Chao Zhang

Achal Agrawal

Vineeth S Varma

Samson Lasaulce

Chao Zhang ˚

Thresholding-based distributed power control for energy-efficient interference networks

Thresholding-based distributed power control for energy-efficient interference networks

I. INTRODUCTION

The design of energy-efficient communications is an issue that has gained a lot of attention in the past years. This issue is naturally relevant in mobile devices with limited battery capacity, but it has also become an important issue for radio base stations and tele-communication operators due to the operational costs [START_REF] Hossain | Green radio communication networks[END_REF]. In [START_REF] Rault | Energy efficiency in wireless sensor networks: A top-down survey[END_REF], an extensive survey is provided on techniques that improve energy efficiency in wireless systems, defined as the ratio between the number of bits successfully transmitted and the power consumed. Amongst the various scenarios that can be considered, the focus of this paper, is on transmission power control. Ideally, to optimize power control in distributed interference networks, a transmitter requires knowledge about global channel state information (CSI). However, in a distributed setting, global CSI is typically not available. The existing techniques to acquire global CSI, typically rely on the existence of inter-transmitter signaling channels (see [START_REF] Gjendemsjø | Binary power control for sum rate maximization over multiple interfering links[END_REF]), which may be unavailable in practice. Some recent works have proposed techniques with which global CSI can be estimated using implicit signalling through the interference channel via power modulation [START_REF] Zhang | Interference coordination via power domain channel estimation[END_REF]. However, these works assume a sufficiently long channel coherence time as global channel acquisition may take a long time. Additionally, the technique proposed does not scale well with a large number of interfering devices. In the present work, we only look at fully distributed power control policies that: provide the transmit power level in one shot that is, without generating extra delay induced by memory reading or exchanges with the backhauling infrastructure; only exploit individual CSI as available information; may be used even in the presence of many (interfering) users.

Energy-efficient distributed power control in the sense adopted in the present paper has been first studied in [START_REF] Goodman | Power control for wireless data[END_REF], in which the problem of power control is treated as a non-cooperative game with each transmitting device attempts to maximize its individual energy-efficiency. Various extensions, see [START_REF] Meshkati | A game-theoretic approach to energy-efficient power control in multicarrier CDMA systems[END_REF]- [START_REF] Zappone | Energy-efficient power control and receiver design in relay-assisted ds/cdma wireless networks via game theory[END_REF] have been proposed to [START_REF] Goodman | Power control for wireless data[END_REF], in which additional features like multi-band channels, OFDMA, MIMO, packet layer, relays, etc., was considered. However, the resulting operating point is at the Nash equilibrium which can be seen to be very inefficient in terms of sum-EE. This work was later improved in [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] in which a pricing function is artificially added to the individual utility in order to incite cooperative behavior in multiple access channels (MAC). While the resulting operating point Pareto dominates the equilibrium from [START_REF] Goodman | Power control for wireless data[END_REF], it is still not designed to be optimal and more importantly, the operating point can not be determined as an explicit function of the channel gain. However, not many works propose a technique that optimizes or improves upon the sum-EE considered in [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF], in the context of an interference channel, which is the primary motivation of this work. To our knowledge, the closest work is given by [START_REF] Kerret | Bestresponse team power control for the interference channel with local CSI[END_REF] in which a thresholding policy was shown to be near-optimal for sum-rate maximization.

The main advantages and features of the proposed technique over the state of the art can be summarized as follows.

1) It is designed for interference channels and not only multiple access channels (as done in [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] and is therefore more general. 2) Once the thresholds are determined offline, the power control at each time instant can be determined in a shot manner and by an explicit function. This means without an iterative online procedure which might not converge and necessitate several and possibly many SINR samples (as in [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] and papers using the best-response dynamics), especially when the number of users increases.

3) It is optimal when the CSI is individual and in extreme regimes of interference level. This paper is structured as follows. In Section II we provide the system model and problem statement, followed by an analysis of the proposed thresholding policy in . We then show some properties of this policy in IV which facilitates in tuning the threshold. In Section V we compare the energy efficiency obtained with the proposed technique with state of the art techniques and provide some concluding remarks in VI.

II. PROBLEM FORMULATION

Consider a wireless network where K transmitters (or transmitter-receiver pairs depending on the model considered) are trying to coordinate the power emitted p i P P i , i P K " t1, ..., Ku. Due to the power constraint at every transmitter, the transmit power at any transmitter i P K should not exceed P max , i.e. p i P r0, P max s. Based on the transmission power profile, the signal to interference plus noise ratio (SINR) at each receiver i can be written as

γ i " p i g ii σ 2 `řK j"1,j‰i p j g ji (1)
where the channel gain coefficient g ji P R ě0 represents the quality of wireless link from the transmitter j to the receiver i, and σ 2 represents the noise level. We define the global channel state G " pg 11 , ..., g KK q P R K 2 , which is in general, a random state which affects the common payoff function for the system, and is not controlled by the coordinating transmitters. The realizations of the channel gain coefficients G at each time instant are assumed to be i.i.d. and follow a probability distribution ρ. In this work, ρ is taken to be an exponential distribution for each channel gain g ij , i.e. we consider a Rayleigh fading channel.

The instantaneous individual utility function u i pG, p 1 , ..., p N q, is the energy efficiency as defined in [START_REF] Goodman | Power control for wireless data[END_REF], i.e.,

u i pG, p 1 , . . . , p K q " ψpγ i q p i (2)
where ψ denotes the expected number of successful bits transmitted as a function of the SINR; ψ may represent the packet success rate and is typically a sigmoidal function. The sum-EE is therefore wpG, p 1 , . . . , p K q " ř K i"1 u i pG, p 1 , . . . , p K q. In this work, we are interested in maximizing the expected sum-EE defined as

E G rwpG, p 1 , . . . , p K qs " ż G P G wpG, p 1 , ..., p N qρpGqdG (3)
Since only individual CSI, i.e. , g ii is available at i, the optimal power control must be tuned based solely on g ii . Although in general, this policy might also depend on past values of the channel, we focus on stationary strategies and our objective is to find an optimal mapping f i pg ii q : R ě0 Ñ r0, P max s. This induces no performance loss as the nature state is considered to be i.i.d. at each time. We use f :" pf 1 p¨q, . . . , f K p¨qq to denote the global power control policy and F to denote the set of all such functions. In general, the optimization problem to be solved can be written as

Maximize f PF E G rwpG, p 1 , . . . , p K qs. (4)
However, optimizing the above functional is not trivial at all in general, and we therefore restrict our family of functions to the following type of thresholding policies,

f λi pg ii q " $ ' ' & ' ' % 0 if g ii ă λ i αiσ 2 gii if g ii ě λ i (5)
where λ i ě 0 is the threshold for Transmitter i and α i ě 0 is a scaling factor to be tuned. For instance, in [START_REF] Goodman | Power control for wireless data[END_REF], choosing α i to be the unique positive solution of γψ 1 pγq ´ψpγq " 0, i.e., α i " γ ‹ , is shown to correspond to the Nash equilibrium solution. This is the choice we will make but other choices are possible.

III. ANALYSIS

Extensive numerical simulations for the case with discrete alphabets for G, i.e., when |G| ă 8, revealed the structure of the optimal solution to be of the form [START_REF] Goodman | Power control for wireless data[END_REF]. These simulations involved an exhaustive search over all possible mappings f i p¨q (which is finite) [START_REF] Zhang | A framework for distributed power control with partial channel state information[END_REF]. Conjecturing a similar continuous power control policy from observations on the discrete case was not aberrant as taking the limit of the alphabet size growing larger brings the system close to the continuous case.

While we have no proof for the optimality of the proposed power control policy (5) in the general case, for asymptotic cases of small and large interference, it can be shown that such a policy is optimal. This is precisely the objective of proposition III.1, wherein we consider the two asymptotic cases of very high and negligible interference. To quantify these terms, we introduce signal-to-interference ratio (SIR) as a measure for high interference and low interference respectively:

SIR max " max i,j,j‰i ˆEpg ii q Epg ji q ˙(6) SIR min " min i,j,j‰i ˆEpg ii q Epg ji q ˙(7)
Since the power control policy is a function of g ii , we must find the optimal power for each value of given g ii . In the following proposition, we prove that when SIR max Ñ 0 (high interference) or SIR min Ñ 8 (low interference), the optimal power control policy is of the form [START_REF] Goodman | Power control for wireless data[END_REF]. For ease of exposition, we assume the case where the power limitation is always met, i.e. P max Ñ 8. For finite P max the power control can be taken as the min of P max and the one provided below.

Proposition III.1. When SIR max Ñ 0 or SIR min Ñ 8, the optimization problem (4) has a solution of the form (5).

Proof:

First of all, if we denote the interference of user i as

I i " ÿ j‰i g ji p j , (8)
knowing that g ji follows the exponential distribution (as assumed in Section II), we have

lim EpgjiqÑ8 Pr ˆgji ą 1 ˙" 1 (9)
for any P R ą0 , i.e., g ji Ñ 8 almost surely in the low SIR limit. Similarly,

lim EpgjiqÑ8 Prpg ji ă q " 1 (10)
which means that g ji Ñ 0 almost surely in the high SIR limit.

When SIR min Ñ 8, since the interference is negligible here, each user i will choose the action which maximizes its own utility, leading to the optimal solution f i pg ii q " γ ‹ σ 2 gii . When SIR max Ñ 0, we can make some relevant observations. First, if p j ą 0, then ψpγiq pi Ñ 0 for all i ‰ j regardless of p i since g ji Ñ 8 and γ i Ñ 0. Therefore, if the right transmitter j is chosen, then p j ą 0, p i " 0. Naturally, since j experiences no interference, p j " γ ‹ σ 2 gjj . This lets us conclude that in the low SIR limit, the optimal power control policy if done in a centralized manner would be to pick the best transmitter (largest g jj ) and switch off all the others.

For a given transmitter i, since individual CSI is available, we must try to optimize the energy efficiency function over all possible realizations of the other gains, i.e. let G ´i " pg 11 , g 12 , ..., g i,i´1 , g i,i`1 , ..., g KK q denote all the other gains and ρ ´ipG ´i|g ii q denote the p.d.f. of the other gains. Then (3) can be rewritten as: [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] where

E G rwpG, P qs " ż G P G wpG, f 1 pg 11 q, ..., f K pg KK qqρpGqdG " ż gii ρ i pg ii q ż G´i wpG, ..., f K pg KK qqρ ´ipG ´i|g ii qdG " ż gii ρ i pg ii qθ i pg ii , f i pg ii qq dg ii
θ i pg ii , f i pg ii qq " ż G´i wpG, f 1 pg 11 q, ..., f K pg KK qqρ ´ipG ´i|g ii qdG ´i (12)
Since g ij Ñ 8 almost surely for all i ‰ j, when I i " 0 for some i, we have wpG, ..., f i pg ii q " w i pG, . . . q, . . . q " ψ ´giifipgiiq σ 2 fi pg ii q (13) and otherwise, wpG, ..., f i pg ii q Ñ 0.

Hence, from ( 13) we can conclude that f i pg ii q "

γ ‹ σ 2 gii
dominates other positive actions almost surely. The optimal action for user i thus belongs to the set t0, γ ‹ σ 2 gii u. Next, we prove that there exists an unique threshold between the two actions. Define the difference between the utility of 2 actions as:

∆pg ii q " θ i pg ii , f i pg ii q " 0q´θ i ˆgii , f i pg ii q " γ ‹ σ 2 g ii (14)
Then three following conditions can be easily checked:

B∆pg ii q g ii ă 0 @g ii ą 0 (15) lim giiÑ0
∆pg ii q ą 0 (16)

lim giiÑ8 ∆pg ii q ă 0 (17)
Note that ∆pg ii q is a continuous and monotonic function. Hence, we can conclude that there exists one unique threshold λ i such that ∆pg ii " λ i q " 0, ∆pg ii q ą 0 if g ii ă λ i and ∆pg ii q ă 0 if g ii ą λ i using the mean value theorem. When the SIR is not in these limits, the threshold policy of the form (5) can not be proven to be optimal. However, through numerical simulations in section V, we shall show that it outperforms the current state of the art on distributed energy efficient power control. While the propositions proved in this section give us some justification for the proposed power control policy, they do not provide a way to compute the optimal thresholds for each transmitter in a practical scenario. In the next section, we shall prove that the expected sumenergy is quasi-concave w.r.t. each individual threshold when the other thresholds are held a constant. This helps us provide a low-complexity distributed algorithm for finding the thresholds for each transmitter, thereby determining their power control policy through equation [START_REF] Goodman | Power control for wireless data[END_REF].

IV. DETERMINING OPTIMAL THRESHOLDS

We shall now proceed to show that if the power control policy is of the form proposed (5), then the payoff is quasi-concave w.r.t. any individual threshold λ i if the other thresholds λ j , j ‰ i are held a constant. In fact, we can even get a closed form expression for the optimal threshold for a transmitter assuming the thresholds for other transmitters are known. For this, we first define θ i pg ii , p i ; λ ´iq " ż G´i wpG, f λ1 pg 11 q, .., p i , .., f λ K pg KK qq ˆρ´i pG ´i|g ii qdG ´i (18) which is the expected sum energy efficiency when transmitter i has channel gain g ii and uses power p i , with the rest of the transmitters using the policy ( 5) with λ ´i denoting the thresholds of all the other transmitters j ‰ i.

Proposition IV.1. Assuming p i " f λi pg ii q as defined in (5), then the expected payoff is quasi-concave w.r.t. the individual threshold λ i when the other thresholds are held constant.

Proof. Similar to the proof of Proposition III.1, the expected payoff (3) can be written as:

E ρ rwpG, f 1 pg 11 q, . . . , f K pg KK qqs " ż λi 0 ρ i pg ii qθ i pg ii , 0; λ ´iq dg ii `ż 8 λi ρ i pg ii qθ i ˆgii , γ ‹ σ 2 g ii λ ´i˙d g ii . ( 19
)
Note that when p i " 0, θ i pg ii , 0; λ ´iq becomes a constant which is independent of g ii , i.e., θ i pg ii , 0; λ ´iq " c i . When f i pg ii q " γ ‹ σ 2 gii , define

a i pg ii q " θ i ˆgii , γ ‹ σ 2 g ii ; λ ´i˙. (20)
, We can easily verify that

Ba i Bg ii ą 0 @g ii ą 0, ( 21
)
lim giiÑ0 a i pg ii q ď c i , ( 22
)
lim giiÑ8 a i pg ii q ą c i . ( 23
)
Therefore, it can be concluded that under the assumption of proposed threshold policy, the expected payoff E ρ rwpG, P qs is increasing w.r.t. λ i when λ i ď a ´1 i pc i q and decreasing w.r.t. λ i when λ i ą a ´1 i pc i q. The optimum λ i to maximize the E ρ rwpG, P qs can be written as λ ‹ i " a ´1 i pc i q.

(24)

Thus it can be seen that for every real number a, C λi " tλ i P R `: ω i pλ i q ě au, (25) is a convex set, which proves our claim about quasiconcavity.

Even though, we have obtained a closed form expression for optimal individual thresholds, this result is not easily exploitable as finding the inverse of the function a i p.q is not easy in general.

Nonetheless, we can use the quasi-concavity property to propose an iterative algorithm to find optimal threshold for each transmitter. An efficient distributed manner to find the individual thresholds λ i , @i P t1, ..., Ku would be to perform best response dynamics with each transmitter updating its threshold which maximizes the expected sum-utility given the other thresholds (functions). To find the expected sum-utility for a given λ i , we evaluate equation ( 19) numerically through montecarlo simulations. It is important to note that this procedure is performed offline, and the functions found are one-shot decision functions which could be exploited straightaway online.

Algorithm 1 Proposed algorithm for finding thresholds λ i @i P t1, ..., Ku

inputs : λ p0q 1 , λ p0q 2 , . . . , λ p0q K , ρpGq,iter max output: λ ‹ 1 , λ ‹ 2 , . . . , λ ‹ K initialization: @i, λ i " λ p0q i ,
θ i ´0, 0; λ piterq ´i ¯" θ i ˜λpiterq i , γ ‹ σ 2 λ piterq i ; λ piterq ´i ¸. (26)
where

λ piterq ´i " pλ piterq 1 , ..., λ piterq i´1 , λ piter´1q i`1 , ...q (27) end end @i, λ ‹ i " λ piterq i
In the next section, we show that our approach brings considerable benefits in terms of sum energy efficiency when compared to state of the art solutions.

V. NUMERICAL ANALYSIS

For the simulation setup, we choose typical efficiency function and model parameters. The efficiency function is chosen to be [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF]:

f pγ i q " p1 ´e´0.5γi q M (28)
where we also choose the total number of bits per frame M " 80. For this chosen utility function, we can obtain γ ‹ " 12.4 by solving γf 1 pγq " f pγq. In all the simulations, we choose P max " 1 W and σ 2 " 1 mW which corresponds to a moderate Signal to Noise Ratio (SNR) of 30 dB.

We compare the proposed threshold policy to two important works for team power control problem:

' The solution in [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF]: Their algorithm is the closest to the proposed policy in terms of information structure assumed to choose the power level.

' Pricing NE from [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF]: Their algorithm requires is more demanding in terms of information as they assume transmitters receiving SINR feedback (possible to recover global CSI G [START_REF] Zhang | Interference coordination via power domain channel estimation[END_REF]), and that for multiple time slots. The proposed equilibrium can only be achieved by an online best-response dynamics (exploration phase) in addition to an offline optimization of the pricing parameter, while our policy has a closed form expression and can be implemented in one shot. Despite these differences, their algorithm is still distributed in terms of information and decision and is considered a reference in cooperative team power control. In Fig. 1, we consider two user case with different power control policies. From Fig. 1 we see that the proposed policy, unsurprisingly, outperforms [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF] by a big margin. Thresholding indeed helps reduce interference as when individual channels are bad, transmitters do not emit at all. In the case of [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF], at lower channel gains, transmitters emit at higher powers thus generating interference.

The Pricing NE performs well by reducing the interference through penalties on higher power emitted. As seen from our simulations, this can be an effective way of containing interference. As mentioned before, their solution however requires time to converge which creates a missed opportunity cost. If one considers the block fading model, i.e. the channel gains remaining constant for a block of T time-slots, if T is small, the average payoff over all time-slots for pricing solution would be considerably smaller than the results indicated in Fig. 1.

We illustrate the extent of this loss through Fig. 2 where we consider blocks of different sizes t P t1, ..., T u. We run the pricing NE algorithm and plot the average payoff for t slots where the channel remains constant. Taking this into account, we see that for blocks of small sizes our algorithm performs much better since it chooses the 'correct' power levels right from the beginning as opposed to pricing NE which takes time to converge.

To demonstrate the scalability of the threshold policy, in Fig. 3 we plot the average EE against the number of Transmitter-Receiver pairs. We see similar performance results and trends as in Fig. 1 for the same aforementioned reasons. It can be also seen that threshold policy has relatively higher gains than [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF] for large systems since the higher interference can be effectively mitigated by using threshold. However, fig. 3 shows that the gap between our policy and pricing NE becomes more significant when we have more transmitterreceiver pairs. Indeed, in that case information about the realization of others' channels become important for coordination. SINR feedback helps transmitters to share some information about the channel realizations. For threshold policy however, the individual channel realizations cannot be exchanged, and therefore its performance suffers slightly when compared to [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] . Exhaustive search knowing G Pricing-based power control policy [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] Proposed power control policy Cooperative power control policy of [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF] Fig. 1: Comparison of our proposed power control policy with state of the art policies in terms of the resulting sum energy efficiency. Note that the proposed policy outperforms [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF] significantly, and is in fact close to [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF], despite requiring no online procedure for converging to the equilibrium.

VI. CONCLUSION

The key takeaway point of our investigations is that thresholding is a powerful tool to naturally incorporate almost-optimal coordination with only individual CSI feedback required to operate. For such simple information structure, our proposed solution gives considerably higher payoff. The fact that it performs almost as well as Pricing NE which requires much more information and preferably stable channel gains is indeed surprising and promising. More analytical results regarding the Proposed power control policy Pricing-based power control policy [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] Fig. 2: In this figure, we compare the average energy efficiency as a function of the channel coherence time (in units of time-slots). As this time increases, the online best response algorithm in [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] is able to converge to the equilibrium resulting in a higher average efficiency. However, when the coherence window is small (as in many mobile applications), our proposed policy has a better performance as the power control is determined in one shot. Pricing-based power control policy [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] Proposed power control policy Cooperative power control policy of [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF] Fig. 3: While other one-shot algorithms like [START_REF] Goodman | Power control for wireless data[END_REF] or [START_REF] Zappone | Energyaware competitive power control in relay-assisted interference wireless networks[END_REF] scale poorly with the number of transmitting devices, the proposed algorithm scales well. The performance is similar to [START_REF] Saraydar | Efficient power control via pricing in wireless data networks[END_REF] which requires some time online before converging to its equilibrium.

optimality of threshold policies are needed to provide a firmer grounding for our conjecture.

A natural extension of our work would be to conjecture similar strategies for more general problems like power allocation and MIMO. If the results for Power Control are anything to go by, it is well worth investigating.

ACKNOWLEDGEMENT

This work was funded by the RTE Chair.


MD, PhD Francis Leclerc
email: fleclercchru@yahoo.fr

PhD Alain Duhamel
email: alain.duhamel@univ-lille2.fr

Valérie Deken

MD Bruno Grandbastien
email: bruno.grandbastien@chru-lille.fr

MD, Phd Stéphane Leteurtre
email: stephane.leteurtre@chru-lille.fr

D Biarent

S Dauger

Francis Pr

Leclerc

Alain Pr

Duhamel

Miss Valérie Deken

CAN THE PELOD-2 SCORE ON DAY 1 BE USED IN CLINICAL CRITERIA FOR SEPSIS IN CHILDREN?

Keywords: sepsis, septic shock, multiple organ dysfunction, PELOD-2 score, children

Abstract.

A recent task force has proposed the use of sequential organ failure assessment (SOFA) in clinical criteria for sepsis in adults. OBJECTIVE. To evaluate the predictive validity for PICU mortality of the PELOD-2 and of a « quick » PELOD-2 on day 1 (d1PELOD-2 and d1qPELOD-2) in children admitted with suspected infection. DESIGN, SETTINGS, PATIENTS. We analyzed the database used for the PELOD-2 development and validation. Only children with infection as the cause of primary disease at entry (defined by physician diagnosis) were enrolled. Children with hypotension-low systolic blood pressure (SBP) or low mean blood pressure (MBP) using age-adapted cutoffs-and lactatemia >2mmol/L were considered in shock.

MEASUREMENTS AND MAIN RESULTS. We developed the d1qPELOD-2 including tachycardia, hypotension and altered mentation (Glasgow<11): one point for each variable (range: 0-3). Outcome was mortality at PICU discharge.

Discrimination (AUROC-95%CI) and calibration (goodness of fit test) of the scores were studied.

This study included 862 children with suspected infection (median age: 12.3 months, mortality: n=60,7.0%). AUC of the d1PELOD-2 score was 0.91 (0.86-0.96) in children with suspected infection, 0.88 (0.79-0.96) in those with low SBP and hyperlactatemia, and 0.91 (0.85-0.97) in those with low MBP and hyperlactatemia; calibration p value was 0.03, 0.36 and 0.49, respectively. A d1PELOD-2 ≥8 reflected an overall risk of mortality ≥ 9.3% in children with suspected infection. AUC of the d1qPELOD-2 was 0.82 (0.76-0.87) with SBP or MBP, calibration p value was 0.89 and 0.72, respectively. A score ≥2 reflected a mortality risk ≥19.8% with SBP and ≥15.9% with MBP.

CONCLUSION. Among children admitted to PICU with suspected infection, d1PELOD-2 was highly predictive of PICU mortality suggesting its use to standardize definitions and diagnostic criteria of pediatric sepsis. Further studies are needed to determine the usefulness of the d1qPELOD-2 outside of the PICU.

Sepsis is a leading cause of death in adults (1) as well as in children [START_REF] Ruth | Pediatric severe sepsis: current trends and outcomes from the Pediatric Health Information Systems database[END_REF][START_REF] Giuliano | Comparison of Pediatric Severe Sepsis Managed in U.S. and European ICUs[END_REF].

The sepsis syndrome is characterized by non-specific physiologic abnormalities that encompass a heterogeneous population, and, thus, remains difficult to define.

Consensus criteria for pediatric sepsis that were proposed in 2005 to facilitate consistent enrollment across research studies (4) are widely adopted for use in clinical practice [START_REF] Brierley | Clinical practice parameters for hemodynamic support of pediatric and neonatal septic shock: 2007 update from the American College of Critical Care Medicine[END_REF]. However, published reports have demonstrated only moderate overlap of physician diagnosis of severe sepsis with consensus criteria, illustrating that many children diagnosed and treated for severe sepsis in clinical practice may have important physiologic and outcome differences from those studied in clinical trials (2 , 6 , 7 , 8). Recently, a task force recommended, for adult patients, elimination of the terms sepsis syndrome, septicemia and severe sepsis and instead defined sepsis as « life threatening organ dysfunction due to a dysregulated host response to infection » [START_REF] Shankar-Hari | Developing a New Definition and Assessing New Clinical Criteria for Septic Shock: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF]. Seymour and colleagues, analyzing 1.3 million electronic health record encounters identified adults with suspected infection and observed that the predictive validity for in-hospital mortality of Sequential Organ Failure Assessment (SOFA) among ICU encounters was statistically greater than SIRS, which supports its use as a diagnostic criteria of sepsis. A simplified « quick » SOFA (qSOFA), including Glasgow Coma Scale, systolic blood pressure and respiratory rate had a good predictive validity for hospital mortality of patients outside the intensive care unit (ICU) [START_REF] Seymour | Assessment of Clinical Criteria for Sepsis: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF].

The aim of this study was to evaluate the predictive validity for Pediatric ICU (PICU) mortality of the PEdiatric Logistic Organ Dysfunction-2 (PELOD-2) and of a « quick » PELOD-2 (qPELOD-2 including Glasgow Coma Scale, systolic or mean blood pressure and heart rate) both on day 1 in children admitted with suspected infection or septic shock in PICUs.

METHODS

We performed a secondary analysis of the database used for the development and validation of the PELOD-2 score [START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF] [START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF]. In brief, patients were monitored until they died or were discharged from PICU. As for previously published severity and multiple organ dysfunction syndrome scores, the most abnormal value of each variable observed during day 1 was considered to calculate the PELOD-2 score on day 1 (d1PELOD-2).

If a variable was not measured, we assumed that it was normal (i.e. the physician considered that the value of the variable was normal). Covariates and cutoffs were those of our previous publication [START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF].

For the current study, only children with infection as the cause of primary disease at entry (defined by physician diagnosis) were enrolled. Among them, those with hypotension -low systolic blood pressure (SBP) using age-adapted cutoffs of the PELOD [START_REF] Leteurtre | Validation of the paediatric logistic organ dysfunction (PELOD) score: prospective, observational, multicentre study[END_REF] or low mean blood pressure (MBP) using age-adapted cutoffs of the PELOD-2 (11) -and hyperlactatemia (serum lactate level >2 mmol/L) were considered as having septic shock [START_REF] Shankar-Hari | Developing a New Definition and Assessing New Clinical Criteria for Septic Shock: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF]. Two other lactate thresholds were considered (>3 and >4 mmol/L).

Also, similarly with what was proposed by the Third International Consensus Task

Force [START_REF] Seymour | Assessment of Clinical Criteria for Sepsis: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Singer | The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF] we developed the quick PELOD-2 on day 1 (d1qPELOD-2) including tachycardia (instead of tachypnea, not collected in the PELOD-2 database) that has a higher predictive value in children ( 14)), hypotension (low SBP or MBP) and altered mentation (Glasgow < 11) (see [START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF][START_REF] Leteurtre | Validation of the paediatric logistic organ dysfunction (PELOD) score: prospective, observational, multicentre study[END_REF] for cutoffs) with a point score of 1 assigned to each variable (range: 0-3) (Table 1). The PICU discharge status (death/survival) was used as the outcome dependent variable.

Statistical Analysis.

The results are expressed by median and interquartile ranges (IQR) for continuous variables and by frequencies and percentages for categorical variables. The comparisons of the d1PELOD-2 and d1qPELOD-2 scores between the two groups (dead/survivor) were performed by an unpaired Wilcoxon test. The discriminant power of the scores was estimated using the areas under receiver operating characteristic curve (AUC) with 95% confidence intervals (CI) and an optimal cutoff was defined using the maximization of the Youden index; calibration was assessed using the Hosmer-Lemeshow chi-square test with a degree of freedom of 8 (a p value > 0.05 indicates a good calibration). We addressed the optimism bias using a bootstrap resampling method. We used a logistic regression to investigate the relation between d1PELOD-2, d1qPELOD-2 and mortality. As no imputation of variables not measured (and considered as normal: see above) was performed we verified that mortality of children with variable not measured was very similar to that of children with normal values, and very dissimilar to that of children with abnormal values. Statistical analyses were performed using SAS software version 9.3 (SAS Institute, Cary, NC). A p value of less than 0.05 was considered statistically significant.

Results.

This study included 862 children with suspected infection among 3,669 patients from the original database (11) (two with incomplete data being excluded). Characteristics of the population are reported in Table 2. The mortality rate was 7.0% (60 deaths /862) close to the 6.0 % of the whole population (222 deaths /3671). The median d1PELOD-2 was 3 (IQR: 1-5) in children with suspected infection who survived and 13 [START_REF] Shankar-Hari | Developing a New Definition and Assessing New Clinical Criteria for Septic Shock: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Seymour | Assessment of Clinical Criteria for Sepsis: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF][START_REF] Leteurtre | Validation of the paediatric logistic organ dysfunction (PELOD) score: prospective, observational, multicentre study[END_REF][START_REF] Singer | The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Scott | The prevalence and diagnostic utility of systemic inflammatory response syndrome vital signs in a pediatric emergency department[END_REF][START_REF] Schlapbach | Mortality related to invasive infections, sepsis, and septic shock in critically ill children in Australia and New Zealand, 2002-13: a multicentre retrospective cohort study[END_REF][START_REF] Leclerc | Cumulative influence of organ dysfunctions and septic state on mortality of critically ill children[END_REF][START_REF] Dellinger | Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock, 2012[END_REF][START_REF] Chapman | Systematic review of paediatric track and trigger systems for hospitalised children[END_REF] in those who died (p=0.0001). A d1PELOD-2 ≥ 8 reflected an overall risk of mortality of 9.3% or more in children with suspected infection. In children having a low SBP with hyperlactatemia (n=69) the d1PELOD-2 was 7.5 [START_REF] Brierley | Clinical practice parameters for hemodynamic support of pediatric and neonatal septic shock: 2007 update from the American College of Critical Care Medicine[END_REF][START_REF] Weiss | Defining pediatric sepsis by different criteria: discrepancies in populations and implications for clinical practice[END_REF][START_REF] Balamuth | Pediatric severe sepsis in U.S. children's hospitals[END_REF][START_REF] Weiss | Discordant identification of pediatric severe sepsis by research and clinical definitions in the SPROUT international point prevalence study[END_REF][START_REF] Shankar-Hari | Developing a New Definition and Assessing New Clinical Criteria for Septic Shock: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Seymour | Assessment of Clinical Criteria for Sepsis: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF] in those who survived (66.7%) and 17 [START_REF] Singer | The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Scott | The prevalence and diagnostic utility of systemic inflammatory response syndrome vital signs in a pediatric emergency department[END_REF][START_REF] Schlapbach | Mortality related to invasive infections, sepsis, and septic shock in critically ill children in Australia and New Zealand, 2002-13: a multicentre retrospective cohort study[END_REF][START_REF] Leclerc | Cumulative influence of organ dysfunctions and septic state on mortality of critically ill children[END_REF][START_REF] Dellinger | Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock, 2012[END_REF][START_REF] Chapman | Systematic review of paediatric track and trigger systems for hospitalised children[END_REF][START_REF] Goncalves | Performance of PRISM III and PELOD-2 scores in a pediatric intensive care unit[END_REF][START_REF] Morin | Refractory septic shock in children: a European Society of Paediatric and Neonatal Intensive Care definition[END_REF] in those who died (33.3%) (p<0.0001). In those having a low MBP with hyperlactatemia (n=88) the d1PELOD-2 was 7 (5-10) in children who survived (69.43%) and 16 [START_REF] Singer | The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Scott | The prevalence and diagnostic utility of systemic inflammatory response syndrome vital signs in a pediatric emergency department[END_REF][START_REF] Schlapbach | Mortality related to invasive infections, sepsis, and septic shock in critically ill children in Australia and New Zealand, 2002-13: a multicentre retrospective cohort study[END_REF][START_REF] Leclerc | Cumulative influence of organ dysfunctions and septic state on mortality of critically ill children[END_REF][START_REF] Dellinger | Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock, 2012[END_REF][START_REF] Chapman | Systematic review of paediatric track and trigger systems for hospitalised children[END_REF][START_REF] Goncalves | Performance of PRISM III and PELOD-2 scores in a pediatric intensive care unit[END_REF][START_REF] Morin | Refractory septic shock in children: a European Society of Paediatric and Neonatal Intensive Care definition[END_REF] in those who died (30.7%) (p=0.0001). The odds ratio of death per unit of the d1PELOD-2 was 1.50 (95%CI :1.39 -1.63) in our population as a whole (table 3).

The AUC of the d1PELOD-2 score was 0.91 (95%CI, 0.86-0.96) in children with suspected infection, 0.88 (95%CI, 0.79-0.96) in those with low SBP and hyperlactatemia, and 0.91 (95%CI, 0.85-0.97) in those with low MBP and hyperlactatemia; after correction for the optimism bias, the AUC (and 95%CI) were strictly identical. The calibration p values were equal to 0.03, 0.36 and 0.49, respectively. Discrimination and calibration were not influenced by the lactate threshold considered (2, 3, or 4 mmol/L). When we considered three categories of age (< 1 year, 1 to 12 years and > 12 years) the AUC of the d1PELOD-2 was 0.93 (95%CI, 0.87-0.98) for children less than one year of age and 0.88 (95%CI, 0.76-0.99) in those between 1 to 12 years; the AUC could not be determined for children of more than 12 years of age because of the small sample size. Among nonsurvivors, 85.0% (sensitivity, Se) had 8 or more d1PELOD-2 points and 88.4% (specificity, Sp) of survivors had less than 8 d1PELOD-2 points; among patients with a score of 8 or more, 35.4% died (positive predictive value, Ppv), while 98.8% of those having a score less than 8 survived (negative predictive value, Npv). Among patients with low SBP and lactatemia > 2 mmol/L, 91.3% (Se) who died had 11 or more d1PELOD-2 points and 69.6% (Sp) of those who survived had less than 11 d1PELOD-2 points (Ppv: 60.0%; Npv: 94.1%). Among patients with low MBP and lactatemia > 2 mmol/L who died, 92.6% (Se) had 11 or more d1PELOD-2 points and 75.4% (Sp) of those who survived had less than 11 d1PELOD-2 points (Ppv: 62.5%; Npv: 95.8%). Mortality of children with variables not measured was very dissimilar to those with abnormal values (all p values were < 0.001, except for MAP but this is due to the small number of patients (n=21) with variable not measured); for each variable included in the PELOD-2 score, when comparing mortality of children with variables not measured and that of children with normal values for this variable, after adjustment for the d1PELOD-2 (computed without the variable), we did not found any significant differences in mortality between the two groups, except for pupillary reaction and ventilation but there were less than 5% of these variables not measured.

The median d1qPELOD-2 were the followings: 2 (IQR: 1-2 with SBP and 1.5-3 with MBP) in children who died and 1 (IQR: 0-1) in those who survived (p<0.0001). Odds ratio of death per unit of the d1qPELOD-2 range from 4.93 (95%CI: 3.45 -7.04) in patients with SBP to 5.43 (95%CI: 3.68 -7.99) in patients with MBP. The d1qPELOD-2 was also a significant prognostic factor (table 3). The AUC of the d1qPELOD-2 was 0.82 (95%CI: 0.76-0.87) either with SBP or MBP; after correction for the optimism bias, the AUC (and 95%CI) were strictly identical. The calibration p values were equal to 0.89 and 0.72 with SBP and MBP respectively. The d1qPELOD-2 with SBP was 0.81 (95%CI, 0.75-0.87) in children less than one year of age and 0.81 (95%CI, 0.71-0.92) in those between 1 to 12 years. The d1qPELOD-2 with MBP was 0.80 (95%CI, 0.74-0.87) in children less than one year of age and 0.82 (95%CI, 0.72-0.93) in those between 1 to 12 years. For these two scores, the AUC could not be determined for children of more than 12 years of age because of the small sample size. Mortality according to d1qPELOD-2 is given in table 4. In brief, a d1qPELOD-2 score ≥ 2 was associated with a mortality rate of 19.8% or more with d1qPELOD-2 SBP and 15.9% or more with d1qPELOD-2 MBP. Among deceased, 66.7% (Se) had 2 or more d1qPELOD-2 SBP points and 85.3% (Sp) of survivors had less than 2 d1qPELOD-2 SBP points (Ppv: 25.3%; Npv: 97.2%). Among deceased 75.0% (Se) had 2 or more d1qPELOD-2 MBP points and 79.1% (Sp) of survivors had less than 2 d1qPELOD-2 MBP points (Ppv: 21.1%; Npv: 97.7%).

Discussion.

In our patients with suspected infection and in those with associated shock the predictive validity for PICU mortality of d1PELOD-2 was excellent. Moreover, in comparison with what was reported by Seymour et al. in critically ill adults for the qSOFA (AUC=0.66; 95%CI: 0.64-0.68), the d1qPELOD-2 had a good predictive validity for PICU mortality (AUC=0.82; 95%CI: 0.76-0.87) [START_REF] Seymour | Assessment of Clinical Criteria for Sepsis: For the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF].

Our patients had a median d1PELOD-2 of 3 (IQR: 2-6), suggesting a moderate severity, while those with shock had a median d1PELOD-2 between 9.5 (IQR: 5-13) (patients with low MBP and hyperlactatemia) and 11 (IQR: 6-15) (patients with low SBP and hyperlactatemie (table 3). The mean PIM2 probability of death of the whole population was 6. 6) who reported that sepsis cases diagnosed by physicians are less severely ill [START_REF] Weiss | Discordant identification of pediatric severe sepsis by research and clinical definitions in the SPROUT international point prevalence study[END_REF]. Several studies have reported a moderate level of agreement in the septic children diagnosed by physicians (clinical criteria), 2005 international consensus guidelines (research criteria) and international classification of diseases (administrative criteria): approximately one third of patients with sepsis diagnosed on clinical criteria would not have been included in studies on sepsis diagnosed on research criteria [START_REF] Weiss | Defining pediatric sepsis by different criteria: discrepancies in populations and implications for clinical practice[END_REF][START_REF] Weiss | Discordant identification of pediatric severe sepsis by research and clinical definitions in the SPROUT international point prevalence study[END_REF].

In 2014, the European Society of Intensive Care Medicine and the Society of Critical care Medicine convened a task force who recommended for adults that: (1) sepsis should be defined as life-threatening organ dysfunction caused by a dysregulated host response to infection; (2) for clinical operationalization, organ dysfunction can be represented by an increase in the SOFA score of 2 points or more. The task force also proposed for out-of-hospital adult patients the qSOFA as a new bedside clinical score to rapidly identify the risk of poor outcomes typical of sepsis [START_REF] Singer | The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF]. In children, the PELOD score, proposed in 2003 [START_REF] Leteurtre | Validation of the paediatric logistic organ dysfunction (PELOD) score: prospective, observational, multicentre study[END_REF], has been updated in 2013 (PELOD-2) [START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF]. Using its first version, we demonstrated that hazard ratio of death significantly increased with the severity of organ dysfunction, as estimated by the PELOD score, and the worst diagnostic category of septic state [START_REF] Leclerc | Cumulative influence of organ dysfunctions and septic state on mortality of critically ill children[END_REF].

A recent study compared children managed with severe sepsis in European and the United States PICUs to identify geographic variation, which may improve the design of future international studies (3). As there were no significant differences in morbidity and mortality between regions after adjusting for several factors the authors suggested that future international clinical trials should use physiologic and laboratory criteria for severe sepsis to establish study eligibility without the requirement for PICU admission [START_REF] Giuliano | Comparison of Pediatric Severe Sepsis Managed in U.S. and European ICUs[END_REF]. In this approach, the PELOD-2 could represent the precise physiologic and laboratory criteria used to identify pediatric sepsis.

Similarly to what was observed in adult patients with suspected infection, i.e. a SOFA ≥2 reflects a mortality risk greater than 10% and can represent organ dysfunction (13), a d1PELOD-2 ≥8 reflected a mortality risk of approximately 10% or more in our children with suspected infection. This cutoff could, thus, be used to identify organ dysfunction in our PICU patients with suspected infection.

In this study we defined hypotension as low SBP or low MBP either for identifying children with suspected infection and shock and for constructing the qPELOD-2 score. In fact, if MBP is used for initial resuscitation as recommended by the Surviving Sepsis Campaign [START_REF] Brierley | Clinical practice parameters for hemodynamic support of pediatric and neonatal septic shock: 2007 update from the American College of Critical Care Medicine[END_REF][START_REF] Singer | The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3)[END_REF][START_REF] Dellinger | Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock, 2012[END_REF], SBP is used in the pediatric track and trigger systems as reviewed by Chapman et al. [START_REF] Chapman | Systematic review of paediatric track and trigger systems for hospitalised children[END_REF].

Our study has some limitations. First, our database is almost 10 years old, and mortality should have improved due to changes in treatments; however, studies conducted on more recent database reported that the PELOD-2 score remains reflective of outcome [START_REF] Goncalves | Performance of PRISM III and PELOD-2 scores in a pediatric intensive care unit[END_REF][START_REF] Morin | Refractory septic shock in children: a European Society of Paediatric and Neonatal Intensive Care definition[END_REF]. Second, as mentioned above, we did not screen our data base with sepsis defined on the basis of 2005 International Sepsis Consensus Conference (4); however, the sensitivity of SIRS criteria has been criticized because they miss patients with infection and organ failure [START_REF] Weiss | Defining pediatric sepsis by different criteria: discrepancies in populations and implications for clinical practice[END_REF][START_REF] Weiss | Discordant identification of pediatric severe sepsis by research and clinical definitions in the SPROUT international point prevalence study[END_REF][START_REF] Kaukonen | Systemic inflammatory response syndrome criteria in defining severe sepsis[END_REF]. Third, our dataset included a small number of children over the age of 12 years (9.7%). Fourth, we did not use volume resuscitation in our definition of shock because this data was not available. Fifth, we only included children admitted in PICU and thus, we did not consider children from different phases of acute care (out of hospital, emergency department, hospital ward). Finally, we did not analyze different types of infection (community and nosocomial). These limitations reduce the generalizability of our findings and emphasize the need for future prospective multicenter studies.

Conclusion.

Among children admitted to PICU with suspected infection, PELOD-2 of the first 24hour period after admission was highly predictive of PICU mortality suggesting its use in clinical criteria for sepsis. This could help to standardize definitions and diagnostic criteria of pediatric sepsis. Further studies in other cohorts from different countries and including more patients, are needed to confirm these results. Prospective studies will have also to determine the usefulness of the d1qPELOD-2 in children with suspected infection outside of the PICU or at admission. S Leteurtre, A Duhamel and V Deken have full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.

  2 %, close to that reported by Schlapbach et al. (between 4.1 and 5.4% in children with invasive infection) (15). This moderate severity is probably explained by the definition we used (physician diagnosis) like in the study by Weiss et al. (

study design was approved by the ethics committee of the Société de Réanimation de Langue Française on April 27, 2007. The requirement for consent was

  waived because the study was strictly observational.

	, which included all consecutive children
	admitted between June 21, 2006, and October 31, 2007, into nine university-affiliated
	PICUs (eight in France and one in Belgium) that are members of the Groupe
	Francophone de Réanimation et Urgences Pédiatriques (GFRUP). Exclusion criteria
	were: age 18 years or older; premature at entry into PICU; pregnancy; total length of
	stay in PICU less than 4 h; admission in a state of continuous cardiopulmonary
	resuscitation without achieving stable vital signs for at least 2 h; transfer from another
	PICU; and admissions for scheduled procedures normally performed in other hospital
	locations.
	Ethical Considerations.
	The study and its database were declared safe and were approved by the French
	authorities (Commission Nationale de l'Informatique et des Libertés) on February 7,
	2007. The Data management.
	Data management, recording and quality control processes are detailed in the article
	by Leteurtre et al

Table 1 . Quick PELOD-2 (qPELOD-2) criteria

 1

	Criteria	Altered mentation	Hypotension		Tachycardia
		Glasgow coma score < 11	SBP 1 (mm Hg) or MBP 2 (mm Hg)
		<1 month	< 65	< 46	< 12 years >195
		1-11 months	< 75	< 55	≥ 12 years > 150
		12-23 months	< 85	< 60
		24-59 months	< 85	< 62
		60-143 months	< 85	< 65
		≥144 months	< 95	< 67
	Score	Absent: 0/ Present: 1	Absent: 0/ Present: 1	Absent: 0/ Present: 1
	Abbreviations: PELOD: PEdiatric Logistic Organ Dysfunction; SBP, systolic blood pressure; MBP, mean blood
	pressure.

1

Adapted from Leteurtre et al. (12); 2 Adapted from Leteurtre et al.

[START_REF] Leteurtre | PELOD-2: an update of the PEdiatric logistic organ dysfunction score[END_REF]

.

Table 2 .

 2 Population characteristics.

	Patients with suspected infection (primary disease at entry)	N=862
	Baseline characteristics
	Gender (male), n (%)	468 (54.3)
	Age, months, median [IQR]	12.3 [2.1; 55.7]
	0 to < 1, n (%)	105 (12.2)
	1 to 11, n (%)	320 (37.1)
	12 to 23, n (%)	93 (10.8)
	24 to 59, n (%)	137 (15.9)
	60 to 143, n (%)	123 (14.3)
	≥ 144, n (%)	84 (9.7)
	PIM2 score (predicted death rate in %) median, [IQR], mean	1.2 [0.7; 3.9],
	Primary reason for PICU admission n (%)
	Respiratory	487 (56.5)
	Neurological	118 (13.7)
	Cardiovascular	152 (17.6)
	Hepatic	0
	Genitourinary	16 (1.9)
	Gastrointestinal	42 (4.9)
	Endocrine	0
	Musculoskeletal	2 (0.2)
	Hematological	8 (0.9)
	Miscellaneous/undetermined	26 (3.0)
	Mixed	11 (1.3)
	Outcomes
	Mechanical ventilation, n (%)	338 (39.2)
	Length of ICU stay, days; median, (IQR)	4 [2 ; 7]
	Mortality, n (%)	60 (7.0)
	Abbreviations: IQR, interquartile range; PIM, paediatric index of mortality; PICU,
	Pediatric Intensive Care Unit.

Table 3 . Description and odds ratios of death of PELOD-2 and qPELOD-2 scores on day 1 among children with suspected infection

 3

		n ()	Median IQR	Odds	95% CI
	Score				Ratio
	PELOD-2	862 (60)	3	2-6	1.50	1.39 -1.63
	PELOD-2 in those with low SBP	69 (23)	11	6-15	1.39	1.19 -1.62
	and hyperlactatemia (> 2 mmol/L)
	PELOD-2 in those with low MBP	88 (27)	9.5	5-13	1.49	1.26 -1.77
	and hyperlactatemia (>2 mmol/L°
	qPELOD-2 (SBP)	862 (60)	1	0-1	4.93	3.45 -7.04
	qPELOD-2 (MBP)	862 (60)	1	0-1	5.43	3.68 -7.99

Abbreviations: qPELOD-2, quick PEdiatric Logistic Organ Dysfunction 2; IQR, interquartile range; SBP, systolic blood pressure; MBP, mean blood pressure; , death.

Table 4 . Mortality rate according to qPELOD-2 on day 1.

 4 Abbreviations: qPELOD-2, quick PEdiatric Logistic Organ Dysfunction 2; SBP, systolic blood pressure; MBP, mean blood pressure.

	q PELOD-2 SBP (score)	Patients (n)	Death (%)
	0	330	0.9
	1	374	4.5
	2	131	19.8
	3	27	51.8
	q PELOD-2 MBP (score)	Patients (n)	Death (%)
	0	249	0.8
	1	400	3.25
	2	182	15.9
	3	31	51.6

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