development

FIELD OF THE INVENTION

The invention relates to the field of diagnostics, especially medical diagnostics. More particularly, the invention is related to the prediction of susceptibility to cardiovascular and metabolic diseases, such as diabetes, insulin resistance, metabolic syndrome, atherosclerosis, heart failure, stroke, etc. Especially, the invention, is related to finding new diagnostic markers derived from the lipoprotein profile,

BACKGROUND

Cardiovascular and metabolic diseases often are partly caused by or accompanied by aberrations from the normal lipid metabolism. Especially serum low-density lipoprotein (LDL) cholesterol and LDL particle

concentrations are known to be positively associated with cardiovascular disease risk (Cromwell, W.C. and Otvos, J.D, 2004. Curr. Atheroscl. Rep.

6:381-387). and reaching low LDL cholesterol concentrations is a primary goal for therapy (Grundy, S.M. et al, 2004, Circulation, 110:227-239).

Technological advances allow the size spectrum of lipoproteins to be measured in increasing detail, creating" a detailed lipoprotein profile (e.g.

Caulfield, M. et al, 2008, Clin. Chem. 54:2088-2089). The detailed lipoprotein profile needs further interpretation and validation to be useful in the clinic. One example of interpreting this detailed data is the pooling of all LDL particles, and reporting an 'LDL particle number'. This diagnostic has proven to be successful at predicting cardiovascular risk (Cromwell and Otvos, supra). However, the detailed lipoprotein profiles contain more information that is discarded when only reporting LDL particles. A computational model that can characterize the state of metabolic processes affecting lipoproteins, based on the additional information contained in a lipoprotein profile, may be of added value in the clinic.

Lipoprotein metabolism of VLDL, IDL and LDL comprises three main processes. The lipoproteins are produced by the liver, then lose triglycerides through lipolysis and are finally taken up from the bloodstream by the liver. The lipolysis process occurs in extrahepatic tissues through lipoprotein lipase (LPL), which mainly affects the larger very-low-density lipoproteins (VLDL) (Olivecrona, T. et al., 1997, Proc. Nutr. Soe. 56:723-729), whereas in the liver lipolysis occurs through hepatic lipase (HL), mainly affecting the smaller IDL and LDL (Demant, T. et al., 1988, J. Lipid Res. 29:1603-1611). Measuring the rates of these processes is generally carried out using stable-isotope or radioactive-isotope tracer techniques. The most popular approaches perform kinetic tracer analysis of the large constituent protein apolipoprotein B to obtain lipoprotein fluxes (Parhofer, K. and Barrett. P., 2006, J. Lipid Res. 47:1620-1630). These techniques are costly and labor-intensive. A good characterization of the status of lipoprotein metabolism is, therefore, an extensive and difficult procedure at this time.

Thus, there is need for an easy-to-use lipoprotein characterization in order to assist with the diagnosis and or prediction of diabetes and/or cardiovascular disease.

SUMMARY OF THE INVENTION

Recently, a new computational model of lipoprotein metabolism ('Particle Profiler') was developed by the current inventor (van Schalkwijk, D. et al., 2009, J. Lipid Res. 50:2398-2411; WO 2009/151324). It appears that it is possible to use this model to derive parameter values that can be used to improve the prediction of risk for metabolic and cardiovascular diseases.

Therefore, the current invention relates to a method to improve the risk analysis of a subject for developing a cardiovascular disease or a (pre- ) diabetic condition, comprising including in the risk analysis lipoprotein metabolic ratios derived from the lipoprotein profile of said subject. Preferably, the risk analysis is performed via a multivariate analysis. Further preferred, the disease is a cardiovascular disease, preferably a disease selected from the group of atrial fibrillation, (congestive) heart failure, coronary heart disease, intermittent claudication, stenosis, thromboembolism, myocardial infarction, coronary insufficiency, angina, ischemic stroke, hemorrhagic stroke, ischemia, and peripheral artery disease.

More particularly, the risk analysis is based on one or more of the classic parameters age of the subject, sex of the subject, systolic and/or diastolic blood pressure, body-mass index, smoking behaviour, serum

cholesterol concentration and serum glucose concentration. In such a method, the lipoprotein metabolic ratios from the lipoprotein profile included in the risk r

analysis are- selected from the group of: prod ar

, TUT or parameters that are

' u.tiver J highly correlated therewith as indicated in Table 2; , '

ll.ilL or parameters A aJivor J

J„

that are highly correlated therewith as indicated in Table , r !LD!. parameters that are highly correlated therewith as indicated in Table 2;

k: ^LDL

r II. Di. or parameters that are highly correlated therewith as indicated in

Table 2 or parameters that are highly correlated therewith as

indicated in Table 2; or L LO!. or parameters that are highly correlated

it;

therewith as indicated in Table 2; and any combinations thereof, and

preferably at least two, preferably at least three, more preferably at least four and most preferably at least five of the lipoprotein metabolic ratios are included in the risk analysis.

In another embodiment, the present invention relates to a method according to the invention, wherein the disease is a (pre-)diabetic condition, preferably a disease selected from the group of diabetes, in particular diabetes type 2, insulin resistance, impaired glucose tolerance, metabolic syndrome, and obesitas. Preferably, therein the risk analysis is based on one or more of the classic parameters: sex of the subject, systolic and/or diastolic blood pressure, body-mass index, smoking behaviour of the spouse, serum HDL cholesterol concentration and serum glucose concentration and, optional, the HDL particle number and the VDL particle number, In this embodiment, the lipoprotein metabolic ratios from the lipoprotein profile included in the risk analysis are selected from the group of: or parameters that are highly correlated liver therewith as indicated in Table 3; or pa ameters that are highly

.O

correlated therewith as indicated in Table 3; or parameters that are

highly correlated therewith as indicated in Table 3; and any combinations thereof.

Further, the subject in any method according to the invention preferably is a human being.

Also part of the invention is the use of lipoprotein metabolic rations from the lipoprotein profile of a subject for improving the risk analysis of a subject for developing" a cardiovascular disease or a (pre-)diabetic condition. LEGENDS TO THE FIGURES

Figures 1-9. Step-by-step explanation of model development for liver-!ipolysis and uptake

For explanation, see text.

Figure 10. ROC curves of the cross-validated multivariate models for general cardiovascular disease, for the datasets indicated in table 6 of example 4,

Figure 11. Data use and generation during model development and model implementation.

During model development. Particle Profiler was used as indicated, below the vertical bar: pooled lipoprotein flux data was used for fitting the model to data of individual subjects, and the fitted model was used to generate lipoprotein particle flux data and lipoprotein metabolic ratios. The light blue area illustrates the usage of the model in its application for generating diagnostic markers for cardiovascular disease and diabetes. In that

application, Particle Profiler was applied to lipoprotein profile data, allowing the quantification of lipoprotein metabolic ratios that were used as diagnostic markers.

Figure 12 - Graphical representation of the VLDL

Performance diagnostic.

When applying the Particle Profiler model to a lipoprotein profile, the uptake / production and lipolysis / production ratios in VLDL was quantified. The information from these ratios was summarized in a single statistic taking the mean of these two ratios, which was visualized as a projection on the identity line. We propose the name VLDL Performance for this projection. It integrates information about production, lipolysis and uptake rates, but can be calculated without metabolic flux information, based on one detailed lipoprotein profile measured in one fasting blood sample.

Figure 13 - Receiver operating characteristic (ROC) curves for dyslipidemia These curves indicate how well a) single diagnostics and b) multivariate regression models distinguish dyslipidemic subjects from

normolipidemic subjects reported in a range of studies described in the text under example 3. The models in b) subsequently include LDLc. HDLc, TG and VLDL performance in cumulative fashion. This ROC curve indicates the sensitivity of the indicated diagnostics for identifying dyslipidemic subjects, when varying the acceptable false-positive rate. The further away from the 1-1 identity line, the bettor the diagnostic, For example, when not accepting false positives, the regression model including LDLc, HDLc and TG has a sensitivity of 66% (0.66), while additionally including the VLDL Performance diagnostic results in a sensitivity of 91% (0.91).

Figure 14 - The average VLDL Performance of various subject groups

Green lines with round ends are normolipidemic subject groups. Groups indicated with darker green were used for the ROC curve in figure 3, those indicated with light green were not. Red lines with crosses represent dyslipidemic subject groups used for the ROC curve. Groups are labeled as follows: 1) hypothyroid patients during T4 treatment; 2) subjects with small LDL peak size; 3 and 8) mixed hyperlipidemia; 4) hypothyroid patients before treatment; 5)kidney disease; membranous glomerulonephritis; 6) patients on HIV treatment; 7) kidney disease: focal segmental glomerulosclerosis. Blue lines with triangles indicate subject groups with specific genetic variant.. FDB: Familial Defective x poB ; FH: Familial Hypercholesterolemia ; S447X: specific single nucleotide polymorphism in the LPL gene. The data from these subjects was taken from the studies mentioned in the text under examples 2 and 3.

Figure 15 - VLDL Performance response to treatment Average VLDL performance response (on identity line) to atorvastatin, simvastatin and fenofibrate treatment in mixed hyperlipidemic patients. P- values for VLDL performance were calculated by the Wilcoxon rank-sum test. Bilz ei /. (2004, J. Lipid Res. 45 :174-185) atorvastatin: n=5, p=0.0925; Bilz fenofibrate: n=5, p=0.0()79; Forster et al (2002, Atherosclerosis 164:129-145) atorvastatin: n==9, p=0.0482; Forster simvastatin: n=ll, p=0.0006. All

treatments caused VLDL performance to move towards healthier values.

Figure 16 - ROC curves of the diabetes risk analysis ROC curves of the cross-validated multivariate models for the classic (black), classic & NMR (very light grey), Classic & NMR & ratios(l) (dotted grey), Classic & NMR & ratios (2) (grey) datasets.

DETAILED DESCRIPTION OF THE INVENTION

The computational model of lipoprotein metabolism called 'Particle Profiler ^' has been extensively described in van Sclialkwijk et al., 2009 (supra) and WO 2009/151324. The Particle Profiler model describes how lipoprotein production, lipolysis and uptake processes depend on lipoprotein size.

Equations for this size dependence cannot be derived mechanistically, since biological knowledge is not sufficiently detailed to allow for such a derivation. Biological knowledge does, however, provide clues as to how these functions should look in a general sense. These clues are mentioned in the 'biology paragraph van Sclialkwijk et al., 2009. and their interpretation is mentioned in the 'Conceptual Model' paragraph of each modelled process in the same article. Based on this information the Particle Profiler equations were

motivated. How this motivation translated into the Particle Profiler equations has been explained in the additional material of the article.

The Particle Profiler model as described in WO 2009/151324 and van Schalkwijk et al., 2009, was used with some modifications, as described below. The description and working example of the model as given on page 9, line 29, to page 29, line 10, of WO 2009/151324 is included herein by reference.

In the Particle Profiler model, the metabolic rate of a particle depends on its size. Figure 11 shows how in the model development phase, reported in the current invention, we chose to derive particle -based lipoprotein fluxes and lipoprotein metabolic ratios from previously published pooled lipoprotein flux data. This 'pooled, lipoprotein flux data ^'' includes particle concentrations and fluxes (production, lipolysis and uptake) in four size classes: VLDL1, VLDL2, IDL and LDL, Figure 11 also shows that the application of Particle Profiler to lipoprotein profiles, as reported in the current invention under Example 4, is not able to produce rticle -based lipoprotein fluxes, but only lipoprotein metabolic ratios. It is impossible to obtain the absolute fluxes, since the lipoprotei profile measurements are taken from a single blood sample and do not contain explicit kinetic

information. Still, the metabolic ratios show whether metabolic processes are well balanced or dysbalanced. Nevertheless, the lipoprotein metabolic ratios can advantageously be applied in the present invention.

In the model development phase, when using pooled lipoprotein flux data as input, the Particle Profiler model can calculate the average metabolic rate of particles in a certain size range of interest, for instance the VLDL size range, The model also distinguishes different metabolic routes, such as particle lipolysis through LPL or HL. It is impossible to measure these quantities directly, even with tracers. Instead, a feasible approach to technical validation is to calibrate the model with pooled lipoprotein flux data from genetically deficient subjects, and subsequently corroborate it with pooled lipoprotein flux data from a range of different normolipidemic and dyslipidemic subjects.

Calibration and subsequent corroboration with pooled lipoprotein flux data is the only available route of technical validation. The mathematical functions describing liver uptake and lipolysis needed further development compared with the original Particle Profiler model (as described in van Schalkwijk et al., 2009 (supra) and WO 2009/151324) for two reasons. First of all, for three out of sixteen previously analyzed subjects, the model was not able to reproduce the lipoprotein fluxes well. The deviation was mainly due to the uptake fluxes, suggesting that the mathematical functions used to model uptake processes were suboptimal, Secondly, a parameter identifiability analysis, using the covariance matrix produced by the

parameter fitting routine (data not shown), showed that detailed lipoprotein profiles, in contrast to lipoprotein kinetics data, did not contain enough information to fit the six parameters in the original model. Because of problems for future model applications to lipoprotein profile data, we decided to reduce the dimensionality of the model by one parameter to five parameters through simplifying the hepatic lipolysis function. Since the two mentioned issues relate to liver-related processes, we introduced new functions for lipoprotein attachment to the liver, and lipoprotein lipolysis and uptake by the liver,

The new model of liver-related aspects of lipoprotein metabolism describes the biological process as two phases, similar to the earlier model. In the first phase, the particle is attached to the liver, via either apoB- or apoE- related, mechanisms. In the second phase, particles attached through the apoB- related mechanism are directly taken up, whereas particles attached through the apoE-related mechanism can be either taken up or lipolyzed. The probability that a particle is taken up or lipolyzed depends on the size of the particle, with larger particles having a greater probability of being taken up instead of lipolyzed.

In our model particles can be processed by the liver in two ways. They can be directly taken up via an apoB-related mechanism . They can also be attached to the liver via an apoE-related mechanism, which can result either in particle uptake or lipolysis. The apoB-related uptake mechanism is modeled to have the same rate at all particle sizes, which therefore always equals ku. po . (see Fig. 1)

For apoE-related attachment to the liver we expect a pattern which first increases and then decreases with particle size. Furthermore, the initial increase should be gradual, so that the liver can gradually increase the lipolysis of smaller particles. The probability density function of the single parameter Rayleigh distribution we initially used (van Schalkwijk et al., 2009), met the first requirement, but not the second. Therefore, we now switched to the more general Weib ll distribution, and constructed a suitable one-parameter version of this distribution. This Weibull distribution is not interpreted as a probability distribution, but it rather describes the apoE related attachment rate at different particle sizes as a fraction (f _a ,apoE(d)) of the maximum. apoE related attachment rate (see Fig. 2). This leads to the following first candidate model:

eq, 1

One problem of the equation in this form is that its maximum value does not equal one. This is undesirable since we would like to introduce a parameter which represents the maximum liver attachment rate. This maximum rate should be reached at the peak of the modeled distribution (Fig, 3). Therefore we now first scale the Weibull probability density function with its maximum value, which can vary according to the parameter values. We can calculate the value of d at which this maximum is reached by equating the derivative hat:

eq. 2

By scaling the Weibull distribution with its maximum, its peak value always equals one, The second candidate model thus becomes: - α.αροεΧ ^α )

Next, the equation needs to be shifted horizontally to start at the smallest particle size at which liver attachment occurs (Fig. 4). The final model for the fraction of maximum apoE -related uptake thus becomes:

for d < d a,apoEm eq.

We can now calculate the apoE related attachment rate, by introducing a parameter representing the maximum liver attachment rate of the apoE-related process. (Fig. 5)

Since liver attachment includes an apoB -related and an apoE- related contribution (Fig. 6), we calculate the total liver attachment rate as follows (eq. 6): -id- e A

⁺ K,a _P eB for d≥d _afipo&

B J A B I

^■ A

OMPOB for d<d _i α,αροΒηνα in the apoB-related mechanism liver attachment is immediately followed by uptake, The apoE-related attachment mechanism can either be followed by lipolysis or uptake. The model for this last process does not include a pool of attached particles. The model rather considers that attachment is directly followed by either uptake or lipolysis. This is obviously a

simplification, but a necessary one since data are not available to parameterize a more detailed process. Because of this simplificatiori. we can state in terms of fluxes (J) that:

eq, 6 which can be rewritten in terms of pools (Q - dimension: # of particles) and rate constants (k - dimension: 1/t) to the following:

Q(d) · K _j to _r id) = Qui) ^■ k _Uiver id) + 0(d) ^■ k _uJiver (d) _{eq 7} and by dividing away the pools we get: k _lMver {d) + k _{u Jiwr} {d)

eq, 8

In order to model how the ratio between uptake and lipolysis in the liver depends on particle size, we apply the consideration that hepatic lipase mainly acts on smaller particles. This means that the fraction of particles taken up after liver attachment increases with increasing particle size (Fig. 7). To model this process we use the cumulative probability density function of the Weibuil distribution, leading to the following equation for the fraction of attached particles that is taken up by the liver instead of lipolysed ( fa ju.i m )

Now, we also need to take into account that in our model hepatic- uptake consists of two contributions, The first is that of apoB-related uptak which is constant irrespective of particle size. The second is that of apoE- related uptake, which does depend on particle size (Fig. 8). In the final

equation for liver uptake we combine the contributions of both processes:

1-e ujwr J for d>d ., .

k ^' ujive.

for d<d aooEnm ea. lO using the relation between hepatic attachment, hepatic uptake and hepatic lipolysis motivated above, we can now calculate hepatic lipolysis as follows (Fig. 9):

Model Calibration

The model equations contain model parameters that are allowed to assume different values for different patients and model constants that are fixed to the same value for all patients. The model constants contain the biological information that, for instance, allows the model to distinguish hepatic lipolysis from extrahepatic lipolysis. Therefore, it is very important that these constants have the correct values. The constants optimized here are: d V

hi , peak ' n iver ^{a p!} and ^G> ^ ^n,ln , which are related to HL lipolysis, liver uptake and LPL lipolysis (2 constants) respectively (see Table 1 for an

overview of all notations). The first two constants are new to the model, the last two were already present in the first version, hut arc now given new values. To estimate the model constants, one needs data from subjects in which particular processes stand out clearly. Below, we first describe what data we used to estimate specific constants, and thereafter we describe how the constants were estimated.

To estimate the HL-related model constant ^ ^ω ·ρ< ^:αΙί _f which indicates the lipoprotein particle size at which HL activity is highest, we used patients with lipoprotein lipase (LPL) deficiency. In these patients the only remaining lipolysis activity is due to HL. Data on lipoprotein metabolic fluxes in such patients came from Demant, T. et al., supra)

S„

To estimate the model constant " ^> ""' ^er . which helps to model the liver uptake rate at different lipoprotein particle sizes, subjects are needed in which uptake processes take place with least interference from lipolysis processes. By inspecting the kinetic data, we found that normolipidemic ApoE

s

3/3 subjects met these criteria best. Therefore, ¹ " ^iver was estimated using data on lipoprotein metabolic fluxes in ApoE 3/3 subjects from Demant, T. e al., 1991, J. Clin. Invest. 88:1490-1501.

To estimate model constants related to LPL lipolysis, subjects with the ApoE 2/2 genotype were used. Subjects with the ApoE 2/2 isoforra are known to have impaired uptake of large VLDL and chylomicron particles. Since VLDL particles can either be taken up by the liver or lipolyzed by LPL, an impaired uptake means that the LPL lipolysis process, that mainly takes place in. the VLDL size range, can be distinguished clearly. Also, the lipolysis of smaller particles was found to be impaired in ApoE 2/2 subjects (Demant, T. e al, 1991, J. Clin. Invest. 88:1490-1501), indicating a less effective hepatic lipase function, which should make the LPL activity even more clearly discern able, also for smaller particles. Therefore, the data, from subjects with the ApoE 2/2 phenotype were useful for estimating two model constants related to LPL: ^{σ a■} ·' ^?■ ' and " ^{Jp! mm} . Because in apoE 2/2 patients hepatic lipase function is inhibited, the model needed to be adjusted slightly. Wo

cl

allowed the \HL peak size' ( ^hl> - ^peak ) parameter to be optimized for each individual apoE 2/2 subject, which is otherwise constant for all subjects. In this way the model could better h andle the special condition of very low HL activity.

In order to determine the model constants via parameter fitting, a double-layered fitting routine was constructed. On the first layer, the algorithm searched for the optimal value for the model constant. The second layer of the routine fitted the parameters of the model at each selected constant value. Both layers used the Levenberg-Marquardt algorithm as implemented in MATLAB's nlinfit method of version 7.7.0 (R2008b) for fitting the constants and parameters respectively. The used error functions can be found in the methods section of the Example. In this way, the model parameters were estimated per individual, while the model constants were estimated for the w hole population, using a group of patients judged most suited for the determination of that constant.

We chose to fit the constants in the same order as they were discussed above: first hepatic lipase constants, then liver uptake constants, and finally LPL li ol sis constants. Each time, the newly found constant value was used in the process of fitting the subsequent constants. The order of fitting and the type of subjects, discussed above, were chosen in such a way that the constants that had not yet bee fitted exerted minimal influence on the constant being fitted. For instance, the LPL deficient patients used for determining the Hepatic Lipase constants have little LPL activity and little liver uptake activity related to the unknown uptake constants.

The model constants obtained from the optimization process are given in Table 1. The constants show that Hepatic Lipase activity is highest in particles around 31 nm in size, which is the 1DL and small VLDL2 size range. Instead, LPL lipolysis affects particles of approximately 25 nm (lower cutoff) and higher, but the large shape parameter ^{σ 1} indicates that the LPL rate very gradually increases with size, and reall becomes important for the larger VLDL2 and the VLDLl particles, which LPL is known to affect more. The translation into exact metabolic rates depends on the model parameters that differ for every subject (shown in Table 1),

Tabie 1 - Overview of state variables, variables, parameters and constants used in this description

State Variables - determine the system state dij nm Lipoprotein particle diameter in the ι-th step of a lipolysis cascade, in the j-th subclass of the size range covered by that cascade step

Particles * dL- ^■ Steady-state particle pool size in a pool with mean particle diameter dij

Vanables - specify processes and out ut

/ nm the radius of the subclass with average

diameter dij

^J l i ^d ij ) Particles * Particle flux into the pool with mean particle

dL-i * day i diameter dij due to extrahepatic lipolysis Particles * Particle flux into the pool with mean particle dLr ¹ * day- ¹ diameter dij due to hepatic lipolysis k id) day ¹ Particle size dependent extrahepatic lipolysis rate

k _a , d) day* Particle size dependent liver attachment rate

(attachment is followed by either lipolysis or uptake)

day ¹ Particle size dependent liver lipolysis rate

KuJ ) day ¹ Particle size dependent liver uptake rate

Molecules * Number of triglyceride molecules in a

article" ¹ lipoprotein particle with diameter dij

Q* Particles * Steady-state particle pool size in the size range dL- ¹ called *

day ¹ Particle size dependent liver uptake rate,

averaged per particle over the size range called k, day ¹ Particle size dependent extrahepatic lipolysis rate, averaged per particle over all particles in the model

Cardiovascular and diabetes risk prediction

When assessing the risk on the occurrence of cardiovascular diseases and metabolic syndrome or diabetes-related diseases, currently such a risk is determined by taking into account various clinical and behavioral parameters ('classical parameters' or 'classical markers'). For cardiovascular diseases such classical parameters are, for instance, the age of the patient, the smoking behavior (either the mere fact of being an (inhaling) smoker or the number of cigarettes per day, the systolic and/or diastolic blood pressure, the HDL cholesterol value (either the concentration or the particle number), the blood glucose concentration, the sex of the subject and the (blood pressure) medication.

These parameters have been assessed in long-term follow up studies, such as the Framingham Heart Study (FHS) (Wilson et al., 1998, Circulation 97:1837-1847; Wang et al, 2003, JAMA 290:1049-1056; D'Agostino et al, 1994, Stroke 25(l):40-43; D'Agostino et al., 2000, Am. Heart J. 139(2 I) 272-281; D'Agostino, 2008, Circulation 118(4):e86), where they have been found to have a predictive characteristic (see also the website dedicated to the FHS

(http://wwwiraminghamheartstudy.org/about/index.html). In the FHS the predictive value of these classical parameters on the development of

cardiovascular diseases have been investigated in a follow-up study over 10 years in length.

The inventors now have found that the parameters that can be derived from the Particle Profiler analysis are able to improve the predictions made on basis of the 'classical parameters' of risk of cardiovascular diseases, As isshown in the Examples (specifically Example 4) addition of one or more of the parameters in the multivariate risk analysis increases the predictive value for 'general cardiovascular disease'. 'General cardiovascular disease' is a composite endpoint, including coronary death, myocardial infarction, coronary insufficiency, angina, ischemic stroke, hemorrhagic stroke, transient ischemic attack, peripheral artery disease, and heart failure (see

http://www.framinghamheartstudy.org/risk/gencardio.html). It has been found that a fair and significant improvement in the result prediction can be achieved when 5 or 6 lipoprotein metabolic ratios derived from the Particle Profiler analysis (which we will refer to in continuation as !iporatios') are included in the multivariate analysis. The liporatios listed in Table 6 of 1ί

Example 4 are examples (although optimal) of parameters that can be used for the improvement of the prediction. Addition of further liporatios did not

.significantly alter the improvement value. Which liporatios to use was determined by calculating for the total set of parameters the improvement caused by adding a single liporatio to the 'classical parameter' set and choosing the one that performed the best. Then, the same was repeated for addition of a second liporatio on the prediction with the set of classical parameters plus the first liporatio, In the same way also the further liporatios were added.

However, although the liporatios given in Table 6 of Example 4 are the most optimal predictors, other liporatios sets of two, three, four, five, six or even more lipora tios are conceivable that would result in similar effects on the risk analysis. This is mainly due to the fact that there is a large amount of correlation between several of the liporatios that are calculated from the Particle Profiler lipoprotein profile. Thus, while the most optimal parameter

k ILDL _k „m.

k! ^or k ^r0T , 1 'Vliver

+

/ J ,

in . TOT ^» T I LDL . Accordingly, as a first

addition to the classical parameters any of the above listed alternatives could have been taken, and the addition thereof would still have a significant impact on the risk analysis. A similar correlation -group can also be established for the second liporatio

The below Table 2a gives the correlation groups for the parameter? that are mentioned in Table 6 of Example 4. Table 2a Correlation groups for Particle Profiler based lipoprotein metabolic ratios (liporatios) for use in risk analysis of cardiovascular disease.

J>

kroT

'-a, liver

ajiver

■ ,liver y liver "aJiyei

» /,,¾:.

'a.livcr J ^/c _a jiv _W y "...liver y Niivci y

J

J I !LDL (see 4)

Oliver

J LDL ll.DL LDL ( _k HDL Λ JLDL kr. DL kS ^I,L r,.!LDL J„

j " ^" ajiver JLDL ) I

According to a preferred embodiment of the invention, in the method of improving the risk analysis .for determining the risk of developing a cardiovascular disease, the additional liporatios (s) that can be added to the multivariate analysis is(are) selected from group 1 of the above table 2a. more preferable one from group 1 and one from group 2, more preferable one from group 1, one from group 2 and one from group 3. more preferable one from group 1, one from group 2, one from group 3 and one from group 4. more preferable one from, group 1, one from group 2, one from group 3, one from group 4 and one from group 5, and even more preferable one from each of the groups 1-6. It is to be understood, that 'group' as mentioned with respect to the above Table means both the optimal liporatio and the liporatios that are highly correlated therewith. Most preferable the liporatios that are combined with, the classical parameters are the parameters as provided in Table 6 of Example 4 (i.e. the optimal parameters from the above Table 2a).

An alternative algorithm, for discovering biomarkers has been based on the work of Salakoski, T. et al. (Co-Regularized Least-Squares for Label. Ranking, In: Preference Learning, ed. Hullermeier, E, and Furnkranz. J,, Springer Verlag, 2010. pages 107-123). For this calculation method, as is described in the Examples, log-transformed lipoprotein metabolic rates were used, and were found to be good predictors for cardiovascular disease. This led to the addition of two extra markers to the classical model, which markers are: In

Similar to what has been discussed above with respect to the non- log-transformed parameters, also for these log-transformed parameters highly correlated alternatives are listed in the below Table 2b.

According to a preferred, em bodiment of the invention, in the method of improving the risk analysis for determining the risk of developing a cardiovascular disease, the additional liporatios(s) that can be added to the multivariate analysis is(are) selected from group 1 of the above table 2b, more preferable one from group 1 and one from group 2. It is to be understood, that 'group' as mentioned with respect to the above Table means both the optimal liporatio and the liporatios that are highly correlated therewith. Most preferable the liporatios that are combined with the classical parameters are the parameters as provided in Table 12 of Example 6 (i.e. the optimal parameters from the above Table 2b).

Use of the additional liporatios derived from the lipoprotein profile in risk analysis, yields a more reliable prediction of the risk on cardiovascular diseases. Such a cardiovascular disease may be a disease selected from the group of atrial fibrillation, (congestive) heart failure, coronary heart disease, intermittent claudication, stenosis, thromboembolism, myocardial infarction, coronary insufficiency, angina, ischemic stroke, hemorrhagic stroke, ischemia, and peripheral artery disease.

According]}?, on basis of a multivariate analysis as shown in the Examples, a more reliable risk determination of the occurrence of a

cardiovascular disease in a subject in the near future can be given. Of course, an improved risk calculation is of importance for determining the treatment or diet of such a subject.

In another embodiment of the invention, lipoprotein metabolic ratios from the lipoprotein profile such as calculated by the Particle Profiler system (liporatios') may also be advantageously used to improve the prediction for diseases related to the metabolic syndrome, such as diabetes, especially diabetes type 2, obesitas, insulin resistance, or any other pre -diabetic condition (see Example 5)

In this case the 'classical parameters' differ slightly from the classical parameter set as developed for cardiovascular diseases. The classical set for (pre-)diabetic conditions comprises: the glucose level in the blood, the body mass index (BMI), smoking behaviour of the spouse of the subject, the sex of the subject, the HDL cholesterol value and the diastolic blood pressure. This set may be completed with the HDL and VLDL particle number.

Now, as shown in Example 5, addition of one, two, three or more liporatios from the Particle profiler system significantly improves the general diabetes risk prediction from a multivariate analysis based on the classical parameters.

Again, as discussed, above for cardiovascular disease risk prediction the parameters as given in Table 9 of Example 5 are optimal parameters, but they can be replaced by highly correlated alternatives as given in the below Table 3. Table 3. Correlation groups for Particle Profiler based lipoprotein metabolic ratios (liporatios) for use in risk analysis of diseases related to metabolic syndrome.

According to a preferred embodiment of the invention, in the method of improving the risk analysis for determining the risk of developing a diabetic condition, the additional liporatios(s) that can be added to the multivariate analysis is (are) selected from group 1 of the above table 2, more preferable one from group 1 and one from group 2, more preferable one from group 1, one from group 2 and one from group 3. Most preferable the liporatios that are combined with the classical parameters are the parameters as provided in Table 9 of Example 5 (i.e. the optimal parameters from the above Table 3) Use of the additional parameter(s) of the lipoprotein profile in risk analysis yields a more reliable prediction of the risk on (pre-)diabetic

conditions. Such a (pre-)diabetic condition may be a disease selected from the group of diabetes, in particular diabetes type 2, insulin resistance, impaired glucose tolerance, metabolic syndrome, and obesitas. It is thus clearly shown in the present invention that parameters (liporatios) that are derived from the Particle profiler system can be applied, for improving the risk analysis for cardiovascular diseases and for (pre-)diabetic conditions.

It goes without saying that the computations that are needed for the claimed method best can be done with the help of a computer program. Such a computer program may be a stand-alone program, or it may be integrated in the apparatus and program that is used for analyzing the sample of the patient. This means that also part of the invention is a program that is executable by a computer. In such a program the Particle Profiler data are introduced, or - if this would be found more advantageous, the program can also provide the actual measurements on the blood sample - and the above- discussed lipoprotein metabolic ratios as given in Tables 2a, 2b and 3 can be calculated. Next, these parameters will be included with the results of the other parameters that have been measured or obtained (other parameters as mentioned in Tables 6, 9 or 12 in the Examples) Thus, the invention comprises a computer program product comprising a program of instructions for a programmable computer that, when executed by the computer, causes the computer to perform a method to improve a risk analysis of a subject for developing a cardiovascular disease or a (pre-)diabetie condition, comprising calculating lipoprotein metabolic ratios from a lipoprotein profile of said subject and including these lipoprotein metabolic ratios in the risk analysis. Computer program product according to claim 1 said lipoprotein metabolic ratios are selected from the group of: or

parameters that are highly correlated therewith as indicated in Table or parameters that are highly correlated therewith as indicated in

Table 2a; or parameters that are highly correlated therewith as k! ^w - indicated in Table 2a; or parameters that are highly correlated

therewith as indicated in Table 2a; or parameters that are highly

HIM correlated therewith as indicated in Table 2a; or or parameters that

are highly correlated therewith as indicated in Table 2a; or any combination thereof; inj | or parameters that are highly correlated therewith as k ^LDL

J

indicated in Table 2b; in or parameters that are highly

correlated therewith as indicated in Table 2b, or any combinations thereof; or or parameters that are highly correlated therewith as indicated in / u, liver J

Table S; or parameters that are highly correlated therewith as

indicated in Table 3; or parameters that are highly correlated

therewith as indicated in Table 3; and any combinations thereof

Model Parametrisation; Overview

The model equations have been parameterized as follows: Production: no fitted parameters (eq, 1&2 in van Schalkwijk et al, 2009, supra)

The Jm ^e s are based directly on the dataset being fitted.

Extrahepatic lipolysis: 1 fitted parameter (eq, 4 in van Schalkwijk et al. 2009, supra)

ki,max maximum rate at which extrahepatic lipolysis takes place 2 fixed model constants:

di,min minimum size at which extrahepatic lipolysis occurs σ' shape parameter for extrahepatic lipolysis

Liver attachment, lipolysis and uptake: 5 fitted parameters (eq, 6&10) ka.amEmax maximum, rate at which liver binding mediated by apoE takes place

ka, poB rate at which liver binding mediated by apoB takes place ^ shape constant for liver binding mediated by apoE

B shape parameter for liver binding mediated by apoE

^G "·' ^' "-·" shape parameter describing how the fraction of liver attachment which is taken up (instead of lipoiyzed) varies with particle size.

2 fixed model constants ^ό u j ⁱ ver sh e constant describing how the fraction of liver attachment which is taken up (instead of lipo!ized) varies with particle size.

d ,apoKmin minimum particle diameter at which liver binding mediated by apoE takes place

Triglyceride loss during !ipoiysis (eq 8 in van Schalkwijk et al., 2009. supra)

1 fixed model constant

¾ fraction of triglycerides lost at each lipolysis step

Model reparameterisation for fitting of flux data

Using the parameters specified above, the fitting routine had difficulty to find the global minimum, mean square error. In order to improve its performance we specified a re arametri zation, specific for the data type used herein. This allows the fitting routine to find a minimum without difficulty.

ki,max maximum rate at which extrahepatic lipolysis takes place (unchanged from original model)

B shape parameter for liver bindin mediated by apoE. (unchanged from original model) ujiver shape parameter describing how the fraction oi liver- attachment which is taken up (instead of lipolized) varies with particle size,

(unchanged from original model.)

h . poB the liver attachment rate due to apoB-related processes (unchanged from original model)

kpeak the total rate of all processes at the particle size at which hepatic lipolysis is at its peak

Fixed model constant

dhi,peak Size at which hepatic lipolysis is at its peak The new parameter is specified as follows;

kpeak — k _t Hver(dkl,p ak) + kl(dkl,pcak) a. 12

This specification of parameters may lead to problems in the fitting routine in specific cases, when the boundary values of processes are reached. Therefore, during the parameter conversion process from fitted parameters to parameters for model calculation, the following fitted parameters were dynamically set to their boundary value. This procedure means that a parameter is only set to its boundary value if necessary, otherwise it is fitted normally.

Condition: ^~ ">'°» '·""

Set bounds: ^ ⁼ * _ta ^o + °-°°«"

25

Condition:

σ

Set bounda

Condition: ¹ , liver o . ooooo i

Set boundary:

Size classes

The size range of each size class has been estimated as follows, modified from [311: Table 4. Size ranges of classes of lipoproteins

Subtraction Minimum size Maximum size

LDL 5 25.0

IDL 25.0 30.0

VLDL2 30.0 36.0

VLDL1 36.0 60

Error function

The nlinfit routine calculates a sum of square difference between data points and model predictions. Before entering into this routine the data was scaled a) to correct for different units of pools data and flux data and b) to indicate the relative importance of each data point. This adjustment is specific for the type of data used. Data and model predictions were divided by the following scaling factors;

Table 5. Scaling factors for Particle profiler model.

The lower weights of the larger particle pools give them more importance in the fitting routine. This is desirable since these pools are also important to estimate the rate of the fluxes correctly.

To indicate the error value between the data and the model fit a percentage error was defined. This score was not used for model fitting, only for reporting an intuitive error score. It takes into account the number of dat points for pools, uptake and lipolysis and the higher importance (double of th flux total) of the pool sizes; they are most important for parameter estimation. It is given by the following formula;

where E stands for error value, Q indicates the pool size, superscript d indicating the data and m the model fit; J sta nds for a flux, superscripts d an m as before, I indicates lipolysis, u indicates uptake. Subscript i indexes the different data points of each lipolysis size class, i.e. LDL, IDL, VLDL2 and

VLDL1.

CCoonnvveerrssiioonnss

TThhee d daattaasseettss ooff PPaacckkaarrdd eelt a aiZ.. ((22000000,, JJ.. LLiippiidd RReess.. 4411 ::3300oo--331188)),, DDeemmaanntt e ett a all. ((11999933,, JJ.. LLiippiidd RReess.. 3344 ::114477--115566 ;; 11999911,, JJ.. CClliinn.. IInnvveesstt.. 8888 ::11449900-- 11550011)),, aanndd BBiillzz eett «a^l.. ( (22000044,, JJ.. LLiippiidd RReess.. 4455 :: 117744-- 118855)) ccoonnttaaiinn eessttiimmaattiioonnss ffoorr tthhee lliippoopprrootteeiinn ppoooollss ooff tthhee vvaarriioouuss ccllaasssseess iinn mmgg,, aanndd ttuurrnnoovveerr ssppeeeeddss iinn ppoooollss ppeerr ddaayy.. TThheessee aarree ccoonnvveerrtteedd ttoo ppaarrttiiccllee ccoonncceennttrraattiioonnss aanndd ppaarrttiiccllee fflluuxxeess rreessppeeccttiivveellyy.. TThhiiss nneeeeddss tthhee aassssuummppttiioonn tthhaatt oonnllyy AAppooBB-- 110000 iiss pprreesseenntt oonn lliippoopprrootteeiinn ppaarrttiicclleess iinn tthhee ffaasstteedd ssttaattee,, wwhhiicchh iiss rreeaassoonnaabbllee ggiivveenn tthhaatt aappooBB-- 4488 iiss pprroodduucceedd bbyy tthhee iinntteessttiinnee mmaaiinnllyy p poossttpprraannddiiaaiillyy.. iq. 14

where n is the number of lipoproteins, MAPOB-IOO the molar mass of ApoB- 100 and Vb!ood the blood volume of an individual person (taken to be 5 L).

Example 1

Comparison of new model with model, described in van Schalkwijk et al, 2009 and WO 2009/151324. With the new model equation and settings, a first test examined whether the results of the model validation in our first paper still hold. For this test, the subjects reported by Packard et al. (Packard, C.J. et ah, 2000, J. Lipid Res. 41:305-318) were fitted with the improved model and the results the results were compared with those from the first model implementation. In the first implementation, the model reproduced a shift in 'LDL peak size', which was independently measured. The model analysis also identified credible changes in relevant biological processes between groups with differing 'LDL peak size'. For the new model, we judged how well the data was fitted, whether the shift in 'LDL peak size' was still reproduced by the model, and whether the model still identified similar differences in biological processes between groups with differing 'LDL peak size'.

The model with optimized constants and one free parameter less than in the first implementation, reproduced the data from Packard et al, well. The overall fit error, defined in Schalkwijk et al,, 2009, was 7.3% ± 3,6%, compared to a 7,2% ± 4.5% error in our first paper. In Schalkwijk et al., 2009, the model calculated a difference in LDL size of 4.2 am between subjects with phenotype 'A' (large LDL particles) versus phenotype ' ^' B' (small LDL particles). This LDL size difference was significant, with a Kruskal-Wallis -value of 0.026. In the new implementation we saw a similar difference, although with 1.9 nm it was less pronounced. The Kruskal-Wallis test indicated a trend, with p=0.089. The most likely cause of this difference is the description of hepatic lipolysis, which lost one free parameter in the new model. This conjecture was confirmed by studying the difference in metabolic processes between subjects with

phenotypes 'A' and 'B' from Packard et al., as analyzed by our initial model versus the new implementation. The latter are shown in table 2. As observed earlier (Schalkwijk et al., 2009), we saw differences in the average particle lipolysis rate in VLDL 1 and VLDL 2, and in the average particle uptake rate in LDL between 'A' and. 'B' phenotypes. In contrast to our first study, no differences between the two phenotypes were found for HL lipolysis in LDL, Instead differences were found in uptake of IDL particles and LPL lipolysis of VLDL and IDL. For particle age, similar differences between 'A' and 'B' phenotypes were found in LDL, VLDL2 and VLDLl, as well as an additional difference in IDL age. For particle size, differences between phenotypes were found for LDL and IDL. and for the new implementation an additional difference in VLDLl particle diameter was found. Overall this comparison indicates that the new implementation made the model less sensitive to changes in LDL metabolism, but increased its power to identify changes in LPL lipolysis in the VLDL and IDL range.

Example 2

Model corroboration

Particle Profiler calculates metabolic process rates averaged per particle, and distinguishes between HL and LPL lipolysis. Because these quantities cannot be measured directly, the best way of validating the model is through corroboration. Patients with different metabolic conditions need to be modeled equally well. Therefore, we applied Particle Profiler to lipoprotein kinetics data from the following studies:

Demant, T. et al„ 1993, J. Lipid Res. 34:147-156

Demand, T. et al. _t 1991, J. Clin. Invest, 88:1490-1501

Packard, C. et al., 2000, J. Lipid Res. 41:305-318

James, R. et al., 1989, J. Lipid Res. 30:159-169

Demand, T. et al., 1996, Am. J. Physiol. 270:E1022-E1036

Demand, T. Et al., 1998, Kidney Int. 54:2064-2080

Lundahl, B. et al., 2006, Am. J. Physiol. Endocrinol. Metab. 290:E739-E745

Schmitz, M. et al., 2001, J. Acquir. Immune Defic. Syndr. 26:225-235

Bilz, S. et al., 2004, J. Lipids Res. 45: 174-185

Forster, L. et al., 2002, Atherosclerosis 164:129-145

Packard, C. et al., 1993, J. Clin. Endocrinol. Metab. 76:1209-1216 ab

In these studies the lipid metabolism data of subjects with a wide range of dyslipideinias that the model had not yet analyzed before were provided, We inspected whether the model was able to fit data from all of these studies well. If successful, this indicates that the biology incorporated in the model in the form of mathematical equations is adequate to describe the measured experimental data, or in other words that the model is consistent with reality.

The overall fit error for the data from the different lipoprotein kinetics studies was 10.4% with a standard deviation of 6.5%. The highest errors were found when analyzing data from Demant et al. 1998, where the fit error was 20.1%±6.4%. Many subjects in this study, including the controls, had a high VLDL2 pool that our model was unable to reproduce in conjunction with the reported flux values. Without these subjects, the average fit error was

8.8%±5.0%.

Example 3

Lipoprotein, metabolic ratios for VLDL metabolism

Since overproduction of large VLDL particles is an important characteristic of the atherogenic lipoprotein phenotype (Austin, M. et al., 1990, Circulation 82:495-506), we first examined VLDL metabolism.. The only current clinical marker reflecting VLDL is total plasma triglycerides, but this marker also includes triglycerides in chylomicrons, IDL, LDL and HDL, The marker introduced here relates more specifically to VLDL.

Based on Particle Profiler, we derived ratios between hepatic VLDL uptake and production, and between LPL-related VLDL lipolysis and production.

Since the model calculates the metabolic rates of VLDL at each particle size, this complex information needs to be integrated into a single value. Therefore, we calculated three ratios of metabolic rates of a VLDL particle. These are ^■■ —"· ,— , and VLDL performance, whose matheniatical definition can

/ J

^ p,VLDL ° p,VLDL

found below. A schematic introduction can be found in Figure 12. When referring to the 'VLDL metabolism ratios', we refer to these three ratios.

-j-PwT

The VLDL uptake - production ratio can be calculated from, modeled

J p, VLDL

values as follows:

WL

" ujiver

eq. 15

where k _u ,Hver(d:j) is the hepatic uptake rate, and Q . d, _.; ) is the concentration of particles in the subclass with average diameter di . The meaning of subindices i and j relates to the position of the subclass in the lipolysis cascade, which is explained in van Schalkwijk et al. 2009, under lipolysis cascades'. QVLDL and Jp. VLDL axe the total concentration of VLDL particles and total VLDL production influx respectively, where VLDL covers the size range from da=30 nm to db ^~ 80 nm.. R is the linearly interpolated small remainder for the boundary subclasses, which partially fall in the selected range; where d„ e \d, ,— d. ^r , , d, , -I-— d' , 1

(eq. 16),

wherein d , represents the radius of the subclass with average diameter di, The ratio between LPL-related lipolysis and production in VLDL (— ) is p,VLDL defined analogously, by replacing A _u ,„,,,, (fl, ,,) in equations 4 and 4a by ki(dij).

To show in a single value how efficiently produced VLDL particles are metabolized, we introduce the 'VLDL performance' diagnostic, which is the average of the previous two ratios.

I VLDL yWL

^u jiver ^ ^K i

n _r ,- ° J D,VWi. ^u J p,V!.D!.

V LDLperfor mance =— ^: ——

^* 2

Both ratios and VLDL performance have the dimension volume * particles- ¹ .

Figure 12 graphically shows how VLDL performance and the two ratios are related, and how different disturbances in VLDL metabolism affect VLDL performance.

General dyslipidemia

In order to obtain an indication of the clinical relevance of our new markers for VLDL metabolism, we applied the Particle Profiler model to a range of published studies with pooled lipoprotein flux data obtained in dysiipidemic subjects. In nearly all these studies, a group of healthy subjects and a group of patients showing a specific type of dyslipidemia were investigated and compared. Our pool of dysiipidemic subjects was defined as all the subjects that were considered to be 'dysiipidemic' in each study. To be included in our analysis, the studies also had to report data of standard clinical chemistry for comparison with our new markers. The set of healthy subjects included normolipidemic control subjects from studies by James et al. (supra) arid

Demant et al. (1998 and 1998, supra), apoE 3/3 subjects from Demant et al. 1991 (supra), phenotype 'A' (large LDL particle size) subjects from Packard et al. (2000, supra) as well as all subjects from Limdahl et al. (supra). The set of dysiipidemic subjects included two subject groups showing mixed dyslipidemia prior to treatment by Bilz et al. (supra) and Forster et al. (supra), kidney patients from Demant et al (1998, supra), hypothyroid subjects with and without T4 therapy from Packard et al, (1993, supra), HIV treatment- associated hyperlipidemic subjects from Schmitz et al. (supra) and phenotype 'B' subjects, with small LDL particle size, from Packard et al. 2000. The latter study was also included in our first paper (van Schalkwijk et al, 2009).

We tested whether Particle Profiler-derived VLDL performance was different for normolipidemic versus dyslipidemic subjects. This test also examined the difference in VLDL performance in relation to differences in triglycerides, HDL cholesterol and LDL cholesterol. These differences were expressed as the ability to correctly predict the known normolipidemic or dyslipidemic state from the diagnostic parameters. The test consisted of two phases: first the predictive power of each diagnostic separately, then the predictive power of multivariate models. For the multivariate models we performed logistic regression, subsequently adding LDL cholesterol, HDL cholesterol,

triglycerides and VLDL performance as predictor variables. The diagnostic accuracy, was quantified using ROC curves (Obuchowski, N., 2005, AJR Am. J. Roentgenol. 184:384-372). We used both the Area Under the Curve (AUG) and Partial Area Under the Curve statistics (pAUC - for false positive rates < 0.2) to quantify the predictive power of each separate diagnostic, and of each multivariate regression model.

The new VLDL performance marker clearly differed between normolipidemic and dyslipidemic subjects. Figure 13a shows ROC curves that describe how well LDL cholesterol, HDL cholesterol, triglycerides, and VLDL performance distinguished normolipidemic from dyslipidemic subjects. Figure 13b shows ROC curves of multivariate regression models that successively incorporate these diagnostics for making the same distinction together. Table 3 shows the partial area-under-the-curve (pAUC) and area-under-the-curve AUG values, indicating diagnostic power for dyslipidemia, for each of the regression models. The table shows that VLDL performance distinguished normolipidcmics better from dyslipidemics than the routine clinical chemistry parameters. Also, VLDL performance improved the distinction when used in combination with LDL cholesterol, HDL cholesterol and triglycerides. When accepting no false positives, the model including VLDL performance had a 91% sensitivity for correctly identifying dyslipidemic subjects, versus a 67% sensitivity when using only triglycerides, HDLc and LDLc. Therefore, VLDL performance had additional value for distinguishing dyslipidemic from normolipidemic subjects compared to standard diagnostics.

Dyslipidemic subgroups

Next, we examined the average value of our VLDL-related diagnostic parameters for each of the studied subgroups. This comparison included subject groups for which no standard clinical chemistry parameters were available (normolipidemic subjects from [16-21]), and subject groups with specific genetic disorders. These genetic disorders include LPL -/ ^' - [15], apoE 2/2 [16], apoE 4/4 [16], homozygous familial hypercholesterolemia [18], homozygous familial defective apoB [28], and S447X [29J, a single nucleotide polymorphism in the LPL gene.

Figure 14 shows the average VLDL metabolism-ratios for all included subject groups. The figure clearly indicates that the normolipidemic groups (green and light-green lines) had. a higher VLDL performance (projection onto the identity line) than dyslipidemic groups. Interestingly, this mainly seems to be due to an increased LPL lipolysis - production ratio in VLDL, although the liver uptake - production ratio in VLDL is generally also higher. In the dyslipidemic patients, the VLDL ratios were lower to a different extent. Hypothyroid patients on T4 treatment (marked with T) seemed to have an improved VLDL performance with respect to the untreated patients (marked with '4'). Patients with small LDL particles showed a relatively light dyslipidemia, whereas mixed hyperlipidemia was associated with different degrees of dyslipidemia ('3' and '8'). Kidney patients, hypothyroid patients and HIV-treated patients fell in between the mixed hyperlipidemias. The patients with genetic deficiencies showed up at the expected locations. LPL deficient patients had the lowest VLDL performance, and also the S447X polymorphism in this gene negatively effected VLDL performance. ApoE 4/4 subjects that are known to display a good VLDL clearance, showed up together with the normolipidemics, whereas apoE 2/2 subjects, known to have impaired VLDL clearance, showed up as slightly dyslipidemic.

Response to treatment

A diagnostic's clinical usefulness increases if there are treatment options when the diagnostic indicates illness. Therefore, we investigated how our VLDL- related diagnostic parameters respond to treatment. For this purpose we used data, on atorvastatin and fenofibrate treatment in mixed dyslipidemic subjects from Bilz et al. . and atorvastatin and simvastatin treatment in mixed dyslipidemic subjects from Forster et al.. All these studies contain lipoprotein kinetics data at baseline and after each treatment, which we used as input for Particle Profiler.

Figure 15 shows how the VLDL metabolism diagnostics responded to treatment in mixed dyslipidemic patients. Fenofibrate and simvastatin clearly raised VLDL performance values. The effect of atorvastatin was borderline significant in the study by Forster et al. , while the study by Bilz et al. had too few subjects to distinguish this effect. Therefore, we conclude that fenofibrate and simvastatin have a stronger effect on VLDL performance than

atorvastatin.

Example 4

Lipoprotein metabolic ratios improve cardiovascular risk prediction.

The Framingham Risk score predicts cardiovascular risk based on six varables: age, diabetes, smoking, treated and untreated systolic blood pressure, total cholesterol, and HDL cholesterol, Newer lipoprotein

measurement methods have attempted to improve risk prediction by quantifying lipoprotein subclasses by size [NMR, HPLC, AF4, ion mobility] or density [VAP] range. The diagnostics that are most often derived from these data are LDL and HDL particle number , although other multivariate measures have been proposed,

Recently, we have developed a computational model to analyze measured lipoprotein subclass profiles in terms of the underlying metabolic activity. The model can calculate ratios of lipoprotein metabolic processes from a single lipoprotein profile measurement . Since metabolic disorders are at the basis of cardiovascula disease, we hypothesized that lipoprotein metabolism ratios can improve cardiovascular disease prediction. We evaluated this hypothesis for subjects from the Framingham offspring cohort.

METHODS

Study Sample and Risk Factors

In this study we used subjects from the Offspring cohort in the Framingham Heart Study (FHS) (see www.framinghamheartstudy.org).

Subjects were included when they had no history of cardiovascular disease, gave written informed consent for general research use, had complete NMR lipoprotein profiles recorded, and had a complete record of classical cardiovascular risk factors.

Computational Modeling

We applied the Particle Profiler computational model to the NMR lipoprotein profiles. All lipoprotein metabolic ratios can be expressed by the following general expressions: . range.

wherein ΜΦ™** i _nf licates the particle size dependent rate of the process denoted by rateprocess, averaged per particle over the size range denoted by range, wherein rateprocess is one of the following processes: Ipl (LPL-related lipolysis), hi (HL-related lipolysis), I (total, lipolysis, sum of LPL- and HL-related lipolysis), u iver (liver uptake), or a,liver (liver attachment) and wherein range is one of the following size ranges: ILDL (IDL and LDL size range, 5-30 nm in the model), VLDL (VLDL size range, 30-80 nm in the model) or TOT (complete modeled size range, 5-80 nm in the model). Please note that the model does not include HDL, so these particles are not included in the smaller size ran e. j _nc i _ca t _es he particle flux denoted by fluxprocess into the size range denoted by range, wherein fluxprocess is one of the following processes: prod (direct production from the liver) or in (total influx due to both production and lipolysis of larger particles) and wherein range is one of the size ranges mentioned above.

The input dataset for constructing the multivariate prediction model consisted of all ratios indicated by expressions 1 , 2, and 3. Because of the large number of zero entries, ratios with ^{' lpi} or P ^{MA> LLJ} -' ^L in the denominator were excluded.

In addition, several averages of ratios were constructed, of the form: ramge I, r mge

raVAirrowsA "raiep'-oc

jlwtprocest,n ge fluxpnxxx, tmxr

9

wherein rateprocessA is one of the following processes: Ipl, hi, or ; rateprocessB is either a,liver or u, liver. All other symbols are defined as

J

described above. Ratios including ^' v ^xo& -- ^{, DL} were excluded, because of the large number of zero entries. These expressions resulted in 124 lipoprotein metabolic ratios from expressions 1 , 2, and 3 and 30 from expression 4, which totalled 154 lipoprotein metabolic ratios.. We calculated ratios of all modeled processes (lipoprotein production, total lipoprotein lipolysis, HL lipolysis, LPL lipolysis, liver lipoprotein attachment, liver lipoprotein uptake) in each of three sets of lipoprotein size ranges (VLDL through LDL, VLDL only, IDL through LDL).

Outcomes

Subjects who experienced a cardiovascular event, as defined by the Framingham study, up to 10 years after the NMR measurement, were designated as 'cases', others as 'controls'.

Statistical Analysis

We used multivariate logistic regression to correlate predictor variables with the CVD outcome. We grouped predictor variables into three sets: 1. classical cardiovascular risk parameters, 2. direct lipoprotein profile - based parameters, and 3. Particle Profiler-based lipoprotein metabolic ratios (liporatios); a complete overview of the variables in these sets can be found in the below table 6:

We constructed multivariate models using set 1, and the combinations of sots 1 and 2, and of sets 1. 2, and 3.

We constructed the multivariate prediction model in two phases. In the first phase, the variables that contributed most to improving the area under the ROC curve {Obuchowski, 2005 supra} were added to the model in a stepwise fashion, until the increase in the area under the ROC curve when changing the predictor variable set of the model equaled zero. In the second phase, the constructed model was cross-validated using 10-fold Venetian blind crossvalidation, and the variable that showed most variation in the regression vector was removed through backward elemination. After the removal of a variable, the cross-validation was repeated. Variable removal was stopped Table 8. Variables included in final multivariate mocleis.

when all variables were stable within the model (95% confidence interval of the regression coefficient did not pass through zero) or when removing more variables would amount to completely eliminating a classical risk factor from the model (for instance, there would be no variables with blood pressure information left).

For the combined sets, two alternatives for the first phase were used: one started the stepwise procedure from scratch, and the other started the stepwise procedure from the final cross-validated model from set 1. All analyses were carried out in Matlab version 7.7.0 with, statistics toolbox version 7.0 and PLS toolbox version 5.0.3.

The multivariate predictions of CVD risk were compared using area under the cross-validated ROC curve statistics, using the method by de Long {DeLong, 1988 1021 /id} and a binomial exact test, calculated in McdCalc, version 11.4.4.0.

RESULTS

Baseline Characteristics

Of the 2142 subjects in the general research use assent group in which NMR lipoprotein profiles were measured with no previous

cardiovascular disease, 145 cases and 1836 controls were found to have a complete record of all parameters to be included in the analysis. Baseline characteristics of the subjects are shown in Table 7. The mean age was 49±9 years, 52% was female.

Multivariate Models The variables included in the final multivariate models are shown in

Table 6.

Table 7 Baseline characteristics of the subjects. *

C aracteristic Men Women

(N=94S) (N=1035)

Mean age · ^■ yr 49,2*8.3 49.5±9.0

Cholesterol - mg/cil

total 204x36 205+40

HDL 44±1 1 56±15

Blood pressure ~ mm Hg

Systolic (nurse) 127*16 1221-19

Diastolic (nurse) 80±10 75±1 Q

Blood pressure medication - no. (%) 126 (1 3.3) 128 (12.4)

Body- mass index 27.8±3.8 25.8+5.1

Smoking

Smokes and inhales 201 (21.2) 219 (21 .2)

Cigarettes per day 5,2+12.1 4.2±9.6

Smokes cigars - no, (%) 46 (4.9) 2 (0.2)

Smokes pipe - no. {%) 28 (3.0) 0 (0)

Spouse smokes - no, (%) 344 (36.4) 450 (43.5)

Glucose - mg/dl 95± 8 91 ±22

* Plus-minus values are means ± SD. To convert the values for cholesterol to rniltimoles per liter, multiply by 0,02588, The body-mass index is the weight in kilograms divided by the square of the height in meters. HDL denotes high-density lipoprotein.

Table 6. Statistical analysis of area under the ROC curve for the cross-validated multivariate models.

Mode! 1 Model 2 Difference AUG Standard Error P value

ROC curve

Classic Classic & NMR 0.00527 0.005S3 0.3658

Classic Classic & NMR 0.0171 0.00851 0.0451

& ratios (1)

Classic Classic & NMR 0.0235 0.00851 0.0057

& ratios (2)

Classic & NMR Classic S NMR 0 01 18 0.00657 0.0731

& ratios (1)

Classic & NMR Classic & NMR 0.0182 0.00326 0.0272

& ratios (2) ROC analysis of Multivariate Models

Receiver-Operating-Characteristic (ROC) curves for general cardiovascular disease are shown in Figure 10. Results of the statistical analyses comparing the curves are shown in Table 8. Adding Particle Profiler lipoprotein metabolic ratios (liporatios) to a model including existing cardiovascular risk factors significantly improved the area under the ROC curve for this population.

Example 5

Lipoprotein metabolic ratios improve diabetes risk prediction.

Study Sample and Risk Factors

In this study we used subjects from the Offspring cohort, in the Framingham Heart St udy (FHS) (Cromwell WC et al. J Clin Lipidology 2007;l(fs):583-592}. Subjects were included when they had no history of diabetes, gave written informed consent for general research use, had complete NMR lipoprotein profiles recorded, and had a complete record of classical diabetes risk factors. Subjects were excluded when no diabetes data was available on the measuring day, or on any of the three earlier exams, or on the last examination day (3 ^rd examination after lipoprotein measure, approx. 9-10 years later).

Computational Modeling

We applied the Particle Profiler computational model to the NMR lipoprotein profiles. Details can be found in the correspondin section of example 4.

Outcomes

Subjects who were recorded as diabetic by Framingham criteria in one of the three examinations following the lipoprotein profile measurement, but not before or at the time of the measurement, were designated as 'cases', subjects that did not develop diabetes at any time as 'controls'.

Statistical Analysis We used multivariate logistic regression to correlate predictor variables with the CVD outcome. We grouped predictor variables into three sets; 1. classical cardiovascular risk parameters, 2. direct lipoprotein profile - based parameters, and 3. Particle Profiler-based parameters (See Table 9). We constructed multivariate models using set 1, and the combinations of sets 1 and 2, and sets 1, 2, and 3. For the combined sets, two models were

constructed; one by starting to add variables from scratch and another by starting to add variables to the finished model constructed using set 1.

We constructed the multivariate prediction model in two phases. In the first phase, the variables that contributed most to improving the area under the ROC curve (Obuchowski, supra) were added to the model in a stepwise fashion, until the increase in the area under the ROC curve when changing the predictor variable set of the model equaled zero. In the second phase, the constructed model was cross-validated using 10-fold Venetian blind cross-validation, and the variable that showed most variation in the regression vector was removed through backward elemination. After the removal of a variable, the cross-validation was repeated, Variable removal was stopped when all variables were stable within the model (05% confidence interval of the regression coefficient did not pass through zero) or when removing more variables would amount to completely eliminating a classical risk factor from the model {for instance, there would be no variables with blood pressure information left),

For the combined sets, two alternatives for the first phase were used: one started the stepwise procedure from scratch, and the other started the stepwise procedure from the final cross- alidated model from set 1, All analyses were carried out in Matlab version 7.7.0 with statistics toolbox version 7,0 and PLS toolbox version 5,0.3.

The multivariate predictions of diabetes risk were compared using area under the cross-validated ROC curve statistics, using the method by cle Long (DeLong, ER et al, 1988, Biometrics 44:837-845) and a binomial exact test, calculated in MedCalc, version 11.4.4.0. RESULTS

Baseline Characteristics

Of the 2142 subjects in the general research use assent group in which NMR lipoprotein profiles were measured with no previous diabetes, 145 eases and 1836 controls were found to have a complete record of all parameters to be included in the analysis. Baseline characteristics of the subjects are shown in Table 10, The mean age was 49±9 years, 52% was female.

* Plus-minus values are means ± SD. To convert the values for cholesterol to miiiimoles per liter, multiply by 0.02568. The body-mass index is the weight in kilograms divided by the square of the height in meters. HDL denotes high-density lipoprotein,

Multivariate Models The variables included in the final multivariate models are shown in

Table 9.

ROC analysis of Multivariate Models

Receiver-Operating-Characteristic (ROC) curves for diabetes development are shown in Figure 16. Results of the statistical analyses comparing the curves are shown in Table 11. Adding Particle Profiler parameters to a model including existing diabetes risk factors significantly improved the area under the ROC curve for this population. Tabie 1 1 . Statistical analysis of area under the ROC curve for the cross-validated multivariate models redictin diabetes develo ment.

Example 6

Log-transformed lipoprotein metabolic ratios improve cardiovascular disease prediction.

We used so-called "re ularized" kernel-based algorithm that is specifically tailored to learn the model that leads to the optimal area under curve

statistics (AUG) for the ROC curve (C-statistic). To conduct the experiment we range-scaled the dataset, randomly shuffled it. and divided it into two independent sets, namely training (70%) and validation (30%), Wc performed parameter estimation and biomarker identification on the training set and used the validation set to evaluate the predictive performance of the obtained biomarkers. The experimental setup included a "forward-selection" procedure for the markers: we started with an initial set of accepted markers (age and sex) and iteratively added the makers one by one. We selected the markers from three consecutive groups. The first group consists of 'classical' markers such as age, sex, blood pressure, blood glucose, smoking habits, body weight, and blood pressure medication use; from, this set we selected two markers (age and sex) we let the algorithm identify four more markers. The second group consists of cholesterol and lipoprotein particle-related markers; from this set we let the algorithm identify two markers. The third group consists of the log- transformed lipoprotein metabolic ratios; we let the algorithm select several markers, and decided how many to include based on ROC performance improvement and on lack of correlation with the already included markers

(r ² <0.25). After the addition of every marker we evaluated the area under the ROC curve to evaluate how good the model performs with the set of markers selected so far.

The selection procedure led to the following sets of markers, in the order in which they were added to the model.

Table 12. Variables included in final multivariate models with log-transformed lipoprotein metabolic ratio's,

Classic markers Classic + LDLp Classical + LDLp + Classical + LDLp + HDLp +

HDLp lipoprotein metabolic ratios

Age Age Age Age

Sex Sex Sex Sex

Cigarettes per day Cigarettes per day Cigarettes per day Cigarettes per day

Biood pressure Blood pressure Blood pressure Blood Pressure medication medication medication medication

Systolic blood Systolic blood Systolic blood Systolic blood pressure pressure (nurse) pressure (nurse) pressure (nurse) (nurse) Glucose Glucose Glucose Glucose

LDL particle number LDL particle LDL particle number

number

HDL particle HDL particle number number

A comparison of the C -statistics of on the test set for the various data sets gave the following results.

Table 1 3. Statistical analysis of area under the ROC curve for the final multivariate model transformed lipoproi ein metabolic ratio's.

Model 1 Model 2 Difference Standard P value

AUC ROC Error

curve

(c-statlstic

difference)

Classic classic + LDLp 0.0352 0.0124 0.0044

Classic classic + LDLp + HDLp 0.0427 0.0141 0.0025

Classic classic + LDLp + HDLp +

Iipoprotein metabolic ratios 0.0545 0.0144 0.0001 classic + LDLp classic + LDLp + HDLp 0.0075 0.0056 0.1857

classic + LDLp classic + LDLp + HDLp +

Iipoprotein metabolic ratios 0.0183 0.0068 0.0048

classic + LDLp + classic + LDLp + HDLp +

HDLp Iipoprotein metabolic ratios 0.01 18 0.0056 0.0354