Kwangpil Chang

Sungteak Kim

Daejun Chang

Junkeon Ahn

Enrico Zio

Kwangpilchang

Uncertainty Analysis for Target SIL Determination in the Offshore Industry

Keywords: SIL Determination, Uncertainty Analysis, Offshore Industry, Risk Graph Method, Minimum SIL Table from OLF70, LOPA, Fuzzy Set, Monte Carlo Simulation

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INTRODUCTION

The importance of safety systems has been increasing in the oil and gas industry [START_REF] Lundteigen | Safety instrumented systems in the oil and gas industry: concepts and methods for safety and reliability assessments in design and operation[END_REF]. In general, safety systems, different and independent from each other, are considered for providing multiple protection layers. The typical multiple protection layers installed in oil and gas facilities are:

-BPCS (Basic Process Control System) -SIS (Safety Instrumented System) -Physical Mitigation System BPCS is a system which handles process control and monitoring for oil and gas facilities. Among the various multiple protection layers, SIS is the most important and critical protection layer to prevent or reduce the risk of abnormal process conditions, which may be hazardous. SIS isinstalledfor reducing risks to allowable levels by detecting hazardous events and taking actions to prevent them from developing into further accidents. SIS is a safety system that includes an electrical, electronic or programmable electronic component to keep "people", "environment", "assets" in safe conditions during oil and gas facility operation periods. Elements of SIS consist of initiators, a logic solver, and final elements, as illustrated in Figure 1.A variety of SISs are installed in the oil and gas plants, for example, fire & gas systems, emergency shutdown systems and process shutdown systems. SIS is the next layer of protection following BPCS and alarm / operator intervention. According to IEC 61508/61511 [START_REF]Functional safety of electrical/electronic/programmable electronic safety-related systems[END_REF][START_REF]Functional safety-safety instrumented systems for the process industry[END_REF], the overall required safety management and technical activities are related to the safety life cycle. The safety life cycle consists of a number of steps which can be grouped into three phases, "analysis", "realization" and "operation" in Figure 2. The purpose of the analysis phase is to identify hazards and specify safety requirements of SIS. Safety requirements specification (SRS) of SIS should contain critical information, which include functional description of each Safety Instrumented Function (SIF), target SIL, mitigated hazards, process parameters, maintenance requirements, response time, etc.The next phase of the safety life cycle is the realization of SIS based on SRS results. All performance targets and functional requirements defined in the SRS are key information for the design, installation and operation of SIS.The defined target SIL would affect the whole SIS lifecycles, including design and operation, since these target values draw the upper limit of the reliability performance. From this point of view, target SIL should be derived carefully in order to not only satisfy the required risk reduction but also to get rid of unnecessary additional SISs upon existing safety systems, which are already in place. As shown in Figure 3, the determination of the target SIL is an important task of the analysis phase of the safety lifecycle. According to IEC 61511, when determining SIL requirement for each identified SIF, one of thefollowing methods can be used [START_REF]Functional safety of electrical/electronic/programmable electronic safety-related systems[END_REF][START_REF]Functional safety-safety instrumented systems for the process industry[END_REF]:

-Risk Graph -LOPA (Layer of Protection Analysis) -Risk Matrix

The criteria for selecting the method is as follows: complexity of the application,guideline of regulatory authorities,nature of the risk and required risk reduction,expertise and experience of the personnel,availability of information on the risk-related parameters and whether the required risk reduction is given explicitly in a numerical form or in a qualitative form. OLF 70 provides"Minimum SIL requirements" based on the existing performance level [START_REF]Application of IEC 61508 and IEC 61511 in the Norwegian petroleum industry[END_REF]. OLF 70 hastheadvantage to give standardization for the determination of the SIL of a safety function compared with methods suggested in IEC 61511. The above mentioned methods have both advantages and disadvantages with respect to rigor and effort, fit with SIL lifecycle, inputs required, etc. Basically, the above methods are required to show consistency in target SIL determination.For example, if a SIF is identified from a SIL determination workshop, the target SIL for this SIF should be the same regardless of the persons who perform the SIL determination and the used methods. As mentioned before, in practice, the more conservative SIL is often assigned as target SIL to resolve the problem of inconsistency in the results of the analysis by offered methods. This approach of conservatism would help a system have sufficient safeguards and keep it safe. However, excessive conservative safety system design may result in increasing cost in terms of CAPEX as well as OPEX, e.g. due to more frequent maintenance.

Assessment of target SIL always involves uncertainties due to the nature of the analysis process: qualitative decision-making based on some statistical data and expert opinion. Assessing and managing these uncertainties should be done carefully to lead the system to be optimized in the sense of setting the appropriate level of system reliability target. Uncertainty analysis for target SIL determination would be the starting point of effective SIL lifecycle management, by checking the uncertainty level in the target SIL and identifying dominant factors which contribute to output uncertainties.

For FPSOs (Floating Production Storage Offloading) which is typical offshore facilities, more than 300 ~ 400 SIFs (Safety Instrumented Function) which are operated by SISs are usually identified during the early design phase. It is mandatory that a SIL sufficientto ensure safety against unwanted accident events be assigned for all identified SIFs by SIL determination methods. The SIL assignment for all identified SIFs of a FPSO demands long times(on average, it takes one or two weeks to full SIL determination for a FPSO) and significant efforts.

It is important to improve theconfidence level of SIL determination by minimizing uncertainties. In this research, the main motivation of the paper is to propose consistent and traceable SIL determination procedures which can prevent unreasonable trade-offs between safety of facilities and costs due to overestimation or underestimation of the required SISs" performances.

The risk graph is most frequently used for SIL determination in the offshore industry, because it is of easy implementation. The risk graph useslinguistic terms such as "minor or critical", "rare or frequent" and "possible or not likely" for each input parameter"s relative importance determination. The use of linguisticterms can help understanding the determination procedures. However, the understanding of linguistic terms for each input parameter can differ among participants to the SIL determination activities, which can lead to subjective results.

There have been many efforts to enhance the shortcomings of the risk graph method. The Fuzzy Set approach, which is a non-probabilistic method,isconsidered to bean appropriate approach to represent,quantify and analyze the uncertainties of SIL determination [START_REF] Nati-Said | Fuzzy risk graph model for determining safety integrity level[END_REF][START_REF] Ouache | Safety instrumented systems between reliability and fuzzy[END_REF][START_REF] Abul-Haggag | Application of fuzzy logic for the determination of safety integrity in light of IEC 61508 & 61511 standards[END_REF]. Monte Carlo simulation is most commonly used for probabilistic uncertainty analysis inreliability and risk assessments. However, its application is still limitedin SIL determination and uncertainty analysis, because of lack of sufficient information available for specific probability distribution assignments.

Thehybrid method, a combination of Monte Carlo simulation and fuzzy set approach,has beenconsideredan effective approach for risk assessments and estimation of SIS performance [START_REF] Innal | Monte Carlo analysis and fuzzy sets for uncertainty propagation in SIS performance assessment[END_REF][START_REF] Arunraj | Modeling uncertainty in risk assessment: An integrated approach with fuzzy set theory and Monte Carlo simulation[END_REF].

In addition to the risk graph method, minimum SIL The paper is organized as follows: an introduction to the methods for target SIL determination, which are popular in the offshore industry is given in Section 2,identification of uncertainty factorsand proposed procedures for uncertainty analysis in SIL determination phase are illustrated in Section 3, case studies performed to show the effects of uncertainty are presentedin Section 4, and conclusions with suggestions for future works are offered in Section 5.

TARGET SIL DETERMINATIONBY USING CONVENTIONAL METHODS

In this section, a short description of some of the most common (conventional) methods used for target SIL determination is given.

2.1Risk Graph

Risk graph isone of the frequently-used methods whendetermining target SIL [START_REF] Kim | Risk-based design for implementation of SIS functional safety in the offshore industry[END_REF]. The risk graph considers likelihood, consequence, occupancy and probability of personnel avoiding hazardswhile hazard matrices consider only likelihood and consequence of an event. These four parameters used in risk graph are combined to indicate the level of unmitigated risks.

Risk graph is suitable for SIS with defined equipment under control (EUC), which is classified as local safety function. On the other hand, global safety functions cannot be easily estimated through the risk graph whena whole platform is the equipment under control (EUC), e.g. Emergency Shut-down (ESD) and Fire and Gas(F&G)safety functions.

2.2LOPA

LOPA(Layer of protection analysis) is a simplified risk assessment to determine if there are sufficient independent protection layers (IPLs) against anaccident scenario [START_REF] Ccps | Layer of protection analysis: simplified process risk assessment[END_REF]. Many types of protection layers can beconsidered against an unwanted accident.The thickness of the arrows represented in Figure 4 indicates the frequency of thespecified consequence for the initiating event. The results of LOPA can be used for thedecision-making. The first step of LOPA is to screen and identify the accident scenarios, based on theconsequence analysis. The consequence is typically identified by a qualitative riskassessment such as a HAZOP study.LOPA is applied to one scenario at a time. A scenario starts from an unwanted and unplanned eventresulting in an undesirable consequence. Each scenario has at least two elements: "aninitiating event" and "a consequence". The initiating event must lead to the consequence.

The next step is to identify the initiating event and determine the frequency ofthe event. Initiating events are classified into three types: "external events", "equipmentfailures", and "human failures". All possible causes from the accident scenario should bereviewed and verified as valid initiating events for the consequence. Examples ofinappropriate initiating events are inadequate operator training/certification, inadequate test and inspection, or unavailability of protection devices.

The enabling events or conditions should be differentiated from the initiating event duringthis step. These consist of operations or conditions that do not directly cause scenarios, butwhich must be present or active in order for the scenarios to proceed.

An IPL is a device, system or action that is capable of preventing a scenario fromproceeding to its undesired consequence. The effectiveness of an IPL is quantified in terms ofits probability of failure on demand. The typical IPLs considered in the process design phase are basic process control systems (BPCSs), critical alarms and human intervention, SIFs, physical protection, and emergency response systems.

Risk is estimated on the basis of the initiating event frequency, probability of failure on demand (PFD) value ofIPL and the consequence value. The frequency for the risk estimation is calculated as follow: : Frequency for consequence C for initiating event : Initiating event frequency for initiating event : Probability of failure on demand on the th IPL

J C I I i i ij i i i ij j C i I i ij f f PFD f PFD PFD PFD fi fi PFD j         (1)
The final step of LOPA is to compare the risk calculated in the previous step to a tolerablerisk criteria or related targets.

2.3Minimum SIL Table from OLF 070

It isdifficult to select the proper methodologywhen applying IEC 61508/61511 standards for determining target SIL. This is due to a variety of methods existing in the standards without detailed description or guideline of which method to be used for which case [START_REF]Application of IEC 61508 and IEC 61511 in the Norwegian petroleum industry[END_REF]. In addition, experience has shown that the risk-based approach such asrisk graph and/or hazard matrix cannot result in consistent target SIL.

In this point of view, OLF 070 [START_REF]Application of IEC 61508 and IEC 61511 in the Norwegian petroleum industry[END_REF]provides minimum SIL tables for target SIL determination. Minimum SIL tablesdeal with the most frequently used safety functions in the oil and gas production plants for both onshore and offshore. The tables illustrate safety function descriptions, functional boundaries and minimum requirements of target SIL. The purpose of minimum SIL requirements is tocheck the minimum safety level of frequently used safety functions,encourage the standardization among the industries, and simplify calculation and documentation.

Minimum SIL requirements are derived based on the typical loop assumption, which only include main items of SISsensors, logic solvers, valves and circuit breakersfor SIL calculation and exclude some details e.g. barriers, relays, cables and signal adapters.The minimum SIL values are estimated by using the industrially verified component reliability data [START_REF]Application of IEC 61508 and IEC 61511 in the Norwegian petroleum industry[END_REF]. The minimum SIL values can be used as input data to the QRA (Quantitative Risk Assessment). If the overall risk levels, which come from QRA results, are too high, it is possibleto define more stringent requirements because the minimum SIL values are literally the minimum requirements. Thus, during SIL verification phase, genuinely purchased and installed items should be checked in terms of compliance with target SIL.

However, plant specific conditions and technological improvements cause deviations from the minimum SIL requirements. In this case, IEC 61508/61511 could be a solution in terms of SIL determination methodology and documentation.

UNCERTAINTY ANALYSIS IN DETERMINING TARGET SIL

Some critical considerations on the representation and description of uncertainties in risk assessments can be found in E. Zio and T. Aven [START_REF] Zio | The Monte Carlo simulation method for system reliability and risk analysis[END_REF][START_REF] Zio | Industrial disasters: extreme events, extremely rare. Some reflections on the treatment of uncertainties in the assessment of the associated risks[END_REF][START_REF] Aven | Model output uncertainty in risk assessment[END_REF]. According to these studies, a number of alternative approaches exist, which are classifiedas "probabilistic methods" and "non-probabilistic methods" [START_REF] Zio | The Monte Carlo simulation method for system reliability and risk analysis[END_REF][START_REF] Zio | Industrial disasters: extreme events, extremely rare. Some reflections on the treatment of uncertainties in the assessment of the associated risks[END_REF], e.g. probabilistic analysis, probability bound analysis, imprecise probability, random sets and possibility theory.

Uncertainty Sources

Uncertainty analysis is performed toestimate the uncertainty in the output of the analysis of a system. In reality, the system under consideration cannot be easily describedperfectly since knowledge of the underlying phenomena is not complete [START_REF] Aven | Some considerations on the treatment of uncertainties in risk assessment for practical decision making[END_REF]. This leads to uncertainties in both parameters and models [START_REF] Aven | Some considerations on the treatment of uncertainties in risk assessment for practical decision making[END_REF].

Uncertainty can beclassifiedinto two different types-randomness due to natural variability of systemand imprecision due to lack of knowledge on the system. The former iscalled as aleatory, whereas the latter iscalled as epistemic, as shown in Figure 5 [START_REF] Aven | Model output uncertainty in risk assessment[END_REF][START_REF] Aven | Some considerations on the treatment of uncertainties in risk assessment for practical decision making[END_REF].

The epistemic uncertainty can be reducedif new knowledge is available, whilethe aleatory uncertainty cannot be reduced due to its inherent nature [START_REF] Abrahamsson | Uncertainty in quantitative risk analysis -characterization and methods of treatment[END_REF]. Several typesof uncertainty,which were classified as aleatory in the past,are now considered as epistemic.This indicatesthat the uncertainty classification could vary when understanding of naturalphenomena increases. In spite of limitations, the classification of uncertainty givesa fundamental concept [START_REF] Jin | Uncertainty assessment of reliability estimates for safety instrumented systems[END_REF].

Figure 5.Uncertainty Classification

Parameter uncertainty has been studiedin the literature [START_REF] Lundteigen | Safety instrumented systems in the oil and gas industry: concepts and methods for safety and reliability assessments in design and operation[END_REF]andis often expressed in terms ofdistributions of the parameter values [START_REF] Jin | Uncertainty assessment of reliability estimates for safety instrumented systems[END_REF]. The causes of parameteruncertainty can be aleatory and/or epistemic [START_REF] Abrahamsson | Uncertainty in quantitative risk analysis -characterization and methods of treatment[END_REF]. For aleatory parameter uncertainty, natural variabilityin the values of the parameters can be described byuncertainty distributions, typically probability distributions. For epistemic parameter uncertainty,the analyst"s knowledge about the parameters"valuesis described by probabilistic and non-probabilistic distributions [START_REF] Jin | Uncertainty assessment of reliability estimates for safety instrumented systems[END_REF].

Model uncertainty existssinceamodel is a simplification of the reality based on assumptions [START_REF] Janbu | Treatment of uncertainties in reliability assessment of safety instrumented systems[END_REF]. In practice, it becomes also relatedto the fact that several differentmodels may be used to analyze the same system [START_REF] Jin | Uncertainty assessment of reliability estimates for safety instrumented systems[END_REF].

Completeness uncertainty has the same causes ofmodel uncertainty-assumptions and simplifications [START_REF] Jin | Uncertainty assessment of reliability estimates for safety instrumented systems[END_REF]. Completeness uncertainty can be distinguished between known and unknown one. The known completeness uncertainty exists due to the factors that are known, but not included for some reasons. The unknown completeness uncertainty, otherwise, exists due to the factors that are not known or not identified as of now. From these concepts, the known completeness uncertainty can be expressed by the impact from the excluded factors. On the other hand, the unknown completeness uncertainty can be measured by the extent of maturity of technology and intelligibility of the environment surrounding the system [START_REF] Jin | Uncertainty assessment of reliability estimates for safety instrumented systems[END_REF].

3.2Uncertainty Classification of SIL Determination Methods

According to the definitions of uncertainty, various target SIL determination methods can be classified as possibly affected by aleatory/epistemic, parameter/model/known completeness/unknown completeness uncertainty, based on the characteristics of each method. The result of the classification is shown in Table 1.

The choice of SIL determinationmethods is dependent on the available information, reliability data, required resources, etc. For example, if it is possible to get sufficient information for a reasonable target SIL with full required resources such as time and experiencedexperts, a fully risk-based approach, risk graph,is preferred to other methods.

As described in the previous section, hazard matrixes are most simple models for SIL determination. Risk graphs are an extension of hazardmatrixes. As shown in Figure 6, the concept of SIL determination by using the risk graph method is based on estimation of frequencies of hazardous events, consequences of hazardous events and effectiveness of non-SIS risk mitigation measures. SIL determination by risk graph methods requires consensus on four categorized parameters as follows:

-Consequence risk parameters(C) -Frequency and risk exposure time parameters(F)

3.3Uncertainty Analysis for Target SIL Determination

Probabilistic methods, non-probabilistic methods and hybrid methods, combination of nonprobabilistic and probabilistic methods are used to perform the uncertainty analysis for target SIL determination in the paper. Specifically, the sampling method, or probabilistic method, is used for OLF 070 due to its quantitative features and the fuzzy set method, or non-probabilistic method, is used for the calibrated risk graph due to its qualitative features. For LOPA, both the sampling method and the fuzzy set method are used and this combined method can be deemed as a hybrid method.

Probabilistic uncertainty analysis can be performed by sampling techniques likeMonte Carlo and Latin Hypercube [START_REF] Janbu | Treatment of uncertainties in reliability assessment of safety instrumented systems[END_REF]. Monte Carlo simulation is a method for generating random samples by using a large number of pseudo-random uniform variables from the interval [0, 1]. Compared to this method, Latin Hypercube sampling is a similar method for random sample generation where an analyst should decide how many sample points to use for a variable by dividing it into some equally probable intervals. These methods generally involve the generation of randomsamples of input random variables, the deterministic evaluations of the performance function atthese samples, and the post-processing to extract the probabilistic characteristics (e.g., statisticalmoments, reliability, and PDF) of the performance function [START_REF] Janbu | Treatment of uncertainties in reliability assessment of safety instrumented systems[END_REF][START_REF] Baraldi | Uncertainty in risk assessment[END_REF][START_REF] Rausand | Reliability of safety-critical systems[END_REF].

Sampling-based method based on Monte Carlo simulationisapplied to quantitative SIL determination methods of OLF 070 minimum SIL requirement in the paper. Input parameters are modeled as assumed probability distributions and this makes the basis for sampling.

The main steps of SIL determination by using Monte Carlo simulation are [START_REF] Zio | The Monte Carlo simulation method for system reliability and risk analysis[END_REF]:

1) Construct a probability distribution for input parameters (component failure rates, common cause beta-factors, test coverage factors,etc.) 2) Generate sample sets of input parameters by using random numbers 3) Quantify output function of PFD (Probability of Failure on Demand) with the sampled sets 4) Repeat steps 2 to 3 and analysis of relevant statistics: mean, standard deviation, coefficient of variation and P α (α% percentile) of each output value

The target SIL distribution is assigned with the corresponding PFD values. Methods for non-probabilistic uncertainty analysis are based on mathematical principles for knowledge representation reflecting degree of truth and attempt to model the approximate sense of words in the linguistic statements of the analysts [START_REF] Abul-Haggag | Application of fuzzy logic for the determination of safety integrity in light of IEC 61508 & 61511 standards[END_REF].The risk graph summarized both in Section 2 and Figure 6 are most frequently used for SIL determination in the offshore industrydue to easy implementation and fast assessments with four input parameters. However, the understanding of linguistic terms for each input parameter can differ between participants during SIL determination activities, which can lead to subjectivity results. The calibrated risk graph is use more quantitative definitions of each input parameter as following Table 2 to supplement the shortcomings of the risk graph method. However, SIL determination results of the calibrated risk graph has dominated by consequence (C) and demand rate (W) parameters, because occupancy (F) and Probability of Avoidance (P) have only two ranges of variability.

Table 2.Definitions of Input Parameters for Calibrated Risk Graph [3]

Input Parameter Classification Consequence (C, Expected injuries)

• C A : < 0.01 • C B : 0.01 ~ 0.1 • C C : 0.1 ~ 1 • C D : > 1

Occupancy or Exposure (F)

• F A : Rare to more frequent exposure in the hazardous zone, Range of F = 0 ~ 10 %) • F B : Rare to more frequent exposure in the hazardous zone, Range of F = 10 ~ 100 %)

Probability of Avoidance(P)

• P A : Use P A if below conditions are satisfied a. Facilities are provided to alert the operator that the SIS has failed; b. Independent facilities are provided to shutdown such that the hazard can be avoided or which enable all persons to escape to a safe area; c. The time between the operator is alerted and a hazardous event occurring exceeds 1 hour or is definitely sufficient for the necessary actions. • P B : Use P B if conditions for P A are not fulfilled.

Demand Rate (W, No. of demands/year)

• W 0 : < 0.01 • W 1 : 0.01 ~ 0.1 • W 2 : 0.1 ~ 1 • W 3 : 1 ~ 10
The application of fuzzy set has most continuously studied among non-probabilistic methods to improve the shortages of the risk graph method including to the calibrated risk graph methoddue to characteristics to handling the ambiguous or imprecise, and uncertain input parameters [START_REF] Nati-Said | Fuzzy risk graph model for determining safety integrity level[END_REF][START_REF] Ouache | Safety instrumented systems between reliability and fuzzy[END_REF][START_REF] Abul-Haggag | Application of fuzzy logic for the determination of safety integrity in light of IEC 61508 & 61511 standards[END_REF].

The overall procedures of fuzzy set approach for SIL assessment used in the paper consist of three sub steps [START_REF] Nati-Said | Fuzzy risk graph model for determining safety integrity level[END_REF].

1) Fuzzification : Generation of membership function for four risk parameters including development of the fuzzy scales ① Degree of membership vs. Fatalities per event (Consequence, C) ② Degree of membership vs. % of Exposure (Exposure, F) ③ Degree of membership vs.Probability of avoidance(Avoidance, P) ④ Degree of membership vs. Demand rate(Demand rate, W) ⑤ Degree of membership vs. SIL 2) Fuzzy inference : Derivation of the fuzzy rules using "If-then rule" If fuzzy inference is considered based on the combination of fourinput parameters and the risk graph model, total of 52 fuzzy rules are generated as summarized in Table 3. For example, the rule #13 indicates that if C is C B and F is F B and P is P A and W is W 0 then SIL is SIL 2.

3) Defuzzification : Determination of point values and assessment of uncertainty

C D F B P B W 0 W 1 W 2 W 3 b b 3 2
A non-probabilistic method of uncertainty representation should be used with the risk graph method, because experts" opinion is the key factor [START_REF] Simon | SIL allocation of SIS by aggregation of experts' opinions[END_REF].LOPA is another appropriate method to apply sampling technique due to its quantitative feature. However, LOPA has also qualitative features simultaneously.

To reflect this qualitative feature into the uncertainty modeling, fuzzyrepresentation should be utilized in combination with a sampling-based method.

The combination of fuzzy set approach and Monte Carlo simulation has been performed to assess the uncertainty in risk assessment, combining probability density functions of random variables and membership functions of fuzzy variables [START_REF] Arunraj | Modeling uncertainty in risk assessment: An integrated approach with fuzzy set theory and Monte Carlo simulation[END_REF]. The PFD calculation of SIS can be done by combining Monte Carlo and fuzzy set on input parameters like component failure rates, diagnostic coverage, common cause failure factor, mean time to repair a detected failure and proof-test interval. The sample set of each input parameteris generated by Monte Carlo simulation and then, fuzzy arithmetic operation is performed to calculate the PFD value [START_REF] Innal | Monte Carlo analysis and fuzzy sets for uncertainty propagation in SIS performance assessment[END_REF].

LOPA has both qualitative and quantitative attributes in its worksheet. The former, qualitative attributes, include the following parameters: target mitigated event likelihood (f TMEL ) as well as consequence (C), since a value of f TMEL directly depends on the C value which is determined by experts" consensus. The latter, quantitative attributes, include initiating cause frequency (f IC ), PFD for independent protection layer (PFD IPL ) and intermediate event likelihood (f IEL ). The relationship among these qualitative and quantitative parameters follows the formula:

Required Not required, otherwise where

TMEL TMEL IEL IEL IEL IC IPL f for f f f PFD f f PFD         (2)
Uncertainty analysis for LOPA has been performed according to the following steps. The first step is to fuzzify the qualitative parameters into membership functions. The qualitative parameters, C and f TMEL, membership functions are modelled using both trapezoidal and triangular shaped functions. For quantitative parameters, f IC and PFD IPL , are assumed to follow uniform distributions due to its large amount of uncertainty. To get the interval of required PFD and SIL, f TMEL is modelled with the discrete distribution and f IEL has been obtained by multiplication of f IC and PFD IPL .

The illustration examples of abovementioned procedures for uncertainty analysis of SIL determination are summarized in Section 4.

CASE STUDIES

4.1System description

An exemplification study has been performed for the local safety function, the MEG Subsea Injection Pump Dischargepressure safety high alarm. This protection function is to prevent overpressure in thedischarge of MEG injection pump, which is of positive displacement type. Any obstruction at the user point or no MEG injection due to process shutdown might lead to this hazard. To prevent this hazard, MEG injection pump should be stopped on highpressurealarm detected at the pump discharge. There will be not only MEG spill as an environmental consequence, but loss of containment with very high pressure and personnel risk.The dangerous undetected failure includes all possible modes of failure leading to any of the following effects:the transmitter failing to signal high pressure on demand,the logic solver failing to initiate pump stop,the circuit breaker failing to stop the pump motor on demand.For this reason, the MEG pumpis not included in the reliability calculation. Figure 7 shows the configuration of this SIF. It is assumed that there are already existing protective measures, so-called non-SIS. One measure isgiven by two pressure safety valves (PSVs) provided on the MEG injection pump discharge, sized for blocked outlet condition. Another measure is the valve that will be open to maintain the pressure in the header. However, if obstruction is sudden, pressure control may not act.

4.2Effects of the Uncertainties on Target SIL

4.2.1Sampling method for OLF 070

As mentioned in Section 2.3, minimum SIL requirements in OLF 070 are derived based on the typical loop assumption and PFD estimationusing industrial verified component reliability data. The uncertainty analysis, applied to the determination of target SIL by the method from OLF 070, can be performed by sampling methods for uncertainty propagation.

To calculate the target SIL of the SIF, the PDS method [START_REF] Sintef | Reliability prediction methods for safety instrumented systems, PDS methodhandbook[END_REF]has been used for maintaining consistency with OLF 070. Since every component has simple configuration, 1oo1, the average of PFD follows the Equation (3) without consideration of common cause failures [START_REF] Rausand | Reliability of safety-critical systems[END_REF]. It should be noted that the probability of the so-called test independent failure (TIF) can be added to the PFD to reflect the effect of incomplete testing. OLF 070 takes P TIF into consideration when calculating PFD. The values for P TIF come from the PDS data handbook [START_REF] Sintef | Reliability data for safety instrumented systems, PDS data handbook[END_REF].

In addition to the above Equation (3), another model has been used in the case study for the purpose of comparison. In order to replace the effect of imperfect testing with P TIF , proof test coverage (PTC) is added to the input parameters [START_REF] Kim | Risk-based design for implementation of SIS functional safety in the offshore industry[END_REF]and the PFD model is modified as follows:

(

        B DU DU T PFD PTC PTC 1 ) 22 
T is the assumed interval of complete testing with which the residual failure modes will be detected. If some failure modes are not able to be tested for, then T should be taken as the lifetime of the equipment. In this case, T is assumed to be 5 years, the periodic overhaul duration of the offshore plant where the SIF would be installed.

Among the parameters, λ DU and PTC are assumed to be random variables due to uncertainties from incompleteness of data. Since it is known that the failure rate is usually represented using lognormal distribution [START_REF]Probabilistic risk assessment procedures guide for NASA managers and practitioners[END_REF], the uncertainty of the DU failure rate is given by a lognormal distribution with median equal to the values in Table 4. The error factors are assumed to have the value of 3 [START_REF] Jin | Uncertainty assessment of reliability estimates for safety instrumented systems[END_REF]. The PTC and P TIF are given by uniform distributions with the intervals shown in Table 4. In regard to proof test coverage, this assumption is due to lack of accumulated data from generic databases in the offshore industry. Also, P TIF hasa certain amount of uncertainty because its value is determined by experts" opinion. On the other hand, the number of components and τ are assumed to be constant, since the uncertainties of configurations and proof test intervals can be controlled [START_REF] Kim | Risk-based design for implementation of SIS functional safety in the offshore industry[END_REF]. The uncertainty propagation has been performed by Monte Carlo simulation. For each simulation run, random values for each uncertain parameter have been generated and then, used as input to calculate target SIL A and SIL B based on PFD A and PFD B , respectively. A total of 50,000 simulation runs have been performed for the precision of results. The target SIL distributions are shown in Figure8, with the input parameter distributions. Also, the statistics of the target SIL simulation results are reported in Table 5, where P α represents α% percentile of each output parameter.

4.2.2Fuzzy set approach for risk graph

At the end of Section 3.3, the fuzzy set approach has been studied for uncertainty analysis associated to the risk graph model. For this case study, the calibrated risk graph has been used as shown in Figure 9, which conveys the deterministic result of the SIL assessment for the SIF. The first step of the fuzzy set approach is to fuzzify the parameters into membership functions. Parameters used here are listed in Figure 10 with corresponding membership functions, respectively. Membership functions are modelled using both trapezoidal and triangular shaped functions. For parameter P, the mark with a star indicates that P A should be selected if only all the following are true; a) facilities are provided to alert the operator that the SIS has failed, b) independent facilities are provided to shutdown such that the hazard can be avoided or which enable all persons to escape to a safe area, c) the time between the operator being alerted and a hazardous event occurring exceeds 1 hour or is definitely sufficient for the necessary actions.

After the fuzzification, the fuzzy inference system is modelled using "If-then rule", for example, If (C is Medium_high) and (F is Low) and (P is High) and (W is Medium_high) then (SIL is SIL 2). In this case study, a total of 52 rules are generatedby experience,summarized in Table 3.The linguistic values are described in Table 6.

The last stage is to defuzzify the results obtained back into a scalar value. There are several methods of defuzzification such as Center-of-Maximum (CoM), Mean-of-Maximum (MoM), Center-of-Area (CoA), etc [START_REF] Simon | SIL allocation of SIS by aggregation of experts' opinions[END_REF]. For this case, CoA has been used because this method can produce sufficiently accurate results in many cases [START_REF] Elaamvazuthi | The application of Mamdani fuzzy model for auto zoom function of a digital camera[END_REF]; the result is shown with its relative frequency respectively in Figure 11. 4.2.3Combination ofboth sampling method and fuzzy set approach for LOPA LOPA has been conducted for the SIF, MEG Subsea Injection Pump DischargePSHH, and the results are shown in Table5. There is a little uncertainty when determining severity level from C C to C D . In terms of personal safety, C C applies to serious illness or significant life-shortening effects and C D includes single or multiple employee fatalities. This uncertainty of C-parameter affects the value of f TMEL , from 1.00 x 10 -4 for C C to 1.00 x 10 -5 for C D . According to [START_REF] Ccps | Layer of protection analysis: simplified process risk assessment[END_REF], f IC and PFD IPL can be assumed to have the range of values in Table 5. Since the SIF has two PSVs for the purpose of high pressures, PFD IPL values are multiplied by 2. Consequently, f IEL has minimum of 2.00 x 10 -5 and maximum of 2.00 x 10 -2 . Uncertainty analysis for LOPA has been performed according to the following steps. The first step is to fuzzify the qualitative parameters into membership functions. Qualitative parameters, C and f TMEL , are shown in Figure 12 with corresponding membership functions, respectively. Membership functions are modelled using both trapezoidal and triangular shaped functions. For quantitative parameters, f IC and PFD IPL ,are assumed to follow uniform distributions due to its large amount of uncertainty [START_REF] Flage | Probability and possibility-based representations of uncertainty in fault tree analysis[END_REF]. To get the interval of required PFD and SIL, f TMEL is modelled with the discrete distribution and f IEL has been obtained by multiplication of f IC and PFD IPL . Figure 13 and Table8summarizesthe results of uncertainty analysis using both Monte Carlo simulation and fuzzy set approach.

Discussions

Without considering uncertainty, SIL 2is obtained for the MEG Subsea Injection Pump Discharge pressure safety high alarm when using calibrated risk graph as shown in Figure 9.Moreover, OLF 070 [START_REF]Application of IEC 61508 and IEC 61511 in the Norwegian petroleum industry[END_REF]refers that the PSD function for PAHH is required to satisfy SIL 2.From OLF 070, the function is defined to start with the pressure sensor and terminates with closing of the critical valve. On the minimum SIL Table, it is noted that the final element of this function could be different from a valve, e.g. a pump which must be stopped. From the viewpoint of OLF 070, MEG Subsea Injection Pump DischargePSHH is also classified in the PSD function for PAHH and SIL 2 requirement can be applied.

On the contrary, the results show differences when considering also the underlying uncertainties. To model the uncertainties, the following modeling techniques are adapted:

 For risk graph: fuzzy set approach; 11shows target SIL valueshavethe ranges from SIL 1 to SIL 3 while the relative frequenciesare 30 %, 63 %, and 7 % respectively. In this case, the required (target) SIL of the case could be determined as SIL 2 with a conservative consideration. However, a situation is likely to occur when there is no dominant target SIL value. For instance, target SIL results have values from SIL 1 to SIL 3 with relative frequencies of 35%, 35%, and 30%, respectively. In this case, other decision-making guidance should be used for a target SIL determination. It is recommended that independent QRA (Quantitative Risk Assessment)e.g. fire & explosion analysisshould be performed for supplementary decision-guide. OLF 70 proposes a general approachto verify SIL requirements by application of QRA [START_REF]Application of IEC 61508 and IEC 61511 in the Norwegian petroleum industry[END_REF].Sampling-based PFD B and the result of LOPA using both methods, Monte Carlo simulation and fuzzy set approach, have derived target SIL values in the range from SIL 0 to SIL 2. Table 9 summarizes the target SIL results on evaluation methods.

Although the distributions of PFD A and PFD B approximate each other in terms of both location and relative variation, the final outputs are distinguished. It can be guessed that the reason of the difference in target SILs mainly comes from the difference in models between PFD A and PFD B . Since PTC shows more sensitivity than other parameters [START_REF] Kim | Risk-based design for implementation of SIS functional safety in the offshore industry[END_REF], the outputs of the analysis by the PFD B model including PTC can be more affected by the parameter uncertainty. Sampling method for OLF-070 with Equation (3) 1 1 2

Fuzzy set approach for Risk graph † 1 2 3

Fuzzy set + Sampling for LOPA 0 1 2 †The relative frequency is 0.30, 0.63, and 0.07 for P 10 , P 50 , and P 90 , respectively.

CONCLUSION

This paper has looked into the problem of treating uncertainty in the target SIL determination phase and proposed a practical approach for offshore industry. In particular, the risk graph method, LOPA, and minimum SIL requirement in OLF 070 have been introduced and studied with respect to the analysis of the uncertainty that affects their SIL outcomes.

Both parameter and model uncertainty contribute to uncertainties in the determined target SIL values, when using different methodologies such asthe risk graph, LOPA, or minimum SIL requirement from OLF 070. To investigate the effect of uncertainties, the fuzzy set approach and Monte Carlo simulation have been used for risk graph and OLF 070 minimum SIL requirement, respectively. For LOPA, the hybrid approach, using fuzzy set approach and Monte Carlo method together, has been proposed to reflect both qualitative and quantitative features of the uncertainty.

According to the case study results summarized in Section 4, the fuzzy set approach based on the risk graph method, LOPA with Monte Carlo simulation and fuzzy set approach and OLF 70 minimum SIL Table by using Monte Carlo simulation show reliable results for SIL determination. LOPA with Monte Carlo simulation and fuzzy set approach shows advantages of less uncertainty than the fuzzy set approachfor SIL determination, if a sufficientinformation available.

The percentage of 80 ~ 90of all identified SIFs in offshore facilities are usually assigned as SIL 1 or SIL 2. Therefore, a guideline on how to apply the methods considered in the paper for SIL determination can be suggested in offshore industry as follows. First, the fuzzy set approach can be used for overall SIL determination, while LOPA with Monte Carlo simulation and fuzzy set approach can be considered as a supplementary tool in order to verify the requirement of SIFs expected to be SIL 3 and strongly disputing between participants for the assigned SIL.

For a future work, practical procedures will be proposed to combine QRA with uncertainty analysis of SIL determination in order to verify or reduce the uncertainty in the results.

Figure 1 .

 1 Figure 1. Safety Instrumented System

Figure 2 .

 2 Figure 2.Safety Lifecycle Approach regarding SIL

Figure 3 .

 3 Figure 3. SIL Determination Methods ( †: Application of IEC61508/61511 in the Norwegian Petroleum Industry)

Figure 4 .

 4 Figure 4. Independent Protection Layers against Accident

Figure 6 .

 6 Figure 6.SIL Determination Concept by Risk Graph Method

[

  Risk and safety integrity concept] [Risk graph method for SIL determination]

2 :

 2 Rate of dangerous undetected failures : Time interval between proof tests : Probability of test independent failures

  10 -5 ~ 7.0•10 -5

Figure 8 .

 8 Figure 8.Input Parameters Distributions and Target SIL Distribution obtained by Monte Carlo Simulation

Figure 9 .

 9 Figure 9.Calibrated Risk Graph and Determined Target SIL for the SIF

Figure 10 .Figure 11 .

 1011 Figure 10.Membership Functions for Risk Graph Parameters

CFigure 12 .Figure 13 .

 1213 Figure 12.TMEL Obtained using the Fuzzy Set Approach

Table from

 from

	OLF 070 and LOPA are used to
	determine SIL in offshore facilities, although their applications are relatively few compared with the
	risk graph method. EspeciallyLOPA is a powerful tool to asses SIL of SIFs when it is difficult to get
	an agreement between participants to the SIL determination studies.
	The objectives of this paper are to (i)identify uncertainty sourcesinSIL determination methods,
	specifically risk graph method, minimum SIL Table from OLF 070and LOPA, (ii) propose
	proceduresfor the uncertainty analysis inSIL determination by risk graph method, minimum SIL Table
	from OLF 070and LOPA, using a Fuzzy Set approach (non-probabilistic method),Monte Carlo
	simulation (probabilistic method) and a combination of Monte Carlo simulationand the Fuzzy Set
	approach.

Table 1 .Uncertainty Sources and their Classification, in SIL Determination Methods

 1 On the other hand, minimum SIL Table or LOPA is a (semi)quantitative method for SIL determination. Minimum SIL Tablesare derived based on the typical loop assumption and are estimated by using the industrially verified component reliability data, including common cause factor, diagnostic coverage and fail-safe design.The PFD calculation model and the required reliability data are contributors to uncertainty for SIL determination by minimum SIL.

	Known
	Unknown

Table 3 .Fuzzy Rule Generation Results based on Calibrated Risk Graph Model

 3

					"If-then"
	Rule
			C	F	P	W	SIL
		1				W 0	a
	1 Group	2 3	C A			W 1 W 2	--
		4				W 3	-
		5				W 0	1
	2 Group	6 7	C B	F A	P A	W 1 W 2	a -
		8				W 3	-
		9				W 0	2
	3 Group	10 11	C B	F A	P B	W 1 W 2	1 a
		12				W 3	-
		13				W 0	2
	4 Group	14 15	C B	F B	P A	W 1 W 2	1 a
		16				W 3	-
	5~11 Group	…	….	….	…	…	…
		45				W 0	b
	12 Group	46 47	C D	F B	P A	W 1 W 2	3 2
		48				W 3	1
		49
	13 Group	50 51
		52

Table 4 .Reliability Data for the SIF Components

 4

	Component	No. of Components	λ DU, perhour Τ, hours	PTC, %	P TIF
	Pressure transmitter	1	0.3•10 -6	8760	80 ~ 99

Table 6 . Linguistic Values of Input Parameters

 6

	Input Parameter	Very Low	Low	Medium Low	Medium High	High	Very High
	C		C A	C B	C C	C D
	F		F A			F B
	P		P A			P B
	W		W 0	W 1	W 2	W 3
	SIL	No SIL	SIL a	SIL 1	SIL 2	SIL 3	SIL b

Table 7 .LOPA Worksheet

 7

	SIL Description	Consequence	TMEL	Initiating Cause	f IC	Independent Protection Layers Add. BPCS Alarms Mitigation	IEL	SIL
	MEG
	Subsea
	Injection
	Pump

Table 8 .Statistics of Target SIL using both Monte Carlo Simulation and Fuzzy Set Approach

 8

  Minimum SIL: Monte Carlo simulation or Latin HypercubeFor the same SIF, sampling-based PFD A and the fuzzy risk graph show similar results in SIL 2. The fuzzy set risk graph of Figure

	 LOPA: Hybrid fuzzy set approach;
	
	Output	Mean		Standard Deviation	Coefficient of Variation	P	10		P	50	P	90
	PFD	8.35 x 10	-2	1.97 x 10	-1	2.36 x 10	1	8.43 x 10	-3	2.58 x 10	-2	1.87 x 10	-1
	SIL	0.968		6.03 x 10	-1	6.22 x 10	-1	0		1	2

Table 9 . Summary of Target SIL on Method

 9

			Target SIL
	Method
		P 10	P 50	P 90
	Sampling method for OLF-070 with Equation (3)	1	2	2

Acknowledgements

The authors would like to thank the Outfitting System Research Department of Corporate Technology Institute, Hyundai Heavy Industries for supplying technical information and comments.


Beverley Balkau
email: balkau@vjf.inserm.fr

J Tuomilehto

P Jousilahti

J Lindström

M P Garancini

G Calori

G Ruotolo

L M Bouter

J M Dekker

R J Heine

G Nijpels

C D A Stehouwer

A Pajak

M Eliasson

B Stegmayr

N Unwin

N Ahmad

K G M M Alberti

L Hayes

K Borch-Johnsen

Q Qiao

Keywords: cardiovascular diseases, epidemiology, obesity, risk factors

Does diagnosis of the metabolic syndrome detect further men at high risk of cardiovascular death beyond those identified by a conventional cardiovascular risk score?

The DECODE Study

The DECODE Study Group

Introduction

Identification of the metabolic or insulin resistance syndrome is currently being recommended to identify people at risk for cardiovascular disease (CVD), and for diabetes [START_REF]Definition, diagnosis and classification of diabetes mellitus and its complications Part 1: Diagnosis and classification of diabetes mellitus[END_REF][START_REF]Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults. Executive Summary of The Third Report of The National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III)[END_REF][START_REF]National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III). Third Report of the National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III) final report[END_REF][4][START_REF] Grundy | Definition of metabolic syndrome: Report of the National Heart, Lung, and Blood Institute/American Heart Association conference on scientific issues related to definition[END_REF]. Numerous studies have shown that both prevalent and incident diabetes and CVD are associated with the syndrome, as defined by the World Health Organization (WHO) [START_REF]Definition, diagnosis and classification of diabetes mellitus and its complications Part 1: Diagnosis and classification of diabetes mellitus[END_REF], by the European Group for the study of Insulin Resistance (EGIR) [START_REF] Balkau | Comment on the provisional report from the WHO consultation. European Group for the Study of Insulin Resistance (EGIR)[END_REF], by the National Cholesterol Education Program, Adult Treatment Panel III (NCEP-ATP III) [START_REF]Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults. Executive Summary of The Third Report of The National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III)[END_REF] or by adaptations of these definitions [START_REF] Isomaa | Cardiovascular morbidity and mortality associated with the metabolic syndrome[END_REF][START_REF] Lakka | The metabolic syndrome and total and cardiovascular disease mortality in middle-aged men[END_REF][START_REF] Klein | Components of the metabolic syndrome and risk of cardiovascular disease and diabetes in Beaver Dam[END_REF][START_REF] Resnick | Strong Heart Study. Insulin resistance, the metabolic syndrome, and risk of incident cardiovascular disease in nondiabetic american indians: the Strong Heart Study[END_REF][START_REF] Sattar | Metabolic syndrome with and without C-reactive protein as 15/15 a predictor of coronary heart disease and diabetes in the West of Scotland Coronary Prevention Study[END_REF][START_REF] Hunt | National Cholesterol Education Program versus World Health Organization metabolic syndrome in relation to all-cause and cardiovascular mortality in the San Antonio Heart Study[END_REF][START_REF] Girman | The metabolic syndrome and risk of major coronary events in the Scandinavian Simvastatin Survival Study (4S) and the Air Force/Texas Coronary Atherosclerosis Prevention Study (AFCAPS/TexCAPS)[END_REF][START_REF] Hu | Prevalence of the metabolic syndrome and its relation to all-cause and cardiovascular mortality in non-diabetic European men and women[END_REF][START_REF] Malik | Impact of the metabolic syndrome on mortality from coronary heart disease, cardiovascular disease, and all causes in United States adults[END_REF][START_REF] Stern | Does the metabolic syndrome improve identification of individuals at risk of type 2 diabetes and/or cardiovascular disease?[END_REF][START_REF] Mcneill | The metabolic syndrome and 11-year risk of incident cardiovascular disease in the Atherosclerosis Risk in Communities study[END_REF][START_REF] Mykkanen | Cardiovascular disease risk factors as predictors of type 2 (non-insulin-dependent) diabetes mellitus in elderly subjects[END_REF][START_REF] Hanson | Components of the "metabolic syndrome" and incidence of type 2 diabetes[END_REF][START_REF] Laaksonen | Metabolic syndrome and development of diabetes mellitus: application and validation of recently suggested definitions of the metabolic syndrome in a prospective cohort study[END_REF][START_REF] Lorenzo | The metabolic syndrome as predictor of type 2 diabetes: the San Antonio heart study[END_REF][START_REF] Ford | Risks for all-cause mortality, cardiovascular disease, and diabetes associated with the metabolic syndrome. A summary of the evidence[END_REF][START_REF] Dekker | Metabolic syndrome and 10-year cardiovascular disease risk in the Hoorn Study[END_REF][START_REF] Sundstrom | Clinical value of the metabolic syndrome for long term prediction of total and cardiovascular mortality: prospective, population based cohort study[END_REF]. Further, in 2005 two additional definitions of the metabolic syndrome have been published, one by the International Diabetes Federation (IDF) [START_REF] Alberti | The metabolic syndrome-a new worldwide definition[END_REF], and a second, a revised version of the NECP-ATP III definition, by the American Heart Association/National Heart, Lung, and Blood Institute (AHA/NHLBI) [START_REF] Grundy | Diagnosis and management of the metabolic syndrome: an American Heart Association/National Heart, Lung, and Blood Institute Scientific Statement[END_REF].

However, while the syndrome may predict diabetes, this is mainly due to those subjects with the syndrome who have high glucose concentrations (impaired glucose tolerance or impaired fasting glucose) at baseline [START_REF] Klein | Components of the metabolic syndrome and risk of cardiovascular disease and diabetes in Beaver Dam[END_REF][START_REF] Sattar | Metabolic syndrome with and without C-reactive protein as 15/15 a predictor of coronary heart disease and diabetes in the West of Scotland Coronary Prevention Study[END_REF][START_REF] Mykkanen | Cardiovascular disease risk factors as predictors of type 2 (non-insulin-dependent) diabetes mellitus in elderly subjects[END_REF][START_REF] Hanson | Components of the "metabolic syndrome" and incidence of type 2 diabetes[END_REF][START_REF] Lorenzo | The metabolic syndrome as predictor of type 2 diabetes: the San Antonio heart study[END_REF][START_REF] Ford | Risks for all-cause mortality, cardiovascular disease, and diabetes associated with the metabolic syndrome. A summary of the evidence[END_REF]. A combination of other diabetes risk factors (glucose and insulin at both fasting and 2 hours post load, triglycerides, HDL-cholesterol, systolic and diastolic blood pressure, weight, height) has been shown to better predict diabetes than either the WHO or the NCEP-ATP III defined syndromes [START_REF] Stern | Does the metabolic syndrome improve identification of individuals at risk of type 2 diabetes and/or cardiovascular disease?[END_REF][START_REF] Hanson | Components of the "metabolic syndrome" and incidence of type 2 diabetes[END_REF]. For cardiovascular mortality, there are many studies [START_REF] Isomaa | Cardiovascular morbidity and mortality associated with the metabolic syndrome[END_REF][START_REF] Lakka | The metabolic syndrome and total and cardiovascular disease mortality in middle-aged men[END_REF][START_REF] Klein | Components of the metabolic syndrome and risk of cardiovascular disease and diabetes in Beaver Dam[END_REF][START_REF] Resnick | Strong Heart Study. Insulin resistance, the metabolic syndrome, and risk of incident cardiovascular disease in nondiabetic american indians: the Strong Heart Study[END_REF][START_REF] Sattar | Metabolic syndrome with and without C-reactive protein as 15/15 a predictor of coronary heart disease and diabetes in the West of Scotland Coronary Prevention Study[END_REF][START_REF] Hunt | National Cholesterol Education Program versus World Health Organization metabolic syndrome in relation to all-cause and cardiovascular mortality in the San Antonio Heart Study[END_REF][START_REF] Girman | The metabolic syndrome and risk of major coronary events in the Scandinavian Simvastatin Survival Study (4S) and the Air Force/Texas Coronary Atherosclerosis Prevention Study (AFCAPS/TexCAPS)[END_REF][START_REF] Hu | Prevalence of the metabolic syndrome and its relation to all-cause and cardiovascular mortality in non-diabetic European men and women[END_REF][START_REF] Malik | Impact of the metabolic syndrome on mortality from coronary heart disease, cardiovascular disease, and all causes in United States adults[END_REF][START_REF] Stern | Does the metabolic syndrome improve identification of individuals at risk of type 2 diabetes and/or cardiovascular disease?[END_REF][START_REF] Mcneill | The metabolic syndrome and 11-year risk of incident cardiovascular disease in the Atherosclerosis Risk in Communities study[END_REF][START_REF] Ford | Risks for all-cause mortality, cardiovascular disease, and diabetes associated with the metabolic syndrome. A summary of the evidence[END_REF][START_REF] Dekker | Metabolic syndrome and 10-year cardiovascular disease risk in the Hoorn Study[END_REF][START_REF] Sundstrom | Clinical value of the metabolic syndrome for long term prediction of total and cardiovascular mortality: prospective, population based cohort study[END_REF], and the syndrome is significantly predictive, even after adjusting for the traditional CVD risk factors (blood pressure, cholesterol, smoking as well as age) [START_REF] Resnick | Strong Heart Study. Insulin resistance, the metabolic syndrome, and risk of incident cardiovascular disease in nondiabetic american indians: the Strong Heart Study[END_REF][START_REF] Sattar | Metabolic syndrome with and without C-reactive protein as 15/15 a predictor of coronary heart disease and diabetes in the West of Scotland Coronary Prevention Study[END_REF][START_REF] Girman | The metabolic syndrome and risk of major coronary events in the Scandinavian Simvastatin Survival Study (4S) and the Air Force/Texas Coronary Atherosclerosis Prevention Study (AFCAPS/TexCAPS)[END_REF][START_REF] Malik | Impact of the metabolic syndrome on mortality from coronary heart disease, cardiovascular disease, and all causes in United States adults[END_REF][START_REF] Mcneill | The metabolic syndrome and 11-year risk of incident cardiovascular disease in the Atherosclerosis Risk in Communities study[END_REF][START_REF] Dekker | Metabolic syndrome and 10-year cardiovascular disease risk in the Hoorn Study[END_REF][START_REF] Sundstrom | Clinical value of the metabolic syndrome for long term prediction of total and cardiovascular mortality: prospective, population based cohort study[END_REF]. However, the Framingham Risk equation appears to have a better predictive value than the metabolic syndrome [START_REF] Stern | Does the metabolic syndrome improve identification of individuals at risk of type 2 diabetes and/or cardiovascular disease?[END_REF].

If the syndrome is to be a useful concept in clinical practice it should identify individuals at risk of CVD beyond those who can already be identified by a cardiovascular risk score. The European SCORE project risk equation [START_REF] Conroy | and the SCORE project group (2003) Estimation of ten-year risk of fatal cardiovascular disease in Europe: the SCORE project[END_REF] is appropriate for identifying those at low and high risk of fatal CVD (10-year risk under and over 5%) in European populations [START_REF]Third joint task force of European and other societies on cardiovascular disease prevention in clinical practice (constituted by representatives of eight societies and by invited experts).European guidelines on cardiovascular disease prevention in clinical practice[END_REF].

In the DECODE cohort, we study whether the syndrome identified individuals who died within 10 years of CVD among those a) at low CVD risk, b) at high CVD risk. Further we study in these two groups the predictive value of the syndrome abnormalities taken singly and as a combination of the two clinical variables, waist circumference and arterial blood pressure, and of the hypertriglyceridaemic waist, which has been proposed as a simple tool for the diagnosis of the syndrome [START_REF] Lemieux | Hypertriglyceridemic waist: A marker of the atherogenic metabolic triad (hyperinsulinemia; hyperapolipoprotein B; small, dense LDL) in men?[END_REF].

Methods

Study population

The methods used to recruit cohorts into the DECODE Study have been reported in previous publications [START_REF] Hu | Prevalence of the metabolic syndrome and its relation to all-cause and cardiovascular mortality in non-diabetic European men and women[END_REF][START_REF]The DECODE Study Group on behalf of the European Diabetes Epidemiology Group (1999) Glucose tolerance and mortality: comparison of WHO and American Diabetes Association diagnostic criteria[END_REF][START_REF] The | Is the current definition for diabetes relevant to mortality risk from all causes and cardiovascular and noncardiovascular diseases?[END_REF][START_REF] Decode | Gender difference in all-cause and cardiovascular mortality related to hyperglycaemia and newly-diagnosed diabetes[END_REF]. Briefly, coordinators of studies with data on mortality from populationbased studies or large studies on occupational groups in Europe, and with measured glucose concentrations at fasting and 2 hours after a 75g OGTT, were contacted and invited to participate. We analyze data from seven population-based studies from the DECODE study cohorts, 2790 men aged 50 to 69 years with measures of fasting glucose, triglycerides, HDL-cholesterol concentrations, waist circumference and systolic and diastolic blood pressures. There were too few cardiovascular events in this DECODE population with the syndrome variables to permit analysis outside this age range. Women were included in the DECODE cohort, but the number of CVD deaths was small, and so results have not been included in this report. Diabetic men, both known and screened (fasting plasma glucose ≥ 7.0 mmol/l) were excluded [START_REF]Definition, diagnosis and classification of diabetes mellitus and its complications Part 1: Diagnosis and classification of diabetes mellitus[END_REF]. All glucose concentrations were transformed to plasma glucose concentrations, as already documented in other DECODE Study publications [START_REF] Hu | Prevalence of the metabolic syndrome and its relation to all-cause and cardiovascular mortality in non-diabetic European men and women[END_REF][START_REF]The DECODE Study Group on behalf of the European Diabetes Epidemiology Group (1999) Glucose tolerance and mortality: comparison of WHO and American Diabetes Association diagnostic criteria[END_REF][START_REF] The | Is the current definition for diabetes relevant to mortality risk from all causes and cardiovascular and noncardiovascular diseases?[END_REF][START_REF] Decode | Gender difference in all-cause and cardiovascular mortality related to hyperglycaemia and newly-diagnosed diabetes[END_REF].

5/5

Each study had ethical approval in accord with local requirements.

Score Risk Equation for CVD risk stratification

The probability of 10-year CVD mortality was calculated for all men in the study, using the formulae developed by the European SCORE project, summing the probabilities of CHD and CVDnon-CHD deaths [START_REF] Conroy | and the SCORE project group (2003) Estimation of ten-year risk of fatal cardiovascular disease in Europe: the SCORE project[END_REF]. This score includes sex, age, smoking status, total cholesterol and systolic blood pressure. These risk equations do not take into account diabetes or glucose concentrations, nor obesity measures. The coefficients for 'low risk countries' were used for Spain, Italy, the Netherlands, and 'high risk countries' for Finland, Sweden, Poland and the UK. Men with a 10-year cardiovascular mortality risk under 5% were identified as being at 'low risk' and men with a risk over 5% as 'high risk', in line with the European guidelines [START_REF] Conroy | and the SCORE project group (2003) Estimation of ten-year risk of fatal cardiovascular disease in Europe: the SCORE project[END_REF].

The metabolic syndrome

The NCEP-ATP III defined metabolic was used, modified to include treatment for hypertension [START_REF]Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults. Executive Summary of The Third Report of The National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III)[END_REF]. This definition requires the presence of at least three of the following five abnormalities: hyperglycaemia: fasting plasma glucose > 6.1 mmol/l; high arterial blood pressure: systolic > 130 mmHg and/or diastolic > 85 mmHg or treatment for hypertension; hypertriglyceridaemia: triglycerides > 1.7 mmol/l; hypo-HDL cholesterolaemia: HDL-cholesterol < 1.04mmol/l; central adiposity: waist circumference > 102 cm.

Vital status

Vital status was followed for the men who attended the baseline examination. Those who emigrated, for whom vital status could not be confirmed, were censored at the time of emigration.

Follow-up was almost complete. Fatal events were classified using the International Classification of Diseases: CVD was defined by codes 401-448 of the Eighth or Ninth Revisions and codes I10-I79 for the Tenth Revision [START_REF]International Classification of Diseases, Injuries and Causes of Death[END_REF][START_REF]International Classification of Diseases, Injuries and Causes of Death[END_REF]. Causes of death were either classified by an independent panel, or death certificates were used.

Statistical Analyses

SPSS for Windows 11.0 has been used for all statistical analyses.

Men were divided into four groups according to < 5%/≥ 5% estimated CVD risk and absence/presence of the NCEP-ATP III metabolic syndrome. The mean values of risk factors and the ranges over the studies, are presented (Table 1).

The Cox proportional hazards model was used to estimate the 10-year hazards ratios for fatal CVD, using men without the syndrome and at low CVD risk, as the reference group. The 10-year CVD cumulative hazards curves were calculated for these four risk groups. Because the syndrome and the CVD risk score include the same variables (arterial blood pressures), and age is included in the SCORE risk equation, models were build successively, with initially no adjustment, and then successive adjustment for centre, for centre and age and finally for centre, age and the estimated CVD risk from the SCORE equation [START_REF] Conroy | and the SCORE project group (2003) Estimation of ten-year risk of fatal cardiovascular disease in Europe: the SCORE project[END_REF]. The final adjustment for the estimated CVD risk aimed to examine whether the residual risk in the men with the syndrome was due to the traditional CVD risk factors or to other factors included in the syndrome, such as abdominal obesity, hyperglycemia and the specific lipid abnormalities.

In order to examine the CVD mortality linked with the syndrome in the high CVD risk group, the hazards ratios were also determined separately, in the groups with low and high CVD risk scores.

To determine which of the syndrome abnormalities was driving the CVD risk, hazards ratios for the individual syndrome abnormalities were estimated, within the two CVD risk groups, with the abnormalities defined according to the NCEP-ATP III thresholds. Finally, the risk associated with the combination of the two clinically determined variables, large waist circumference and high arterial blood pressure was evaluated, and also the risk associated with the combination of high triglycerides and large waist circumference [START_REF] Lemieux | Hypertriglyceridemic waist: A marker of the atherogenic metabolic triad (hyperinsulinemia; hyperapolipoprotein B; small, dense LDL) in men?[END_REF].

Results

The characteristics of the men, aged 50 to 69 years, included in this study are shown (Table 1). The follow-up in this analysis was limited to ten years. The most frequent abnormality contributing to the metabolic syndrome was high arterial blood pressure, with a frequency of 72% and the syndrome was present in 24% of the men.

The SCORE CVD risk equation identified 51% of the men (n=1416) as having a risk of fatal CVD under 5% over the next 10 years (Table 2). Of these, 22% (n=306) had the metabolic syndrome.

Overall 4.2% (n=118) of the men died of CVD, 2.2% (33/1416) of those at low CVD risk and 6.2% (85/1374) of those at high CVD risk. In both the low and the high CVD risk groups, the mean values of all variables indicated a higher risk in those with the metabolic syndrome (Table 2). This was particularly true for the syndrome variables.

The primary objective of this analysis was to determine, in men at low CVD risk, whether those with the metabolic syndrome had significantly higher CVD mortality than those without the syndrome. The hazards ratios changed little after adjustment, and even after adjusting for the estimated CVD risk, the metabolic syndrome remained predictive with a hazards ratio (95% confidence interval) of 2.42 (1.20-4.88) (p < 0.05) (Table 3). For the high CVD risk men, the hazards ratios were more affected by the adjustments: when adjusted for centre alone, the risks of fatal CVD were higher than for the low CVD risk men with the syndrome, but after adjustment for age and centre, the hazards ratios were similar to the men with low CVD risk and the syndrome.

Further, adjusting for the estimated 10-year CVD risk using the SCORE equation, the observed hazards ratio in the high risk men was greatly reduced, showing that the risk was due to high values of the classical CVD risk factors. Analyzing the two CVD risk groups separately, showed that the metabolic syndrome did not predict CVD mortality in the high risk men, with hazards ratios very close to one.

The cumulative hazards for the four groups of men are shown in Figure 1, and illustrate the similar risks in men at high CVD risk, with and without the syndrome and in men at low CVD risk with the syndrome.

Among the individual syndrome abnormalities, for the men in the low CVD risk group, large waist, high blood pressure, low HDL-cholesterol were predictive of fatal CVD with similar hazards ratios of 2.24 (1.05-4.76), 2.67 (1.21-5.88) and 2.72 (1.35-5.45) respectively (Table 4). The highest hazards ratio was associated with the combination of large waist and high arterial blood pressure, 3.54 (1.65-7.59). These men were 13% of those at low CVD risk, a smaller target group for potential intervention than the 22% with the metabolic syndrome in this group.

The individual metabolic syndrome variables were not predictive of 10 year CVD mortality in the high CVD risk men.

Discussion

In men with a low risk of fatal CVD, as estimated by the SCORE project risk equations [START_REF] Conroy | and the SCORE project group (2003) Estimation of ten-year risk of fatal cardiovascular disease in Europe: the SCORE project[END_REF], presence of the metabolic syndrome at baseline increased the chances of fatal CVD over the 10-year follow-up, using the clinical definition of the metabolic syndrome given by the NCEP-ATP III [START_REF]Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults. Executive Summary of The Third Report of The National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III)[END_REF]. This risk was related to syndrome abnormalities and not to the risk identified by the SCORE equation for CVD mortality, as the syndrome remained predictive after adjustment by the estimated CVD risk. The positive predictive values for fatal CVD in men using the waist circumference alone was 4.1% and for the metabolic syndrome 4.2%, with hazards ratios of 2.24 and 2.71 respectively;

the waist criteria provides a simpler alternative to the syndrome as screening could be targeted towards a smaller fraction of the population, 17% versus 22% of the men at low CVD risk. The high blood pressure, large waist criteria had an associated hazards ratio of 3.54, a positive predictive value of 5.3% and screened 13% of the low risk population: these two variables are readily available in general practice.

Limitations of the Study

Our study is limited by the small number of cardiovascular deaths. In contrast to other studies, we have limited the analysis to subjects between 50 and 69 years, as there were too few men with an estimated risk of fatal CVD deaths over 5% before 50 years of age and too few subjects over 69 years, thus there has been no extrapolation of the results to other age groups, based on few deaths in these age groups. Unfortunately we do not have access to cardiovascular morbidity in most of these DECODE populations. The CVD risk score developed for Europe is appropriate, but scores such as the Framingham risk equation should provide similar results, and would rank subjects similarly, although many of these score are for morbidity and not mortality. Of the men identified by the SCORE risk equation as being at high fatal CVD risk, 6.1% died of CVD, in contrast to the expected 5%. However, the SCORE equation is not country specific, and only stratifies according 10/10 to 'high' and 'low' risk countries. The data were also analyzed deleting the 44 men who were diabetic according to the 2-hour post-load glucose criteria. The hazards ratios were little altered.

A further limitation is the use of the NCEP-ATP III criteria for the definition of the metabolic syndrome, which we have already discussed [START_REF] Balkau | The incidence and persistence of the NCEP (National Cholesterol Education Program) metabolic syndrome. The French D.E.S.I.R. study[END_REF]. This definition was designed for clinical use, and our study was designed to provide practical answers. It was a consensus definition from an expert committee in the United States, where the blood pressure levels are lower than in Europe [START_REF] Wolf-Maier | Hypertension Prevalence and Blood Pressure Levels in 6 European Countries, Canada, and the United States[END_REF] and the waist circumferences are larger [START_REF] Balkau | The incidence and persistence of the NCEP (National Cholesterol Education Program) metabolic syndrome. The French D.E.S.I.R. study[END_REF]. Using the thresholds of the NCEP-ATP III syndrome, we classified two thirds of our population as having high arterial blood pressure. In almost all populations, the waist circumference criteria of the NCEP-ATP III screen more women than men. These thresholds were not chosen on the basis of CVD mortality, and given the higher rate of CVD in men, waist circumference thresholds which screen more men than women would seem appropriate. With better adapted thresholds, the waist circumference might provide a very convenient first screening tool, without the need for taking a blood sample. The syndrome criteria are not optimal, and indeed it would be preferable to have a continuous metabolic score rather than a dichotomous classification [START_REF] Hillier | Practical way to assess metabolic syndrome using a continuous score obtained from principal components analysis: The D[END_REF].

We have chosen to study only the NCEP-ATP III syndrome [START_REF]Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults. Executive Summary of The Third Report of The National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III)[END_REF], so that these results can be compared with other publications, most of which use this syndrome definition. This study is only of mortality as morbidity data were not available in all of the populations in this study. Further the follow-up is limited to 10 years. The metabolic syndrome may be a risk factor for a higher lifetime risk of cardiovascular consequences, and studying only mortality and for only 10 years, may limit findings on the utility of the metabolic syndrome. Altough Type 2 diabetes has been identified as a CVD risk equivalent to established CVD [START_REF]Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults. Executive Summary of The Third Report of The National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III)[END_REF], we have studied only one outcome of the metabolic syndrome in these analyses, fatal CVD and not progression to diabetes, which in the long term would have CVD consequences, although not necessarily yet within a 10-year period. [START_REF] Qiao | Predictive properties of impaired glucose tolerance for cardiovascular risk are not explained by the development of overt diabetes during follow-up[END_REF]. Using a 11/11 combined endpoint, diabetes and CVD events may have an important impact on the risk associated with the syndrome. Information on incident diabetes is not available in these populations. It should be noted, that these results are for European Caucasians aged 50 to 69 years, thus similar analyses are required in other populations and age groups to determine whether they can be generalized.

Other Studies

A previous analysis of the DECODE cohort [START_REF] Hu | Prevalence of the metabolic syndrome and its relation to all-cause and cardiovascular mortality in non-diabetic European men and women[END_REF] examined the risk associated with the metabolic syndrome, using adaptations of the WHO syndrome definition, and using various combinations of the abnormalities. Indeed, all syndrome definitions used were predictive of CVD mortality in men, in accord with our results.

One published study analyzed major CVD events, stratifying subjects on the 10-year CVD risk (fatal and non-fatal events) estimated from the Framingham score, with high risk being a > 20% probability of an event [START_REF] Girman | The metabolic syndrome and risk of major coronary events in the Scandinavian Simvastatin Survival Study (4S) and the Air Force/Texas Coronary Atherosclerosis Prevention Study (AFCAPS/TexCAPS)[END_REF]. Participants were from the placebo groups of two clinical trials (4S and AFCAPS/TexCAPS) on cholesterol lowering in high risk individuals, average age 58 years, and more than 75% were men. In men at low CVD risk, those with the syndrome had a higher cumulative incidence of a major coronary event than those without the syndrome, but this was not formally tested. In these two clinical trials, the metabolic syndrome conferred statistically significant age-adjusted hazards ratios of 1.5 and 1.4 for a major coronary event. In our study, the corresponding fatal CVD hazards ratio for the syndrome was higher in men at low CVD risk, being 2.7.

Data from the population based San Antonio Study [START_REF] Stern | Does the metabolic syndrome improve identification of individuals at risk of type 2 diabetes and/or cardiovascular disease?[END_REF] show that while the metabolic syndrome had an odds ratio of almost 4 for CVD events, after adjustment by the Framingham CVD risk score, this risk was reduced to non-significant 1.14 (0.76-1.71). These data were not analyzed by sex, and could well be compatible with our results, where the metabolic syndrome was only found to be predictive in the low risk men. ROC curves show that the Framingham risk score has higher sensitivity/specificity for CVD events than the metabolic syndrome, but this is not surprising given that the Framingham score has been specifically developed to include variables that best predict CVD events, in contrast to the metabolic syndrome which is a combination of potential risk factors, published by an expert committee.

In the ARIC cohort, more than 1000 incident events in men and women 45 to 64 years, over a follow-up of 11 years, were registered [START_REF] Mcneill | The metabolic syndrome and 11-year risk of incident cardiovascular disease in the Atherosclerosis Risk in Communities study[END_REF]. The metabolic syndrome was found to be predictive of CVD events, both in men and women, but as in the San Antonio Study, the metabolic syndrome did not improve the coronary risk prediction beyond the level achieved by the Framingham risk score.

The Hoorn Study, a European cohort of middle aged men and women, adjusting for the Framingham category reduced the hazards ratio of fatal and non-fatal CVD events associated with the metabolic syndrome, to 1.64 (1.11-2.44) in men and 1.17 (0.73-1.87) in women [START_REF] Dekker | Metabolic syndrome and 10-year cardiovascular disease risk in the Hoorn Study[END_REF].

Analyses need to be repeated in other studies with more subjects and so more CVD deaths and with an extended age range. The sensitivity of the results to the actual thresholds used in the metabolic syndrome definition should also be studied.

Conclusions

Our study has shown that the metabolic syndrome, as defined by NCEP-ATP III, is predictive of fatal cardiovascular disease, but only in the men with a low risk of fatal CVD. The syndrome provides no further predictive information in men at high CVD risk. Of note is the predictive value of the waist circumference with similar odds ratios to the NCEP-ATP III syndrome in the low risk men. It is a simple screening tool and it could be included as a risk factor in CVD risk scores.

  Data were collated and analyzed in the Diabetes and Genetic Epidemiology Unit of the National Public Health Institute in Helsinki, Finland.

Table 1 Characteristics (numbers, % and means (SD)) of 2790 non-diabetic men aged 50 to 69 years, according to sex. The DECODE Study.

 1

	Mean or	Range
	percentage	across centres

Table 2 Characteristics (mean (SD)) of the non-diabetic men aged 50-69 years, according to the estimated cardiovascular risk from the SCORE project equation and absence/presence of the NCEP-ATP III metabolic syndrome. The DECODE Study.

 2

		CVD risk over 10 years from the SCORE project equation
		< 5%		> 5%
		no syndrome	syndrome	no syndrome	syndrome
		20 deaths,	13 deaths,	57 deaths,	28 deaths,
		1110 men	306 men	941 men	433 men
	Age (years)	56 (5)	56 (4)	62 (5)	61 (5)
	Waist (cm)	92 (8)	102 (9)	93 (8)	103 (9)
	BMI (kg/m²)	25.6 (2.8) 29.0 (3.6)	25.8 (3.0)	29.1 (3.5)
	Systolic blood pressure (mmHg) 128 (15)	139 (14)	146 (21)	153 (18)
	Fasting glucose (mmol/l)	5.4 (0.5)	5.8 (0.6)	5.4 (0.5)	5.9 (0.6)
	Total cholesterol (mmol/l)	6.0 (1.1)	6.1 (1.1)	6.3 (1.1)	6.5 (1.2)
	HDL-cholesterol (mmol/l)	1.3 (0.3)	1.0 (0.2)	1.4 (0.3)	1.0 (0.2)
	Triglycerides (mmol/l)	1.3 (0.6)	2.4 (1.2)	1.4 (0.6)	2.5 (1.3)

Table 3 Hazards ratios (95% confidence intervals) of the 118 fatal cardiovascular events in 2790 non-diabetic men aged 50-69 year, according to the estimated cardiovascular risk from the SCORE project equation and absence/presence of the NCEP-ATP III metabolic syndrome. The DECODE Study.

 3

	CVD risk over 10 years from the SCORE project equation
		< 5%	> 5%
	no syndrome	with syndrome	no syndrome	with syndrome
	20 deaths,	13 deaths,	57 deaths,	28 deaths,
	1110 men	306 men	941 men	433 men
	No adjustments
	1	2.36 (1.17-4.74)	3.44 (2.06-5.73)	3.52 (1.98-6.27)
	Adjusting for centre
	1	2.44 (1.21-4.91)	3.65 (2.16-6.16)	3.97 (2.20-7.17)
	Adjusting for centre, age
	1	2.47 (1.22-4.99)	2.17 (1.20-3.93)	2.50 (1.31-4.74)
	Adjusting for centre, age and the estimated 10-year CVD risk
	1	2.42 (1.20-4.88)	1.70 (0.91-3.17)	1.87 (0.95-3.68)
	Dividing men according to CVD risk group
	No adjustments
	1	2.37 (1.17-4.76)	1	1.02 (0.65-1.62)
	Adjusting for centre
	1	2.52 (1.24-5.09)	1	1.10 (0.69-1.74)
	Adjusting for centre and age
	1	2.71 (1.33-5.51)	1	1.13 (0.71-1.80)
	Adjusting for centre, age and the estimated 10-year CVD risk
	1	2.26 (1.09-4.68)	1	1.08 (0.68-1.72)

Table 4 Hazards ratios of the 118 fatal cardiovascular events in 2790 non-diabetic men aged 50-69 years, according to the estimated cardiovascular risk from the SCORE project equation and the NCEP-ATPIII defined abnormalities. Adjustment has been made for age and study centre. The DECODE Study.

 4

		CVD risk over 10 years from the SCORE project equation
			< 5%	> 5%
	WAIST	WC < 102 cm	WC ≥ 102 cm	WC < 102 cm	WC ≥ 102 cm
		23 deaths,	10 deaths,	67 deaths,	18 deaths,
		1174 men	242 men	1060 men	314 men
		1	2.24 (1.05-4.76)	1	0.93 (0.54-1.58)
	BLOOD	SBP/DBP	SBP/DBP	SBP/DBP	SBP/DBP
	PRESSURE	< 130/85	≥ 130/85	< 130/85	≥ 130/85
		9 deaths,	24 deaths,	8 deaths,	77 deaths,
		576 men	840 men	192 men	1182 men
		1	2.67 (1.21-5.88)	1	1.82 (0.86-3.83)
	FASTING	Glucose	Glucose	Glucose	Glucose
	GLUCOSE	< 6.1 mmol/l	≥ 6.1 mmol/l	< 6.1 mmol/l	≥ 6.1 mmol/l
		25 deaths,	8 deaths,	62 deaths,	23 deaths,
		1195 men	221 men	1056 men	318 men
		1	1.73 (0.76-3.91)	1	1.05 (0.99-1.11)
	HDL-	HDL-C	HDL-C	HDL-C	HDL-C
	CHOLESTEROL	≥ 1.04 mmol/l	< 1.04 mmol/l	≥ 1.04 mmol/l	< 1.04 mmol/l
		15 deaths,	18 deaths,	59 deaths,	26 deaths,
		997 men	419 men	1020 men	354 men
		1	2.72 (1.35-5.45)	1	1.30 (0.81-2.09)
	TRIGLYCERIDE	TRIG	TRIG	TRIG	TRIG
		< 1.70 mmol/l	≥ 1.70 mmol/l	< 1.70 mmol/l	≥ 1.70 mmol/l
		21 deaths,	12 deaths,	53 deaths,	32 deaths,
		940 men	476 men	824 men	550 men
		1	1.29 (0.63-2.65)	1	0.96 (0.61-1.50)
	BLOOD PRESSURE & WAIST	SBP/DBP < 130/85 &/or WC < 102 cm	SBP/DBP ≥ 130/85 & WC ≥ 102 cm	SBP/DBP < 130/85 &/or WC < 102 cm	SBP/DBP ≥ 130/85 & WC ≥ 102 cm
		23 deaths,	10 deaths,	68 deaths,	17 deaths,
		1229 men	187 men	1077 men	297 men
		1	3.54 (1.65-7.59)	1	0.93 (0.54-1.59)
		TRIG	TRIG	TRIG	TRIG
	TRIGLYCERIDE	< 1.7 mmol/l	≥ 1.7 mmol/l	< 1.7 mmol/l	≥ 1.7 mmol/l
	& WAIST	&/or	&	&/or	&
		WC < 102 cm	WC ≥ 102 cm	WC < 102 cm	WC ≥ 102 cm
		29 deaths,	4 deaths,	78 deaths,	7 deaths,
		1299 men	117 men	1205 men	169 men
		1	1.91 (0.66-5.54)	1	0.69 (0.31-1.51)

Acknowledgements

We would like to thank Tony Fitzgerald for discussions on the analyses with the European SCORE equation.

This analysis has been carried out with the help of grants from Novartis Pharma AG, Basel Switzerland, Sweden; from Paulo Foundation and from Future Forum Research Grant 2004. The DECODE Study was initially funded by Novo Nordisk, Bagsvaerd, Denmark, Novo Nordisk Foundation 2005.

Organization

The DECODE Study (Diabetes Epidemiology: Collaborative analysis Of Diagnostic Criteria in Europe) was undertaken in 1997 upon the initiative of the European Diabetes Epidemiology Group.

Conflict of Interest

Legend to Figure :   Cumulative hazards of 10 year cardiovascular mortality in non-diabetic men aged 50 to 69 years, stratified according to the estimated cardiovascular risk from the SCORE project equation (10 year fatal risk of CVD </> 5%) and absence/presence of the NCEP-ATP III metabolic syndrome.

Note: the curves for the two groups of men with a high CVD risk score, with and without the syndrome, are superimposed, and that the scale for the hazards for women and men differ. The DECODE Study.