Patent Application: US-45517109-A

Abstract:
a computer based calculation of a prognostic index i of osteoarthritis based on biochemical and imaging based biomarkers a mathematical combination of said values , wherein a first imaging based biomarker is a measure of the quantity of a cartilage in a joint compartment , a second imaging based biomarker relating to the quality of said cartilage in said joint compartment , and wherein a value of said first biomarker indicative of a larger quantity of cartilage affects the index to make it predictive of more disease progression , and a value of said second biochemical marker indicative of a greater departure from the quality of disease free cartilage affects the index to make it predictive of more risk of disease progression , exemplified by i = yhom + zvol + ∑ n = 1 n  a n  other n where y and z are numerical coefficients , hom is the measured homogeneity , vol is the measured cartilage volume , and where other n represents n further biomarkers each having a respective numerical coefficient a n , n being zero or an integer .

Description:
to investigate how biomarker values can be combined to discriminate between patients with early stage osteoarthritis with a higher and lower probability of disease progression we carried out the following study . biomarkers from radiographs , urine samples , and mri for this study were acquired at baseline ( bl ), after 1 week for a subgroup , and then at follow - up after 21 months ( fu ). a subgroup had bl data re - acquired for precision evaluation . the study included 159 randomly selected men and women such that the population had a normal group with a large age span as well as a large group with elevated risk of having knee oa . the risk group was selected based on age and known knee problems . the exclusion criteria ensured that none of the subjects had previous knee joint replacement , other joint diseases ( e . g . rheumatoid arthritis , paget &# 39 ; s disease , joint fractures , hyperparathyroidism , hyper - and hypothyroidism ), contraindications for performing mri examination , or were receiving medication affecting bone and / or cartilage ( e . g . bisphosphonates , vitamin d , hormones , serms , prednisolone , anabolic androgens , and pth ). from this base collection of 318 left and right knees , 5 knees were excluded due to inferior imaging quality . another 25 knees were used for training of the automatic mri quantification methods and excluded from the evaluation set . furthermore , a single subject was excluded since a urine sample was not acquired . thereby a total of 287 knees were in the evaluation set at bl . a subgroup of 31 knees had imaging data acquired again a week after bl . at fu , 250 knees attended . for each test subject age , sex , weight , and height were recorded at baseline and follow - up . at bl , 51 % of the evaluation knees were healthy with a distribution of level of oa scored by kellgren and lawrence index ( kl ) of [ 145 , 87 , 30 , 24 , 1 ] ( for kl 0 , 1 , 2 , 3 and 4 ). for the rescan subgroup , 35 % were healthy with kl [ 11 , 13 , 2 , 5 , 0 ]. at fu , 103 of the healthy had remained at kl 0 and 25 had progressed . additionally , 10 of those with oa at bl had progressed . digital radiographs of the knees were acquired with the subject standing in a weight bearing position with the knees slightly flexed and the feet rotated externally . the synaflex ( developed by synarc ) was used to ensure reproducibility of the foot orientation and knee flexing . focus film distance was 1 . 0 m and tube angulation 10 ° ( the mtp view modified for fixed angle . radiographs were acquired in the posterior - anterior position , while the central beam was displayed directly to the mid point of the line through both popliteal regions . radiographs of both knees were acquired simultaneously . for each x - ray , the medial tibio - femoral compartment was scored by inspection by a trained radiologist . kl was scored by qualitative evaluation of osteophytes , joint gap narrowing , and subchondral bone sclerosis for severe cases . jsw was measured by manually marking the narrowest gap between tibia and femur . in addition , the width of the tibial plateau was measured as a quantification of the knee size — covering both medial and lateral compartments but excluding possible osteophytes . for all subjects , fasting morning urine sample were collected ( second void ). from these , urinary levels of collagen type ii c - telopeptide fragments were measured by the cartilaps elisa assay ( ctx - ii ). this assay uses a highly specific monoclonal antibody mabf46 specific for a 6 - amino acid epitope ( ekgpdp ) derived from the collagen type ii c - telopeptide ( 3 ). ctx - ii was corrected to urinary creatinine as assessed by a standard calorimetric method . to reduce the variability of the ctx - ii measurements and to allow precision evaluation , baseline values were calculated as the mean of two separate determinations . for the statistical analysis done per knee , we used the simplifying assumption that each knee contributed equally to the ctx - ii scores . furthermore , for the statistical analysis , the ctx - ii values were logarithmically transformed to obtain normality and symmetry of variance . mri scans were acquired from a low - field 0 . 18t esaote c - span scanner dedicated to extremity imaging . a single knee coil was used . we used a sagittal turbo 3d t1 sequence with near - isotropic voxels ( 40 ° flip angle , tr 50 ms , te 16 ms , scan time approximately 10 minutes , resolution 0 . 7 mm × 0 . 7 mm × 0 . 8 mm ). the scans had approximately 110 slices ( depending on the knee size ) and each slice 256 × 256 pixels . near - isotropic voxels are suitable for 3d image analysis and shape modeling in general — and are also suitable for cartilage quantification ( 20 ). the subjects were scanned in supine position with no load - bearing during or prior to scanning — except for the short walk to the scanner . the 25 scans in the training collection were segmented by slice - wise outlining of the medial tibial and femoral cartilage compartments by an expert radiologist . these segmentations were used to train a voxel classification scheme based on supervised learning in a knn framework including multi - scale gaussian derivative features ( 21 ). this voxel classification method provides automatic segmentation of the tibial and femoral cartilage compartments . from the segmentations , volume and surface area were computed ( mt . vc , mf . vc , mtf . vc , mt . ac , mf . ac , and mtf . ac using the nomenclature of ( 22 )). furthermore , the cartilage homogeneity was quantified as 1 - entropy , with signal intensity entropy computed in the compartments ( 14 ) ( mt . homc , mf . homc , mtf . homc ). entropy quantifies the complexity of the intensity histogram , so cartilage with more uniform intensity has lower entropy ( higher homogeneity ). since the scans are t1 , this measure of homogeneity is related to water distribution and proteoglycan concentration . also , clear definition of the internal cartilage layers will be imaged by separate intensities and contribute to higher entropy . therefore , a loss of structural integrity may lead to lower entropy and higher cartilage homogeneity . the surface roughness ( inverse smoothness ) was quantified for the tibial compartment by measuring the mean surface curvature over a region - of - interest ( roi ) including the central load - bearing region and approximately half of the cartilage surface ( mt . smoclab ). the surface curvature was estimated using a surface evolution scheme driven by a partial differential equation at fine - scale resolution ( 8 , 26 , 23 ). fibrillation and minor focal lesions lead to decreased smoothness . for the remaining quantifications , a statistical cartilage sheet shape model was fitted to the segmented tibial cartilage sheets . by training the model on healthy knees , the resulting cartilage model covers the bone area that the a healthy cartilage sheet would cover ( 24 ). thereby , the measured mean thickness was including denuded regions with zero thickness ( mt . thctab ). additionally , the thickness map 10 % quantile was used as a measure targeting focal thinning related to local lesions ( denoted mt . thcq ). finally , the mean surface curvature of the shape model was analyzed . due to model regularization this coarse scale curvature relates to the overall bending of the sheet and is therefore indirectly related to the congruity of the joint . this simplified congruity measure ( mt . conclab ) was quantified as the mean inverse curvature across the roi ( fig2 d ) also used for the roughness measure ( 27 , 8 , 26 , 23 ). all steps performed on the mri — including segmentation , shape model deformation and marker quantification — are done in a fully automated computer - based framework in 3d ( rather than in each individual mri slice ). we investigated the performance of combinations of the individual markers . within the field of pattern recognition , various methods exist for combining markers in linear , non - linear or non - parametric fashion ( such as quadratic discriminant analysis , support vector machines or knn classifiers ). we chose to limit ourselves to combinations defined by linear discriminant analysis ( lda ) since it offers direct understanding of the aggregate biomarker as a simple weighted sum of the individual markers . we investigated combinations of all the available markers . however , using only a subset of markers may in some cases provide better performance — both since some individual markers may not provide discrimination by themselves but also because of potential problems with overfitting and lack of generalization caused by the classical “ high dimensionality , low sample size ” problem . we composed groups of markers defined by the marker modalities : demographic ( d ), biochemical ( b ), radiographic ( x ), and mri ( m ). accordingly , we denote an aggregate marker composed of biochemical , mri , and radiographic markers by bmx . furthermore , we investigated pseudo - optimal subsets of these groups ( as explained below ). the full group was denoted all bmx whereas the optimal subset was denoted opti bmx . due to the combinatorial explosion it was in - feasible to evaluate all possible marker subsets ( with 19 individual markers , there are 2 19 = 524288 possible subsets ). therefore , we used a heuristic approach where we evaluated all subsets with up to three markers ; and additionally by a “ greedy forward selection ” scheme where each subset was composed by first selecting the optimal individual marker , and by iteratively adding the single marker that provided the optimal combination with the already selected marker subset . this heuristic feature selection approach does not guarantee that the optimal subset is discovered — hence the term pseudo - optimal . finally , we evaluated combinations of biochemical and mri - based markers for cartilage breakdown , quantity and quality . we denote a combination of ctx - ii , volume , and homogeneity as an aggregate marker longevity basic . a more comprehensive combination adding area ( that combined with volume can provide an additional aspect of quality ) and roughness ( additional marker for quality ), we denoted longevity prog . we evaluated the diagnostic and prognostic biomarker performance for individual and aggregate markers equivalently ( individual markers are trivial aggregate markers consisting of a single marker ). when performing lda using several biomarkers , the resulting combination is prone to overfitting / overtraining when the number of weighting parameters is high relative to the sample size , and the aggregate marker weights can be optimized to model arbitrary measurement variations that are not representative of the actual disease progression . thereby , the apparent performance for the resulting aggregate marker will not generalize to other populations . therefore , we performed an evaluation where the population was repeatedly split randomly into two sub - populations with approximately equal size and distribution of levels of oa . for each split , we optimized the weights for the aggregate biomarker on one training sub - population ( using lda ) and evaluated the resulting aggregate marker on the other evaluation sub - population . the median performance on the evaluation sub - populations gives an estimate of the actual performance of the aggregate marker that will reveal lack of generalization . we used 500 repetitions . the diagnostic performance was defined as the ability of the bl marker values to separate healthy or borderline cases ( kl ≦ 1 ) from oa knees ( kl & gt ; 1 ) and evaluated by p - value from manova ( p ) ( based on hotelling &# 39 ; s t 2 test , by corresponding required sample size from power analysis ( n ), and the area under the receiver - operator - characteristics curve ( auc ). the prognostic performance was defined as the ability of the bl values to separate healthy non - progressors ( kl 0 at bl and fu ) from early progressors ( kl 0 at bl and kl & gt ; 0 at fu ) and evaluated by p , n , and the odd &# 39 ; s ratio ( or ). due to the number of evaluated biomarkers , bonferroni correction suggests that a significance level of around p = 0 . 005 is appropriate . the diagnostic and prognostic abilities of each individual and the aggregate markers are shown in table 1 . jsw performed well as diagnostic marker ( auc 0 . 73 ). since it is contained in the definition of kl , this was expected . the best individual diagnostic marker was cartilage roughness ( auc 0 . 78 , n 29 ). the best aggregate diagnostic marker was the one combining all available individual markers ( auc 0 . 86 , n 15 ). however , many of the other aggregate markers also demonstrated good diagnostic performance , including those combining all mri markers ( auc 0 . 82 , n 20 ) and the cartilage longevity marker ( auc 0 . 81 , n 22 ). several individual markers demonstrated prognostic ability , among these ctx - ii ( or 5 . 9 ), cartilage volume ( or 5 . 2 ), and cartilage homogeneity ( or 5 . 1 ). jsw seemed inappropriate as a prognostic marker ( p = 0 . 27 ). again , several of the aggregate markers demonstrated superior performance compared to the individual markers . the cartilage longevity prog marker proved to be the optimal subset of all available individual biochemical , mri , and radiograph markers ( or 12 . 4 ). this was composed of uctx - ii , homogeneity ( mt . homc ), volume ( mf . vc ), smoothness ( mt . smoclab ), and area ( mf . ac ) and is designated longevity prog . when the individual biomarkers are expressed in the units in which they are measured , the weights for each biomarker assigned by lda are unit dependent , e . g . when the individual markers are rescaled to have standard deviation one ( denoted by underlining them below ), the optimal weights used in the aggregate markers give an impression of the importance of each marker . as examples , the diagnostic and prognostic cartilage longevity markers were ( hom : mt . homc , rough : mt . roughc , vol : mf . vc , area : mf . ac ): the sign of the weights show whether increased values are prognostic of progression of oa . however , it is irrelevant whether the weights are expressed such that the index is positive or negative i . e . one can multiply all of the weights by − 1 , or indeed by any number . elevated ctx - ii reduces cartilage longevity ( i . e . an increased risk of oa progression ). increased homogeneity and roughness reduce longevity . increased volume and decreased area reduce longevity . that increased homogeneity is prognostic of oa progression is not surprising since increased homogeneity has also been shown to be related to the current degree of oa . however , it is surprising that increased volume implies an increased risk of oa progression . in the following , we show further results for these aggregate cartilage longevity markers . these aggregate cartilage longevity markers are compared to the key individual markers ( ctx - ii , jsw , volume , and homogeneity ) in fig1 and 2 . the roc curves in fig1 show that both jsw and longevity diag were able to diagnose 47 % true positives with 4 . 7 % false positives . from there , the longevity diag marker proved better at diagnosing the more borderline cases . fig2 elaborates on the prognostic performance . for each marker the scores were split into quartiles and the predictive power of elevated scores were computed by comparison to the lowest quartile . scores in the two upper quartiles of the longevity prog cartilage marker provided superior predictive ability ( or & gt ; 30 ). when adjusting the longevity markers for gender , age and bmi , the diagnostic marker retained the performance of the unadjusted ( auc 0 . 80 , n 22 ). contrarily , the best unadjusted diagnostic marker combining all available individual markers had a drop in performance after adjustment ( auc 0 . 74 , n 30 ). the prognostic longevity prog marker also retains equivalent performance ( or 12 . 0 ). for comparison , the aggregate marker combining the optimal subset of all markers goes to 4 . 7 after adjustment . the results above were evaluated with analysis per knee . when the radiograph and mri measurements for left and right knees are averaged , analysis per subject can be performed . this leaves the performance of both the diagnostic longevity diag marker ( auc 0 . 82 , n 18 ) and the prognostic longevity prog marker ( or 22 . 0 ) similar or improved compared to the per - knee results . the weights in the linear combinations allow specialization of the aggregate markers to other tasks . for instance , the diagnostic markers can be trained to diagnose very early oa ( kl 0 from kl & gt ; 0 ). for that task , the golden standard marker jsw performs somewhat worse ( n 66 , auc 0 . 68 compared to n 37 , auc 0 . 73 ) whereas the best aggregate marker , opti bmxd , remains similar ( n 16 , auc 0 . 84 compared to n 17 , auc 0 . 83 ). we have previously used mri cartilage markers normalized by the width of the tibial plateau to adjust for joint size . this improved the diagnostic ability of the individual markers ( 27 ) and can also be used in the aggregate markers ( 28 ). using mri markers normalized by knee width ( 27 ), the performance of the prognostic longevity improved from or 12 . 4 to 16 . 1 . the complexity of oa implies that biomarker development is challenging . there are many factors in the onset of oa including genetics , trauma , biomechanics , weight , and exercise . in addition , the different phases of oa may entail different driving pathological mechanisms — e . g . during very early oa , structural changes are observed that cause increased turnover of cartilage and bone . this may be followed by cartilage fibrillation , thickening of the subchondral bone , bone lesion edema , osteophytes , focal cartilage lesions , and during the later stages of oa cartilage loss leading to denudation may be observed ( for models of these stages , see ( 29 , 30 )). the fact that aggregate markers were superior supports that markers from different modalities can complement each other . however , an aggregate index combining all possible markers which could be included is not optimal . this introduces a risk for severe performance overestimation due to too small population if the evaluation is carried out directly on the entire population . instead , we use repeated random sampling of sub - populations . as an example of the need for such an evaluation strategy , a comparison of the median performance for the prognostic “ all bmxd ” aggregate marker in the training subsets ( n 8 , or ∞) demonstrates severe overtraining compared to the performance in the evaluation subsets ( n 108 , or 4 . 3 ). therefore , a robust subset selection method like the one employed here is essential . even with very similar markers , superior performance of aggregate markers could be achieved through improved precision due to reducing measurement variation by repeated similar quantifications . however , for instance , for the cartilage longevity prog marker the precision is 1 . 1 % ( cv on the scan - rescan pairs and the repeated ctx - ii measurements ). for comparison , cartilage homogeneity has 0 . 9 %. therefore , improved performance is rather due to the combination of the different aspects of cartilage quantity , quality , and breakdown measured from different modalities . currently , the accepted outcome measures in clinical studies of dmoads are pain , function , and jsw . both pain and function are complicated to measure in an objective way , and jsw is likely not a very sensitive marker for oa progression . therefore , the most solid clinical end point , jrs , remains the most reliable outcome measure . due to the slow progression of oa , an estimate of the time to jrs is a more appealing efficacy marker for a clinical study . however , a lack of an objective estimation makes this unfeasible at the moment . therefore , jsw , pain , and function so far remain the most accepted clinical study outcome measures . clinical studies do not rely on outcome measures alone . the ability to select a study population with a risk for disease progression is equally crucial . the above results demonstrate that use of jsw in clinical studies may not be optimal . jsw was unsuitable as a prognostic marker and the performance as diagnostic marker was expected since jsw is an integral part of the kl score used to define the level of oa . even with this inherent bias , jsw was outperformed by the individual roughness marker from mri . furthermore , when inspecting the roc diagram in fig1 , it is apparent that jsw is particularly effective in diagnosing the “ easy ” subjects ( left end of curves )— the ones with severe oa corresponding to very low jsw . however , for the earlier stages of oa , also homogeneity and in particular cartilage longevity outperforms jsw . the aggregate biomarker framework is very general as exemplified by the alternative aggregate diagnostic opti bmxd marker for very early oa . the generality allows inclusion of alternative cartilage markers , such as the markers normalized by knee size . these normalized markers are by themselves non - linear combinations of the included mri markers and the width marker . a natural extension of the work described above is to include mri markers targeting bone , meniscus , and other joint structures ; and to include additional biochemical markers targeting bone turnover , cartilage formation , synovitis and other central processes . thereby , the aggregate markers could become more similar to frameworks such as worms and the “ knee osteoarthritis scoring system ”, koss ( 35 ). these scoring systems provide a semi - quantitative score based on inspection of mri for the presence / severity of disease - related parameters such as cartilage lesions , bone marrow abnormalities , and meniscal abnormalities . however , in addition to the computational methodology that allow specialization to different biomarker tasks , a major difference between worms / koss and the above described framework is the use of continuous markers , rather than categorical . continuous markers are likely to provide higher sensitivity . the combination of cartilage quantity , quality , and breakdown may also be used to provide an estimate of the remaining cartilage life - span which could be a central factor in an objective estimate for a time - to - jrs marker . the use of aggregate markers implies quantification of several individual markers , introducing a potential measurement bottle - neck . even for volumetric mri markers , manual or semi - automatic annotation is quite time - consuming . for advanced 3d shape - related markers ( such as the congruity or roughness markers ) manual annotation is not feasible . the present study relied on fully automated computer - based low - field mri methods for cartilage status assessment and a standardized biochemical marker that is measured through simple standard elisa techniques . thereby , the presented aggregate markers can be readily applied in large , multi - center studies without the introduction of a reader bottle - neck . in particular , the prognostic cartilage longevity prog marker could by itself ensure the selection of a suitable high - risk study population and thereby facilitate a positive clinical study outcome for a dmoad . we here demonstrate that combinations of biochemical and mri - based biomarkers can provide a superior prognostic oa marker or index . it is particularly surprising that a relatively large cartilage volume should predispose to a higher rate of oa progression in the measured joint . indeed , we do not currently have a fully convincing explanation for this phenomenon . it is not for instance the result of a correlation between the age of the patient and the volume of cartilage , with younger patients having a higher volume and a predisposition to more active disease . whilst we find that disease free women do indeed seem to lose some cartilage volume with age , we do not find this in men . fig3 shows the difference in volume measurements for patients categorised as ‘ non - progressors ’ and as ‘ progressors ’ in our study population . fig4 shows the same but with the volume measurements corrected to allow for expected age related changes . as shown in fig3 and 4 if the age related changes in cartilage volume in our study group of patients are taken into account , the age corrected volumes are more rather than less predictive of oa progression . looking further at optimised aggregate prognostic markers , in the following , we investigate the sensitivity of the prognostic longevity markers with respect to the weights in the optimal linear combinations . this is done for the basic longevity marker ( composed of ctx - ii , homogeneity mt . homc , and volume mf . vc ) and the longevity prog marker ( composed of ctx - ii , homogeneity mt . homc , roughness mt . roughc , volume mf . vc , and area mf . ac ). for comparison , a marker using only the quantitative volume and area markers would be : the effect of variations in these markers has been explored as follows . the performances , as odds ratios , for each of these aggregate markers are as follows : the performance of the specific longevity prog marker is evaluated to or 24 . 1 . note that this is higher than the 12 . 4 given as the result above . this over - estimation of the or is due to the choice of a specific set of weights determined from the entire population . the evaluation is performed by repeated generation of training and test sub - populations . when the weights are set to specific values , they are not chosen during training , and therefore there will be no possibility for poor generalization to the test set . and the performance will be better because the general weights were determined on the entire population — and thereby partly on the test populations . therefore , the results reported below on the test sets will be over - estimating the performance compared to the previous ( more correct ) results . the purpose of the investigation here is rather to see how sensitive the aggregate markers are to changes in the weights rather than to see the actual performance . the results above demonstrate how cartilage markers from mri and systemic samples can be combined into a cartilage longevity marker . for a more comprehensive marker of “ joint longevity ” it could be relevant to add markers for other joint processes . these could be markers for presence of osteophytes , changes in the trabecular bone structure , or meniscal lesions — such as suggested by the aggregate worms score ( based on semi - quantitative manual mri observations of different tissues ). here , we demonstrate this by adding the serum - based ctx - i marker that quantifies breakdown of collagen type i in bone . we denote the combination of ctx - i and the cartilage longevity marker as “ joint longevity ”. the joint longevity marker is in fact superior to the cartilage longevity marker ( or 27 . 6 versus 24 . 1 ). in the following , we investigate how sensitive these aggregate markers are to changes in the weightings / parameters . this is done by evaluating the result of replacing each weight with double the value , half the value , and zero . the results are given in the table below . each column treats an aggregate marker . the first row gives the or for predicting early progression for the specific markers given above . for each individual marker are then given three numbers : the or when the weight is doubled , halved , and set to zero . joint longevity prog longevity basic longevity prog quantity prog 24 . 1 16 . 3 27 . 6 5 . 2 ctx - ii 20 . 5 / 19 . 5 / 15 . 0 16 . 1 / 16 . 3 / 15 . 7 22 . 2 / 18 . 9 / 12 . 4 ctx - i 20 . 2 / 24 . 5 / 22 . 0 hom 18 . 9 / 18 . 5 / 12 . 0 16 . 1 / 15 . 0 / 6 . 6 20 . 5 / 20 . 2 / 15 . 0 rough 20 . 2 / 23 . 8 / 20 . 2 29 . 1 / 22 . 5 / 20 . 2 vol 10 . 0 / 6 . 1 / 1 . 4 14 . 5 / 14 . 5 / 7 . 5 13 . 2 / 12 . 4 / 1 . 8 5 . 2 / 5 . 2 / 5 . 6 area 5 . 6 / 22 . 0 / 14 . 5 11 . 4 / 22 . 0 / 18 . 5 5 . 2 / 5 . 2 / 5 . 2 the ors in the table reveal that in particular quantity and quality , represented here by homogeneity and volume , are essential for the aggregate markers . however , while volume is essential as an ingredient , it is not very effective on its own ( or 5 . 2 ); neither is the aggregate marker focusing on cartilage quantity combining volume and area . the roughness marker seems to be least essential , and fairly large changes of the weight are possible with relatively small performance drop . these results support that the presence of measures of quantity and quality are essential , although all aspects ( quantity , quality , and breakdown ) are important . in order to establish appropriate ranges for each weight in each aggregate marker , we defined less and more preferred fiducial performance thresholds of ( 1 ) one half of the performance of longevity prog ( so or 12 ), and ( 2 ) two - thirds the performance of longevity prog ( so or 16 ) and determined the limits for each weight where the performance drops below each of these thresholds . this results in the weight intervals given in the table below . the weights are those corresponding to the individual biomarkers rescaled to unit standard deviation . for each weight is given the optimal value and then the interval . mri - vaprog is an aggregate marker based on volume and area of cartilage determined by mri and mri - hvprog is an index based on a combination of mri determined homogeneity and volume . the term “ none ” means that the aggregate marker using only cartilage quantity ( volume ) and area performs below the threshold for any weights and that the aggregate marker based just on volume and homogeneity performs below the higher threshold of or = 16 ). notably , ‘ area ’ can substitute for homogeneity as a quality biomarker in the more sophisticated indices , for instance an odds ratio of 16 can be achieved using the longbasic prog index with the coefficient for hom set at zero . it should be noted that the performance of each aggregate marker is invariant to overall scaling of the weights — i . e . if all weights are doubled simultaneously or reversed in sign , the performance is not affected . therefore , we consider any two combinations of weights to be equivalent if the inter - weight ratios are identical . also , the performance of the aggregate markers is invariant to the choice of units — but this affects the specific weights . if , for instance , the volume is measured in litres instead of mm 3 , the weight will simply be rescaled by the appropriate number of order of magnitudes . therefore , we consider differences in weights due to differences in units to be irrelevant — and to result in equivalent aggregate markers . when the individual markers are rescaled to standard deviation one , the invariance to choice of units is automatically obtained . in this specification , unless expressly otherwise indicated , the word ‘ or ’ is used in the sense of an operator that returns a true value when either or both of the stated conditions is met , as opposed to the operator ‘ exclusive or ’ which requires that only one of the conditions is met . the word ‘ comprising ’ is used in the sense of ‘ including ’ rather than in to mean ‘ consisting of ’. all prior teachings acknowledged above are hereby incorporated by reference in their entirety . acknowledgement of prior art in this specification is not an admission or representation that such prior art forms part of the common general knowledge in australia or elsewhere . 1 . bauer d c , hunter d j , abramson s b , attur m , corr m , felson d et al ( 2006 ) classification of osteoarthritis biomarkers : a proposed approach . osteoarthritis cartilage 14 ( 8 ): 723 - 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