_REF] Dunbar | Neocortex size as a constraint on group size in primates[END_REF], individuals are generally able to maintain strong ties with about Φ ≈ 50 other people.

A way to realistically model networks' construction would be to assume that job seekers at a managerial level randomly meet individuals from other companies during, for example, networking events. In this context, the idea is that job seekers draw connections through a series of events in a fashion which is very similar to what is observed in the standard statistical "urn problem" [START_REF] Johnson | Urn models and their application: an approach to modern discrete probability theory[END_REF]. Assuming for instance, that during every events, individuals build/maintain one meaningful connection and that they partake to 50 events a year to structure their network. The probability of them meeting someone who knows about a hidden open position is about the same as picking a random opportunity in a space where the vast majority of positions are already filled.

Lemma 1. In the shadow labor market, the compounded networking efforts yield a yearly probability Ψ of discovering an interesting opportunity:

Ψ = k≤Φ k≥0 Φ! k!.(Φ -k)! . j n l, j * m j * µ.(1 -θ) N (4)
In a labor market where parameters are similar to what was used to described the situation in France, this leads to a probability of accessing at least one interesting opportunity Ψ ≈ 16% for a network of size Φ = 50. A quick sensitivity analysis to the size of one's professional network to his/her chances to access an interesting opportunity can be found in table (6).

In this set up, it also becomes clear that since opportunity discovery is based on networking, it is easier to get access to venues where one can meet VPs (i.e. individuals at managerial level l = 3) or SVPs (managerial level l = 4) than CEOs of large companies. This is however not something which we will discuss in the context of this article. However, what is also worth noting is that professional networks come with chances to encounter a meaningful opportunity that are equivalent if not superior compared to internal succession schemes (i.e. µ ≈ 10%).

Given that internal promotion chances are independent of external network effects, it would appear wise for individuals seeking to a promotion to play both the internal pipeline and the shadow labor market. They would indeed end up by having a 70% to 80% chance to find at least one internal or external fitting opportunity over the course of a 3 years tenure in their job.

Competing for opportunities:

If accessing a job opportunity on the shadow job market is one thing, landing it is another one. To convert a job opportunity into an employment, there is some competition at play between all the incumbents who will have been made aware of the opportunity through their network. As seen in the previous sub-section, accessing suitable opportunities require some effort. Partaking in about Φ = 50 events over a year (i.e. at least 1 every week) on top of one's daily job is indeed an investment. As this requires time, only a portion ρ of individuals will dedicate the energy to do so. Now, the probability ϵ(k, l) that another k individuals access the same opportunity at a level l is about the same as having k individuals getting the same pick out of a pool of ρ * Φ * j n l-1, j * m j (with a probability ξ = 1 j n l-1, j * m j ). This is indeed the same as an experiment where they would draw a ball out of an urn of the same size and replace it:

ϵ(k, l) = ρ * Φ * j n l-1, j * m j k (ξ) k (ξ) ρ * Φ * j n l-1, j * m j -k (5)
Lemma 2. On average, networking efforts yield a number of competitors for one position of:

∀l, ρ. j (n l-1, j .m j ) * Φ j n l, j .m j (6)
The results of the lemma (2) for a labor market of a size and structure similar to the one observed in France are illustrated in figures ( 3) & (4). Those numerical results highlight three main proprieties of this set up. First, competition on the external labor market is much more important than in an internal succession set up. For network of size Φ = 50, assuming networking efforts from ρ = 20% of individuals yields a competition for a role between 50 stakeholders. This is 10 times the competitive pressure found within a succession pipeline. Second, the higher the managerial level l of the desired role , the more complex the competition. Third, network size matters as set-ups where individuals maintain Φ = 20 meaningful relationships come with about 20 to 30 competitors for a role on average (with small variation across managerial levels), while networks of size Φ = 50 come with a 50 to 70 competitors. For a given opportunity with k competitors, a selection process similar to the one described in the succession schemes occurs. Individuals are interviewed and deemed worthy with a probability θ and an offer gets extended to one of the individuals who is considered interesting by the company.

Lemma 3. The probability γ l of getting a promotion (i.e. a job at a level l while coming from level l -1) through networking is therefore worth:

γ l = k (ϵ(k, l) * θ * h<k k h 1 h θ h .θ k-h ) (7)
Quantitative results associated to lemma (3) are displayed in figures ( 5) and ( 6). They show that chances of getting promoted across managerial levels decrease slightly. However, there are significant differences within a given labor market depending in the networking efforts of individuals and their usual network size. A reasonable set up where networks are of size Φ = 30 and where ρ = 20% of individuals actively engage in networking activities then yields a 8% (at managerial level l = 0) to 4% (at managerial level l = 6) chance to land a promotion every year. Compared to internal succession pipelines, networking activities are therefore 4 to 8 times more efficient in terms of career advancement. In comparison, a 5 years networking efforts for a role, comes with a chance of promotion of 30% to 40% (compared to about 5% to 10% in the case of a succession pipeline). Moreover, one would have to wait about 10 years to get promoted on the external labor market with 50% chance, compared to 40+ years in the case of an internal succession. So, in a nutshell, networking pays off, on average, much more than being a company person... And this illustrates why organizational careers are nowadays in the decline in favor of more protean/ self-driven careers.

4. Discussion:

Implications:

The modeling exercises from the previous sections come with three core implications. First, for an individual seeking to constantly maximize his/her earnings, networking efforts are the strategy of choice. Second, because of the compounded effects of networking over time, the level of earnings achieved (because of human capital/ educational background reasons) when entering the labor market can yield significant differences. Third, although all careers have their own journey, a general navigation pattern emerges for individuals involved in networking activities.

When it comes to the compounded interest of networking, the associated advantages can be quickly grasped by playing with a toy model. A career is a journey of τ ≈ 40 -50 years spent on the labor market / in the workforce. Assume that careers start with an entry wage ω 0 ≈ 50k€/year and that promotions occur on a year on year basis with a probability p while yielding a salary increase of δ ≈ 10%. If we remove the fixed effects of inflation, the average wage of an individual after t years on the market simply follows:

ω t = ω 0 .(1 + k≤t k t .(1 + δ) k .p k (1 -p) k ) (8)
Assume, as seen in the previous sections, that the promotion probability p is of 1.9% (resp. 6%) for individuals playing the internal labor market of their firms (resp. the external labor market). The effects of those strategies on earnings are significant. They are summarized in figure (7). After 5 years in the workforce, earnings diverge by about 20% depending in the strategy of choice of the individual. Finally,when reaching the end of one's career, differences peak at 30 to 40% . In a similar fashion, initial wage differences (at entry level) can yield a toll on the overall span of a career. As seen in figure (8), individuals who come in the labor market with an entry wage of ω 0 = 35k€/year and those who come in with a wage of ω 0 = 50k€/year, end up, on average with a salary gap of 30k€ per year. What this means is that differences between students who come out of a tier A university or school and those who come from a tier B or tier C place will, on average, carry on if they all follow the same strategy. If we consider that individuals from tier B or tier C educational establishments do not benefit from the same coaching and opportunities in terms of networking, this means that the labor market and its structure will actually only accentuate differences who were existing between students.

Finally, what's interesting with the notion of networking is For instance, first level managers who start in very large firms (i.e 40000+ employees) have a 70% chance to join a smaller company when there are promoted through network effects. On the other hand, individuals who work in small and medium enterprises are a 70% chance to get promoted by taking a job at a larger firm. There is therefore a form of oscillation. Note that higher level managerial roles are however reserved to large societies.

Limitations & potential areas of further research:

The modeling efforts supporting sections (2) and (3) are not exempt from shortcomings.

The first series of limitations pertains to the way internal labor market are depicted. Looking at surviving firms, the assumption that succession chances (represented by the parameter µ) are constant and set at a level which is representative of the overall workforce turnover observed on the market is rather generic. Situations at a micro level are yet more heterogeneous. Some managers, for example, are set to retire at a fixed date, which will automatically translates into succession opportunities. On the other hand, certain firms and industries may be paying their workers above the market, which translates into lower chances of a manager leaving and of his/her direct report to have a promotion opportunity. What could be potentially interesting on this front, would be to explicit a set of guidelines enabling an assessment of whether or not the context of a company and of a position translates into high succession chances to a point where external networking efforts are potentially not necessary. This could for instance be the subject of a small companion letter to this article. A second limitation of this article is associated to the way growth is considered in section (2.2). The underlying assumption here is that growth is organic and that it triggers job openings and promotions. If it is true that organic growth is a com-mon (if not predominant) pattern, exogenous growth (via mergers and acquisitions) is an important phenomenon which is not described here. Exogenous growth still generates opportunities from a career standpoint, but they are very often triggered by reorganizations and handled, seemingly, on a case by case basis. It would therefore be interesting to explore, for instance via a survey, the effects of such operations on individuals careers and assess if there are any general trends here.

The second series of remarks and potential improvements for this article are associated to the way networking activities (and their impact) are modeled. First, the proposed model was build using a generic distribution (i.e. the Zipf law). If this holds empirically true at a country level, this may be subject to reviews and adjustments when considering specific industrial sectors. This first order approximation can be understood as equivalent to considering that resources are fungible across jobs, which, to an extent, bypasses the notion of professions. This would, for instance, implicitly imply that a lawyer could get a job as financial auditor. It would therefore prove interesting to open a further strand of research to understand, at a macro-economic level, to which extent the patterns described at a country level hold true within a given profession or industry. What would be especially interesting here, is to understand how the consolidation (resp. the dis-agregation) of a profession or an industry (i.e. one where there is few small (resp. large) firms) impacts external promotion chances and networking strategies. Another important element to consider is the role of recruitment intermediaries (e.g. staffing agencies) in the process of landing a job on the labor market. Section (3) indeed assumed that networking was uniquely opened to individuals seeking a job. Nonetheless, staffing represents an entire industry dedicated to providing job seekers and enterprises with potential matches. Some additional research here could be welcomed. This could notably help understanding the pros and cons of those staffing agencies and/or how to best leverage them from an individual standpoint. A way to approach this could be, for example, to assume that staffing agencies generate a network expansion at an individual level (i.e. higher Φ) but come at the cost of having a lower chance to land a job as additional intermediaries have a potentially skewed view on one's performance (i.e. lower θ)...

Conclusion:

The models and illustrations developed in this article offer a blueprint to navigate one's career as efficiently as possible. Efficiency here is looked at from the angle of increasing one's income thanks to promotions. Within this framework, individuals face two options: playing the internal labor market of their firm and/or playing the external labor market. Within all firms, the internal labor market presents a chance of promotion through succession schemes. In this case, a manager leaves and one of his/her team members takes back the reins of the team. This occur with a chance quantified in this article around 1 to 2% per year. On the other hand, individuals can try to access opportunities within other firms and then compete for it. This can be done independently of internal succession opportunities and comes with an extra 8 to 10% chance of landing a promotion. So in a nutshell, for individuals to maximize their income, they should both be playing the internal and the external labor market in a consistent fashion. However, the efforts deployed on the external market are more likely to yield the desired pay off.

This article also shows that there may be a general way for individual to accelerate their career by carefully selecting the firms they work for. Partaking to a fast growing small or medium firm (i.E. ¡150 employees) at the beginning one's career come with significant additional opportunities (i.e. an extra 10 to 50% chance over a 3 years tenure) for an individual contributor or a first level manager to get a promotion. This is linked to the firm organic growth pattern and the associated internal evolution. Moving afterwards as a proximity manager or a director (i.e. a manager of manager) to an organically fast growing (i.e. growth rate above 10%) medium sized firm (i.e. ≈ 500 individuals) then presents very high extra chances (i.e + 10 to 50%) of promotion over the course of a 3 to 5 years tenure. However, once the managerial level of "Vice President" (i.e. managers of managers of managers) has been reached, there is no extra chance of promotion stemming consistently from firm growth. Past that point, career thus mechanically slow down to a rate driven by individuals networking efforts.

If there are, of course, individual deviations to this generic pattern (highlighted for instance in section (4)), as well as certain limitations in the proposed modeling exercise (and thus the associated numerical illustrations), there are two core lessons here. First, individuals should constantly review their options (based on firm's growth trajectory) early in their career and second, they should continuously position themselves both on the market and internally for advancement.

Figure 1 :

 1 Figure 1: Probability of being promoted based on firm original size and growth rate because of the firm's evolution over a 3 years period.

Figure 2 :

 2 Figure 2: Probability of being promoted based on firm original size and growth rate because of the firm's evolution over a 5 years period.

  3.1. Competing in a perfect market: 3.1.1. Assessing the size of the market:

Figure 3 :

 3 Figure 3: Competition intensity to the networking efforts for individuals building/maintaining a network of size Φ = 50.

Figure 4 :

 4 Figure 4: Competition intensity to network size when ρ = 20% individuals dedicate some of level of effort on the external labor market.

Figure 5 :

 5 Figure 5: Promotion chances sensitivity to the networking efforts for individuals building/maintaining a network of size Φ = 50.

Figure 6 :

 6 Figure 6: Promotion chances sensitivity to network size when ρ = 20% individuals dedicate some of level of effort on the external labor market.

Figure 7 :

 7 Figure 7: Approximated average salary evolution for individuals across the span of their career

Figure 8 :

 8 Figure 8: Approximated average salary evolution for individuals across the span of their career

Table 1 :

 1 Firm distribution according to their size in a market of M = 4 million enterprises for management layers below l ≤ 3 (i.e.'vice president' level)

	Firm size (FTEs) [s j , s j+1 ] l = 4 l = 5 l = 6 l = 7
	[0,1]
	[2 ; 6]
	[7;31]
	[32;153]
	[154;781]	1
	[782;3 906]	5	1
	[3 907;40 000]	25	5	1
	40 000+	125	25	5	1

Table 2 :

 2

Firm distribution according to their size in a market of M = 4 million enterprises for management layers above l > 3 (i.e.

'vice president' level)

table (

 (

	3)
	Firm size (FTEs) [s j , s j+1 ] Number of firms m j
	[0,1]	3 313 773
	[2 ; 6]	552 295
	[7;31]	106 895
	[32;153]	21 658
	[154;781]	4 242
	[782;3 906]	848
	[3 907;40 000]	202
	40 000+	82

Table 3 :

 3 Firms' distribution according to their size in a market of M = 4 million enterprises.

Table 4 :

 4 Number of positions in the labor market per management level.

	Management level l Number of positions
	0	23 M
	1	4.6 M
	2	812 k
	3	141 k
	4	24 k
	5	4 k
	6	616
	7	82

Table 5 :

 5 Promotion chances for incumbents when leveraging the labor market in a perfectly competitive set up.

Table 6 :

 6 Yearly average access chances to at least interesting managerial opportunity.

Some early attempts(Perthame et al.,

2018;[START_REF] Ribes | Organizational sustainability and career frameworks in professional services firms[END_REF] can be found in earlier research, but their focus was very narrow.

Those segments are indeed traditionally used in administration and economic databases to classify firms based on their size.

3 As a reminder, the convention here is that the level l = 0 is the one of individual contributors (i.e. individuals without any managerial responsibility)

This could for instance represent the situation observed in France


Timothée Vergne

Mathilde C Paul

Wanida Chaengprachak

Benoit Durand

Marius Gilbert

Barbara Dufour

François Roger

Suwicha Kasemsuwan

Vladimir Grosbois

Zero-inflated models for identifying disease risk factors when case detection is imperfect: Application to highly pathogenic avian influenza H5N1 in Thailand

Keywords: ARDS, acute respiratory distress syndrome A-a, alveolar-arterial (gradient) BAL, bronchoalveolar lavage BP, blood pressure BOAS, brachycephalic obstructive airway syndrome CT, computed tomography NPPE, negative-pressure pulmonary edema PBF, pulmonary blood flow PE, pulmonary edema SpO2, blood oxygen saturation measured with pulse oximetry TP, total protein

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

Introduction

Pulmonary edema (PE) is the accumulation of serous or serohemorrhagic fluid in the pulmonary interstitial space and alveoli. Patients with PE have been traditionally classified as having cardiogenic PE or non-cardiogenic PE . [START_REF] Ware | Clinical practice. Acute pulmonary edema[END_REF] The pathophysiological classification of PE based on changes of the pulmonary parenchyma and pulmonary vasculature differentiates 3 groups of PE: highpressure PE, increased-permeability PE and mixed-cause PE. [START_REF] Adamantos | Pulmonary edema[END_REF] High-pressure PE is due to an increase in pulmonary hydrostatic pressure and is associated with leftsided congestive heart failure and/or overzealous fluid therapy. Increasedpermeability PE occurs secondary to damage of the respiratory membrane as seen in acute respiratory distress syndrome (ARDS), pulmonary thromboembolism, ventilator-associated lung injury or inhalation of toxins. Mixed-cause PE is produced by concurrent changes in pulmonary vascular pressures and permeability of the vascular beds. Mixed-cause PE include neurogenic PE (produced by seizures, traumatic brain injury or electrocution), re-expansion PE and negative-pressure PE (NPPE). [START_REF] Adamantos | Pulmonary edema[END_REF] NPPE, also called "post-obstructive PE", occurs due to vigorous inspiratory efforts against an obstructed airway. In human medicine this is known as the Müller maneuver and is used diagnostically in certain settings. [START_REF] Faber | Available techniques for objective assessment of upper airway narrowing in snoring and sleep apnea[END_REF] These efforts produce large negative pleural pressures that increase transvascular fluid filtration and precipitate interstitial and alveolar edema. The pathophysiology of NPPE could be explained by a rise in pulmonary capillary pressure associated with the transient drop in intrathoracic pressure and subsequent increase in venous return to the right side of the heart. In addition, the negative pleural pressure transmits to the pericardium increasing cardiac afterload. The increase in afterload elevates left ventricular, left atrial and hence pulmonary capillary pressures. This upsurge in pressure promotes fluid movement from the pulmonary capillaries towards the pulmonary interstitial space and alveoli. Moreover, nervousness associated with airway obstruction and hypoxemia may produce sympathetic activation contributing towards further increases in cardiac afterload. [START_REF] Fremont | Postobstructive Pulmonary Edema: A Case for Hydrostatic Mechanisms[END_REF][START_REF] Bhattacharya | Negative-pressure pulmonary edema[END_REF][START_REF] Lemyze | Understanding negative pressure pulmonary edema[END_REF] In the majority of human patients these mechanisms produce a lowprotein edema fluid, demonstrated by a low edema fluid-to-plasma protein ratio (<0.65), although a small subset of patients present with values above this cutoff suggesting an additional increased permeability mechanism. This may be due to pressure-induced rupture of pulmonary capillaries as some patients present with blood-tinged pulmonary secretions. [START_REF] Bhattacharya | Negative-pressure pulmonary edema[END_REF][START_REF] West | Stress failure in pulmonary capillaries[END_REF] There is a lack of veterinary information relating to this condition and no information from multiple centers. Two veterinary publications have described NPPE in companion animals. One described 9 adult dogs with PE due to anatomical upper airway obstruction including laryngeal paralysis, laryngeal edema, laryngeal polyps and laryngeal fibrosarcoma. All dogs survived to discharge. [START_REF] Kerr | Pulmonary edema secondary to upper airway obstruction in the dog: a review of nine cases[END_REF] The second publication described a population of 26 dogs and cats with non-cardiogenic PE of which 6 dogs and 2 cats had presumed NPPE secondary to airway obstruction. Six of these animals with NPPE were less than 1 year old and causes included leash tugs, human physical restraint and brachycephalic obstructive airway syndrome (BOAS). Amongst the cats and dogs with NPPE there was a 50% mortality rate. Six out of 26 patients with noncardiogenic PE required mechanical ventilation and only 1 of these survived to discharge. [START_REF] Drobatz | Noncardiogenic pulmonary edema in dogs and cats: 26 cases (1987-1993)[END_REF] The objective of our study is to describe a population of dogs presenting with NPPE to 5 clinics in XXXX. A secondary objective was to evaluate any associations with morbidity and mortality.

Materials and Methods

This study was approved by the primary author's institution's Ethics and Welfare committee (ethics reference number M2016 0080). The databases of 3 teaching hospitals and 2 private practices in XXXX were retrospectively searched for dogs with a clinical diagnosis of NPPE presenting between 2006 and 2018. Dogs were included in the study if they had acute signs of tachypnea and/or dyspnea and a clinical history compatible with NPPE. The clinical history was suggestive of NPPE when there was a witnessed or suspected episode of upper respiratory tract obstruction.

Data collected included patient demographics, clinical history, admission physical examination findings, blood test results [arterial and venous blood gases, PCV and refractometric total protein (TP), WBC, platelet count, serum biochemistry], blood pressure (systolic Doppler blood pressure or mean oscillometric blood pressure), blood oxygen saturation (SpO2) with pulse oximetry, thoracic radiographs and computed tomography (CT) scans, echocardiograms, cytological and microbiological results of bronchoalveolar lavage, treatments performed including medications and type of oxygen administration, length of hospitalization and outcome. A board-certified radiologist (XX) reviewed all available radiographs. In patients where arterial blood gas analysis was performed on room air, these results are reported as PaO2 and alveolar-arterial (A-a) gradient. In patients where arterial blood gas analysis was performed on supplemental oxygen, these results are reported as PaO2/FiO2 ratio. A-a gradients were calculated in patients breathing room air at sea level using the following formula: (A-a) gradient= PAO2 -PaO2 = [150 -PaCO2/0.8] -PaO2

To further classify the type of upper airway obstruction causing NPPE 5 categories were created. Category 1 was injury produced by pulling hard on the dog´s leash either by the dog or the dog owner/care giver. Category 2 was an episode of near hanging. Category 3 was choking on foodstuffs or toys. Category 4 had an anatomical obstruction to airflow. Category 5 had purposeful airway obstruction by the owner/care giver.

Patients that did not survive were categorized into natural death or euthanasia.

Statistical methods

Statistics were performed using a commercial statistical software. a Normality of the data was assessed using the Shapiro-Wilk test. Continuous parametric data was described as mean and SD and non-parametric data as median and range. A Chi-square test or Fisher´s exact test was performed to evaluate the relationship between categorical variables. A Student's t-test was performed to evaluate continuous, normally distributed data and a Mann-Whitney U test for continuous, not normally distributed data. In order to control familywise error from performing multiple comparisons the Bonferroni correction was applied. After applying the Bonferroni correction, the significance threshold was set at p<0.002.

Results

Thirty-five cases met the inclusion criteria. There were 19 different breeds represented in the study. Most dogs were crossbreed (6), followed by English Bulldog (4), Cocker Spaniel (3), Labrador Retriever (3) and Staffordshire Bull Terrier (3). Fourteen dogs (40%) were brachycephalic including English bulldog, French bulldog, Staffordshire bull terrier, Chihuahua, pug, Pomeranian, Lhasa Apso and shih tzu. The median age was 4 months (range 2-90) and the median weight was 7.1 kg (range 1.7-37.2). There were 19 entire males (54.3%), 2 castrated males (5.7%), 13 entire females (37.1%) and 1 neutered female (2.9%).

The majority of cases were referred from a primary care veterinarian (85.7%) and the rest (14.3%) presented as primary care emergencies. There were 10 dogs (28.6%) with NPPE caused by a leash pull (category 1).

Six dogs (17.1%) had an episode of near hanging (category 2); two were hanged by their leashes on becoming trapped outside an ascending elevator, one got his head stuck between fencing panels and 3 had a near hanging episode at the groomers´ table. Fourteen dogs (40%) had accidental choking (category 3). Nine choked on foodstuffs and 5 choked on toys or balls. There were 3 dogs (8.6%) with an anatomical obstruction to airflow (category 4); one each of laryngeal paralysis, laryngeal collapse and presumed BOAS. All dogs in category 4 were older than 24 months of age. Two dogs (5.7%) had purposeful airway obstruction by the owner/care giver (category 5). One dog was restrained round the neck by a dog trainer during a puppy class and the other dog bit its owner whilst playing and in response the owner clamped the muzzle shut while pinning the dog on its back for several seconds.

On physical examination 15 (42.9%) dogs were reported as alert, 10 (25.7%) were obtunded and one arrived anesthetized to the hospital (2.9%).

Mucous membranes were pale in 5 (14.3%), pink in 20 (57.1%), cyanotic in 4 (11.4%) and white in 2 (5.7%). The median heart rate was 142 beats per minute (range 56-180), the median respiratory rate 80 breaths per minute (range 20-180) and the median rectal temperature 38.1ºC (range 34.9-38.8). Eight dogs were hypothermic on presentation (rectal temperature < 37.9ºC) and there were no hyperthermic dogs. Blood pressure (BP) was measured on presentation using the Doppler method in 7 dogs and oscillometric method in 4 dogs. The median Doppler BP was 110 mmHg (range 80-120) and the median mean arterial pressure with the oscillometric method was 90 mmHg (range 72-130). Only 2 dogs were classified as hypotensive on presentation (Doppler BP < 100).

Pulse oximetry was performed in 15 dogs (42%). Median SpO2 was 90% (range 56-99). FiO2 could only be obtained from the medical records from 5 dogs who had pulse oximetry performed; 3 of them were breathing room air and 2 of them were on mechanical ventilation with various FiO2. One dog had a FiO2 of 0.6 with a SpO2 of 99% and another dog had a FiO2 of 1 with a SpO2 of 91%. Arterial blood gas analysis was performed on 9 patients, 6 of them breathing room air and 3 on supplemental oxygen. Patients breathing room air had a low mean PaO2 [7.5 ± 2.5 KPa, RI 10.6-14 (56 ± 19 mmHg, RI 80-105)] with an increased mean (A-a) gradient [6.9 ± 2.4 KPa, RI<2 (52 ± 18 mmHg, RI <15)]. Patients on supplemental oxygen had a low median PaO2/FiO2 ratio {10 (10-61) kPa, RI 50.5-66. 5 [75 (75-458)]. Two of these patients had a PaO2 of 75mmHg with a FiO2 of 1 and the remaining patient had a PaO2 of 275mmHg with an FiO2 of 0.6. The rest of blood test results are displayed in Table 1.

Bronchoalveolar lavage (BAL) was performed in 7 (20%) dogs. In 5 dogs BAL was performed soon after commencing mechanical ventilation and one dog after a thoracic CT scan. Cytology in these dogs was consistent with neutrophilic inflammation and microbiological culture was negative. In the remaining dog it was performed 48 hours after commencing mechanical ventilation and cultured Escherichia coli, Enterococcus spp. and a multi-drug resistant Pseudomonas aeruginosa due to presumed ventilator-associated pneumonia.

Echocardiography was performed in 3 (8.6%) dogs. One dog had reduced systolic function which had resolved 8 days later.

Thoracic radiographs were obtained in 32 (91.4%) dogs. One dog had a CT scan only, 3 had CT scan and radiographs and the remaining 2 did not have thoracic imaging due to severe respiratory compromise. Thirty-one radiographic studies were retrieved for review. The pattern of infiltration was defined as alveolar in 26 (74.3%) cases, interstitial to alveolar in 4 (11.4%) cases and purely interstitial in 1 (2.9%) case. The pattern of infiltration was predominantly caudodorsal in 23 (65.7%) cases. All lung lobes were affected in 13 cases (37.1%).

The 3 thoracic CT scans documented alveolar patterns in various lung lobes compatible with pulmonary edema.

Oxygen therapy was administered to 33 (94.3%) dogs. Two (5.7%) dogs received nasal oxygen through cannulae and 24 (68.6%) dogs via oxygen cages.

Seven (20%) dogs had endotracheal intubation and mechanical ventilation. Two (5.7%) dogs had tachypnea and radiographic features of NPPE but improved soon after presentation and did not require oxygen therapy. Antibiotics were administered to 12 (34.2%) dogs. Eight dogs received amoxicillin-clavulanic acid b and 4 dogs received cefuroxime c . Eighteen (51.4%) dogs received furosemide d at any time point. In 10 (28.5%) dogs this was prior to referral and 8 (22.9%) dogs at the referral hospital. Median dose of furosemide was 2 mg/kg (range 0.5-6.5). Nine (25.7%) dogs received corticosteroid at any time point. Dexamethasone e was administered to 5 (14.3%) dogs prior to referral and to 4 (11.4%) dogs at the referral hospitals. Median dose of dexamethasone was 0.2 mg/kg (range 0.13-0.37).

Twenty-eight (80%) dogs survived to discharge. Of the 7 (20%) dogs that did not survive, 4 were euthanized and 3 died naturally. It was not possible to tell from the medical records if euthanasia was financially driven or if it was due to a perceived poor prognosis. Dogs that were mechanically ventilated had a survival rate of 28.6%. Necropsy was performed in 1 non-survivor and identified congested and collapsed lungs consistent with pulmonary edema. The median length of hospitalization was 2 days (range 0-14).

Univariate statistical analysis was performed to identify factors that were associated with survival. These results are displayed in tables 2 and 3. PaO2, A-a gradient, PaO2/FiO2 ratio, bicarbonate, BE, total and ionized calcium, albumin, ALT, ALP, total bilirubin, urea and the number of brachycephalic dogs were not included in the analysis as these parameters were only measured in one nonsurvivor each. Requirement for mechanical ventilation (p<0.001) was the only parameter associated with mortality.

Discussion

To the authors' knowledge, this is the largest study of dogs with NPPE.

The most common incident causing NPPE was choking on foodstuffs or toys (40% of cases). Choking and near hanging had not been previously described as causes of non-cardiogenic PE in veterinary medicine but are well known causes in human medicine, both in infants and adults. [START_REF] Toukan | Negative pressure pulmonary edema following choking on a cookie[END_REF][START_REF] Miyazaki | Negative-pressure pulmonary oedema following choking on a rice ball[END_REF][START_REF] Berdai | Postobstructive pulmonary edema following accidental near-hanging[END_REF] In order to avoid choking or neck leash injuries in puppies veterinarians may choose to advise their clients to avoid large chews that could block the airway or recommend the use of a body harness instead of a neck collar or neck leash. Although there are a variety of causes producing NPPE we did not find significant differences as regards mortality amongst the different groups.

In our study 85% of the cases were less than 1 year old. It is reported that young, healthy people can achieve up to -140 cmH2O of negative intrathoracic pressure. [START_REF] Cook | Maximum and minimum airway pressures at various lung volumes in normal children and adults[END_REF] It is possible that juvenile dogs, as seen in young humans, can produce larger negative intra-thoracic pressures than adults. Other age-related factors such as the tendency to chew and eat voraciously, tug on the leash and undergo training, may also be a factor. The 3 dogs with an anatomical obstruction to airflow were older than 24 months of age. This is probably because the majority of anatomical obstructions to airflow happen in older dogs, as it is the case of laryngeal paralysis, or develop slowly over the course of months or years, as is the case in BOAS.

The majority of thoracic radiographs (65.7% of cases) showed an alveolar or interstitial pattern in the caudodorsal area as previously described in the literature (Figure 1). [START_REF] Kerr | Pulmonary edema secondary to upper airway obstruction in the dog: a review of nine cases[END_REF][START_REF] Drobatz | Noncardiogenic pulmonary edema in dogs and cats: 26 cases (1987-1993)[END_REF][START_REF] Bouyssou | Radiographic appearance of presumed noncardiogenic pulmonary edema and correlation with the underlying cause in dogs and cats[END_REF] A recent radiographic study found that NPPE produces caudodorsal lung patterns more frequently than the other causes of noncardiogenic PE. [START_REF] Bouyssou | Radiographic appearance of presumed noncardiogenic pulmonary edema and correlation with the underlying cause in dogs and cats[END_REF] It is unknown why NPPE has this predilection for the caudodorsal area, but it could be that because dogs have increased pulmonary blood volume and flow in the caudal lung lobes [START_REF] Amis | A conscious dog model for study of regional lung function[END_REF] they are more likely to have transvascular fluid filtration associated with NPPE in this region. This increase of pulmonary blood flow (PBF) in the dorsocaudal area against gravity is also seen in other standing quadrupeds like horses. [START_REF] Robinson | Pulmonary blood flow[END_REF] Studies of canine PBF under anesthesia and mechanical ventilation show a gravitational effect on PBF [START_REF] Chon | Regional pulmonary blood flow in dogs by 4D-X-ray CT[END_REF][START_REF] Hoi | Characterization of the pulmonary circulation according to hemodynamic changes by computed tomography[END_REF] as is the case of conscious human subjects [START_REF] West | Blood flow and metabolism[END_REF] but this may not represent what happens in non-anesthetized dogs. Another factor that may play a role in the development of caudodorsal PE is the normal presence of pleural pressure gradients. Dogs have more negative pleural pressures in the dorsal regions of the lung in comparison with the ventral regions. [START_REF] Casha | Pleural pressure theory revisited: a role for capillary equilibrium[END_REF] In situations of airway obstruction in dogs, pleural pressures may be more negative in the dorsal area hence favouring the development of a caudorsal pattern.

Thoracic CT scan was performed in 3 dogs that had thoracic radiography performed. We could not tell from the medical records the indication for this study but one dog had laryngeal paralysis and one dog had laryngeal collapse so a CT might have been performed to rule out concurrent underlying diseases.

In human medicine it is common to measure protein concentration of the edema fluid to then calculate the edema fluid-to-plasma protein ratio. [START_REF] Ware | Determining the aetiology of pulmonary oedema by the oedema fluid-to-plasma protein ratio[END_REF] A ratio of <0.65 suggests a low-protein edema as seen in cases of cardiogenic PE but also in the majority of humans with NPPE. [START_REF] Bhattacharya | Negative-pressure pulmonary edema[END_REF] Higher ratios are consistent with increasedpermeability PE and mixed-cause PE. [START_REF] Ware | Determining the aetiology of pulmonary oedema by the oedema fluid-to-plasma protein ratio[END_REF] This is uncommonly performed in veterinary medicine and the majority of clinicians perform BAL infusing sterile saline solution into the airway, which would affect the fluid-to-plasma protein ration. The bronchoalveolar fluid obtained in our cases revealed neutrophilic inflammation. This inflammatory response may be due to rupture of pulmonary capillaries resulting from large negative pulmonary pressures.

The recommended treatment for NPPE in human medicine is oxygen supplementation and, if necessary, endotracheal intubation and mechanical ventilation with protective ventilation strategies. [START_REF] Bhattacharya | Negative-pressure pulmonary edema[END_REF] Antimicrobials are not indicated, unless there is evidence of additional diseases such as ventilatorassociated pneumonia. Furosemide can be considered given that the edema is a low-protein fluid in most cases but there is not strong evidence suggesting its efficacy. [START_REF] Bhattacharya | Negative-pressure pulmonary edema[END_REF] Edema fluid-to-plasma protein ratios have not been measured in veterinary medicine so it is not known whether dogs might benefit from furosemide. Since most events that cause NPPE are transient and there is no persistence of increased pulmonary capillary pressures, furosemide is unlikely to be helpful. The use of furosemide could potentially be deleterious as it may lead to hypovolemia and decreased tissue perfusion. Judicious use of fluid therapy with isotonic crystalloids should be considered to avoid dehydration.

Glucocorticoids are not indicated. [START_REF] Bhattacharya | Negative-pressure pulmonary edema[END_REF] They may predispose the patient to gastrointestinal ulceration or increase predisposition to infection among other adverse effects. The administration of corticosteroids or furosemide were not associated with survival in our study, but because of the retrospective observational nature of the study and the small number of dogs that received these drugs, their role in the resolution of the disease cannot be completely excluded.

Statistical analysis found that mechanical ventilation requirement was the only parameter associated with mortality. Our study demonstrated an overall survival rate of 80% which is between previous reported values of dogs with NPPE (50% and 100%). [START_REF] Kerr | Pulmonary edema secondary to upper airway obstruction in the dog: a review of nine cases[END_REF][START_REF] Drobatz | Noncardiogenic pulmonary edema in dogs and cats: 26 cases (1987-1993)[END_REF] The survival rate of dogs requiring mechanical ventilation due to NPPE of our study (28.6%) is lower than the reported survival rates of mechanically ventilated dogs with cardiogenic PE (77%) [START_REF] Edwards | Outcome of positivepressure ventilation in dogs and cats with congestive heart failure: 16 cases (1992-2012)[END_REF] but is higher than the overall canine ARDS population requiring mechanical ventilation (8.3% and 16%). 23,24 The higher survival rate of ventilated patients with cardiogenic PE compared to NPPE ventilated patients may be related to the effectiveness of diuretic therapy in reducing pulmonary hydrostatic pressure and rapid correction of the underlying mechanism of edema formation in these patients. As patients severely affected by NPPE likely have microvascular permeability alterations and capillary rupture, the edema fluid may be richer in protein and less likely to be eliminated by diuretics.

Our study has several limitations. Due to its retrospective nature there were some missing data that may have affected our results. Another limitation is the small number of cases. Despite being a multi-institutional study NPPE remains an uncommon cause of PE. Also, because it is an observational study, we cannot draw valid conclusions regarding influence of treatment strategies such as type of oxygen supplementation and use of diuretics. Additionally, we could not ascertain from the medical records whether euthanasia was performed due to a perceived poor prognosis or financial motives and this could have impacted outcome. Another limitation is that by applying the Bonferroni correction a type II statistical error could be committed reducing statistical power.

In conclusion, most cases of NPPE occur in juvenile dogs. NPPE can happen due to choking on foodstuffs or toys, leash tugs, near hanging, purposeful obstruction by humans or anatomical obstructions. Choking and near hanging have not been previously described in the veterinary literature as inciting causes of NPPE. The overall prognosis is good with a short hospitalization period, unless severe respiratory distress that requires mechanical ventilation ensues.

  23. Balakrishnan A, Drobatz KJ, Silverstein DC. Retrospective evaluation of the prevalence, risk factors, management, outcome, and necropsy findings of acute lung injury and acute respiratory distress syndrome in dogs and cats: 29 cases (2011-2013). J Vet Emerg Crit Care 2017;27(6):662-673. 24. Boiron L, Hopper K, Borchers A. Risk factors, characteristics, and outcomes of acute respiratory distress syndrome in dogs and cats: 54 cases. J Vet Emerg Crit Care 2019;29(2):173-179.

Figure 1 :

 1 Figure 1: Dorsoventral and right lateral thoracic radiographs of a 4 month-old

Table 1 :

 1 Summary of blood tests results obtained on admission from dogs with NPPE. TP: total protein.

	Parameter	Number of	SI units	Reference	Conventional	Reference
		cases	Mean ±	interval	units	interval
		where test	SD		Mean ± SD
		was	Median		Median
		performed	(range)		(range)
	PCV	25	0.39 ±	0.37-0.55	39.7 ± 5.8 % 37-55
			0.06

Table 2 :

 2 Comparison between survivors and non-survivors of patients´ 435 characteristics, type of injury and physical examination findings in dogs with 436

	437	NPPE.
	438
		Parameter	Survivors	Non-	p value
					survivors
		Sex	Male	16	5	0.676
			Female	12	2
		Sexually intact	26	6	0.499
		Age (months)		4 (2-90)	4 (2.5-60)	0.732
		Weight (kg)		6.4(1.7-	9(2.7-19.2)	0.466
				37.2)
		Type of	Category 1	9	1	0.376
		injury	Category 2	6	0
			Category 3	10	4
			Category 4	2	1
			Category 5	1	1
		Mentation Alert	15	0	0.022
		Obtunded	5	5

Table 3 :

 3 Comparison between survivors and non-survivors of diagnostic test results and treatments in dogs with NPPE. The number of times each test was performed can be found on table 1. SpO2: blood oxygen saturation measured with pulse oximetry, TP: total protein.

	Parameter	Survivors	Non-	p value
			survivors
	PCO2	4.9 (3.7-6.7)	7.7 (4.6-	0.203
		KPa	11.9) KPa
		37.2(27.6-	58(34.4-
		50.4) mmHg	89.5) mmHg
	pH	7.379	7.261	0.641
		(7.240--	(7.083-
		7.490)	7.440)
	SpO2	91(81-99) % 87(56-91) % 0.365
	Lactate	2.2 ± 1.5	1.4 ± 0.1	0.480
		mmol/L	mmol/L
		19.8 ± 13.5	12.6 ± 0.9
		mg/dL	mg/dL
	Na	145±5	143±1	0.660
		mmol/L	mmol/L
		145±5	143±1
		mEq/L	mEq/L

Acknowledgments

Footnotes a. IBM SPSS Statistics version 23. IBM United Kingdom Limited, PO Box 41, North Harbour , Portsmouth, Hampshire, PO6 3AU. b. Augmentin ® 500mg/100mg powder for solution for injection. GlaxoSmithKline UK, Stockley Park West, Uxbridge Middlesex UB11 1BT. United Kingdom. c. Zinacef ® 1.5g powder for solution for injection. GlaxoSmithKline UK, Stockley Park West, Uxbridge Middlesex UB11 1BT. United Kingdom. d. Dimazon ® 50 mg/ml solution for injection. NOAH, MSD Animal Health. Walton Manor, Walton, Milton Keynes MK7 7AJ, United Kingdom e. Dexafort ® 4 mg/ml suspension for injection. NOAH, MSD Animal Health. Walton Manor, Walton, Milton Keynes MK7 7AJ, United Kingdom