absolute fracture risk varies with bone densitometry technique used

IntroductionOver the past decade, bone density scans have

assumed an essential role in the diagnosis of osteo-porosis (1). At the present time, dual X-ray absorp-

tiometry (DXA) scans to measure bone mineral den-sity (BMD) at the spine and femur are the preferredmethod of investigating patients’ skeletal status(2–4). The reasons for this choice are the evidencefrom prospective studies that the femur is the opti-mum BMD measurement site for predicting hip frac-ture risk (5–7); the sensitivity of spine BMD to thechanges owing to aging, disease, and response totreatment (3); and the fact that BMD measurementsof the spine and hip are readily interpreted using the

Absolute Fracture Risk Varies with Bone DensitometryTechnique Used

A Theoretical and In Vivo Study of Fracture Cases

Glen M. Blake, PHD, Karen M. Knapp, BSC, and Ignac Fogelman, MD

Department of Nuclear Medicine, Guy’s Hospital, St. Thomas Street, London, UK

Abstract

The lack of consensus of how the results of peripheral bone mineral density (BMD) measurements shouldbe interpreted is proving a barrier to the wider use of these devices. One approach is to interpret peripheralmeasurements using thresholds (so-called equivalent T-scores) defined to have the same absolute fracture riskas a femoral neck T-score of –2.5. For this concept to be valid, the estimates of fracture risk for a populationshould be the same irrespective of the measurement technique used. We tested this prediction both theoreti-cally and in vivo using data for 63 postmenopausal women with Colles fracture and 191 control subjects. Thetheoretical analysis showed that if the normal population has a Gaussian BMD distribution and fracture riskvaries exponentially with Z-score as exp(–βZ) then patients who experience a low-trauma fracture have a frac-ture risk that is larger by a factor exp(β2) compared with the fracture risk of the whole population. Using datafrom the in vivo study, fracture risk predictions were compared for seven different types of measurement (lum-bar spine; femoral neck; total hip BMD; and speed of sound [SOS] at the radius, tibia, phalanx, andmetatarsal). When quantitative estimates of fracture risk were made for individual subjects, the average riskof fracture for the Colles group varied between 1.03 times larger (for tibial SOS) and 2.77 times larger (fortotal hip BMD) than the average fracture risk for the whole population. As predicted by the theoretical study,fracture risk varied according to the odds ratio determined by logistic regression analysis. Therefore, estimatesof fracture risk derived for the same group of patients varied almost threefold according to the type of mea-surement. It was concluded that equating estimates of absolute fracture risk for different types of scan shouldnot be used as the basis of deriving equivalent T-scores for interpreting peripheral measurements.

Key Words: Absolute fracture risk; bone densitometry; equivalent T-scores.

Received 08/16/01; Revised 10/15/01; Accepted 10/22/01.Address correspondence to Dr. G. M. Blake, Department of

Nuclear Medicine, Guy’s Hospital, St. Thomas Street, London,SE1 9RT, UK. E-mail: [email protected]

109

Original Article

Journal of Clinical Densitometry, vol. 5, no. 2, 109–116, Summer 2002© Copyright 2002 by Humana Press Inc. All rights of any nature whatsoever reserved. 1094-6950/02/5:109–116/$12.00

World Health Organization (WHO) definition ofosteoporosis as a T-score ≤–2.5 (8,9). In addition totabletop DXA scanners that measure the spine andfemur, a wide variety of different types of equipmentfor measuring sites in the peripheral skeleton isavailable (10–13). Such equipment is cheaper andsimpler to operate than tabletop DXA systems andmay be more suitable for use in a primary care set-ting. However, the poor correlation among differenttypes of measurement (14,15) and a lack of consen-sus on how results from peripheral sites should beinterpreted have proved barriers to the more wide-spread use of these devices.

To arrive at a consensus view on the future role ofperipheral measurements and how they should beinterpreted is arguably the most pressing currentproblem in bone densitometry. It is clear that theWHO T-score definition of osteoporosis cannot beapplied uncritically to measurements other than thespine or hip (16–19). A new approach to scan inter-pretation is required if the optimum agreement is tobe achieved among different types of measurement(20). Several different approaches can be envisagedto set revised thresholds for peripheral devices (so-called equivalent T-scores) that replicate the WHOdefinition of osteoporosis. Given the clinical impor-tance of hip fractures (21) and the superior discrimi-nation of femur BMD for predicting risk of hipfracture (5–7), there is an argument for setting thresh-olds for peripheral devices that reproduce as closelyas possible the outcome of a femur DXA scan (4,22).If the femur is chosen as the “gold standard” site forthe definition of osteoporosis, several different waysof setting equivalent T-scores for other devices can beenvisaged. These include definitions that result in thetreatment of the same percentage of postmenopausalwomen, treatment of the same percentage of futurefracture cases, or treatment at the same threshold ofabsolute fracture risk that correspond to a femoralneck T-score of –2.5 (20).

The concept that the findings from different typesof bone densitometry devices might be standardizedby converting the measurements into absolute frac-ture risk is an attractive paradigm (22). However,behind this approach to the definition of equivalentT-scores is a presumption that it is valid to equate theabsolute fracture risk predicted by different types ofmeasurement. It is this presumption that is ques-

tioned in the present study. Just as the usefulness ofthe WHO definition of osteoporosis is limited by thefact that T-scores are a function of the type of deviceselected as well as the skeletal status of the patient(16), we show that a similar problem arises withquantitative evaluations of fracture risk. In particu-lar, we show that such estimations depend on the rel-ative risk (RR) index of the technique (defined as theincreased fracture risk for each 1 SD decrease inBMD) as well as the skeletal status of the patient.

Materials and MethodsTheoretical Analysis of Fracture Risk

That quantitative estimates of fracture risk deter-mined from bone densitometry are a function of theRR index of the measurement technique can beappreciated from Fig. 1. In Fig. 1, the BMD distrib-ution of a study population is modeled by a Gaussianfunction of the Z-score (Z):

(1)

Also shown in Fig. 1 are curves of fracture riskagainst Z-score. These are based on the proportionalhazards models commonly used to evaluate fracturerisk in prospective studies (5–7,23–25) and assume anexponential dependence of fracture risk on Z-score:

p(Z) = p0 exp(–β2/2) · exp(–βZ) (2)

In Eq. 2 p0 is the mean fracture risk of the wholepopulation, β = ln(RR), and the factor exp(–β2/2) isrequired to ensure that the total number of fractures isthe same whatever the measurement technique. Ascan be seen from Fig. 1, a group of patients with sys-tematically negative (or positive) Z-score values mea-sured on a device with a higher RR index will have ahigher (or lower) estimate of absolute fracture riskcompared with measurements of the same patientsperformed on a device with a lower RR value.

The Z-score distribution of the fracture popula-tion, Nf(Z), can be derived by multiplying the distri-bution of the whole population (Eq. 1) by thefracture probablility (Eq. 2). After rearrangementone obtains:

(3)1Nf(Z) = —– p0 exp[–(Z + β)2/2]√2π

1N(Z) = —– exp(–Z2/2)√2π

110 Blake et al.

Journal of Clinical Densitometry Volume 5, 2002

Equation 3 shows that the Z-score distribution ofthe fracture population is a Gaussian function withthe same SD as the initial study population but withits peak offset by β (20). Finally, the mean fracturerisk pf of the fracture population can be derived bymultiplying the distribution of the fracture popula-tion (Eq. 3) by the fracture probability (Eq. 2), inte-grating over all Z-score values, and normalizing tothe number of fracture cases:

pf = p0 exp(β2) (4)

Equation 4 shows that the mean fracture risk ofthe subpopulation that experiences a low-traumafracture is a factor exp(β2) higher than the meanfracture risk of the whole population.

Subjects and Measurements for In Vivo StudyThe theoretical relationship between β and mean

fracture risk (Eq. 4) was compared with quantitativeestimates of fracture risk derived for a group of 63postmenopausal women with a history of low-trauma Colles fracture. The subjects were studied

using measurements of spine and femur BMDperformed on a QDR4500 DXA densitometer(Hologic, Bedford, MA) and ultrasound measure-ments of speed of sound (SOS) at the one-thirdradius, third proximal phalanx, midshaft tibia, andfifth metatarsal performed using a SunlightOmnisense system (Sunlight, Rehovot, Israel) (26).BMD and SOS data for the Colles fracture patientswere compared with those of 191 healthy post-menopausal women without any risk factors forosteoporosis or history of drugs or diseases knownto affect bone metabolism. Subjects were recruitedfrom hospital personnel and volunteers from thegeneral population as well as patients referred forDXA investigations by their general practitioner.Additional subjects with Colles fracture wererecruited from patients attending osteoporosis clin-ics at Guy’s, St. Thomas, and Chingford hospitals.The study was approved by the Guy’s and StThomas hospitals research ethics committees andthe Forest Healthcare NHS Trust ethics committee.Full details are reported elsewhere (27). For the pur-

Bone Densitometry and Absolute Fracture Risk 111


Fig. 1. BMD distribution of a study population represented by a Gaussian function (solid curve). The BMD val-ues are represented as Z-scores. The Gaussian curve has been normalized (right-hand axis) so that the total area underthe curve is unity. The three exponential functions (dashed curves) show the curve of fracture risk against Z-score forRR values (defined as the increased fracture risk for each unit decrease in Z-Score) of 1.1, 1.5, and 2.5, respectively.The fracture risk curves have been normalized (left-hand axis) to the mean fracture risk of the study population.Patients with negative (positive) Z-score will tend to have a higher (lower) absolute fracture risk when measured ona device with a larger RR value.

poses of the present study, the aforementioned datawere evaluated for information on RR values foreach different SOS and BMD variable, and theresulting figures were used to derive estimates ofindividual fracture risk using Eq. 2.

Data AnalysesThe BMD and SOS data for the Colles fracture

and healthy postmenopausal control groups wereanalyzed using age-adjusted logistic regression toestimate the odds ratios (OR) for fracture discrim-ination defined as the increased fracture riskbetween subjects with Z-scores of 0 and –1 (28).For the purpose of comparison with the predictionsof Eq. 4, OR figures were assumed to be equivalentto estimates of RR (29). The OR values were there-fore used to calculate the fracture risk in individualpatients as a factor of p0 using Eq. 2. Mean fracturerisk and its SE were calculated for each of the fourSOS sites and for spine, femoral neck, and totalhip BMD. The population SDs of the BMD andSOS Z-scores for the Colles fracture group werecompared with the predicted figure of unity usingthe F-test. Statistical analysis was performed usinga commercial program (Stata, College Station,TX). A significance level of p < 0.05 was adoptedfor all analyses.

ResultsQuantitative results of the theoretical analysis of

the relationship between the increased risk of frac-ture predicted by Eq. 4 and the RR value of the mea-surement technique are given in Table 1. Patientdemographic data for the in vivo study are given inTable 2. Mean age of the subjects with Colles frac-ture was 69.3 yr (range: 51–95 yr) and of the controlsubjects was 59.0 yr (range: 46–79 yr). The patientswith fracture were shorter than the control subjects,although their weight and body mass index were notsignificantly different. Fifty-four of the 63 patientswith Colles fracture had never received any treat-ment for osteoporosis while the remaining 9 weretreated with only calcium supplements. Mean SOSat each of the four measurement sites and meanspine, femoral neck, and total hip BMD were lowerin the patients with fracture than the control subjects(p < 0.001) (Table 2). Data for the three BMD vari-

ables and for radius and tibia SOS were complete inall 63 patients with Colles fracture and 191 controlsubjects. However, because the Omnisense probesfor the phalanx and metatarsal sites were not avail-able at the start of the study, phalanx SOS was mea-sured in 49 patients with fracture and 128 controlsubjects and metatarsal SOS in 35 patients with frac-ture and 116 control subjects.

Results for OR for the SOS and BMD variablestogether with their 68% confidence interval (CI) andstatistical significance are given in Table 3. OR val-ues for the four SOS sites varied from 1.22 to 1.72and were all statistically significantly different fromunity at the p < 0.05 level except for the tibia site.Larger OR values were found for the BMD mea-surements ranging from 1.82 to 2.48. PopulationSDs for the Colles fracture group expressed in Z-score units varied between 0.86 and 1.30 (Table 3).When compared with the predicted SD of 1.0 (Eq.3), the SD of the fracture group was outside the 95%confidence limits for only one of the seven variables.The estimates of mean fracture risk (and SEM) forthe subjects with Colles fracture compared with themean fracture risk for the whole population are listedin Table 3 and are shown plotted as a function of ORin Fig. 2.

DiscussionA wide variety of different types of equipment is

available for bone densitometry studies includingDXA, quantitative computed tomography (QCT),peripheral DXA, peripheral QCT, and several typesof quantitative ultrasound (QUS) devices (10–13).When results in individual patients are compared,

112 Blake et al.


Table 1Relationship Between RR, Z-score Offset of FracturePopulation β = Ln(RR), and Increased Fracture Risk

of Fracture Population exp(β2)

RR β exp(β2)

1.0 0 1.001.5 0.41 1.182.0 0.69 1.622.5 0.92 2.323.0 1.10 3.34

these different types of measurement often correlatepoorly with correlation coefficients in the range r =0.6–0.8 among different BMD sites and r = 0.4–0.6between QUS and BMD (11,14,15). The difficulty inreconciling the apparently conflicting findings of dif-ferent types of measurement is proving a seriousobstacle to the wider use of BMD and QUS mea-surements in the peripheral skeleton. However, whencomparing different types of measurement, it isimportant to bear in mind that the key parameter for

assessing the clinical value of a bone densitometrytechnique is its RR value inferred from prospectivefracture studies since this relates directly to the abil-ity of the measurements to identify patients at risk offracture (20). The larger the RR value, the better atechnique identifies those individuals who will sub-sequently suffer a fracture. At the present time, theoptimum bone densitometry investigation is the useof femur BMD to predict hip fracture risk for whichRR = 2.7 (5–7). By comparison, measurements at



Table 2Patient Demographic Data and Mean SOS and BMD

Patients with Colles fracture Control Subjects Statistical Variable (mean [SD]) (n = 63)a (mean [SD]) (n = 191)b significancec

Age (yr) 69.3 (7.5) 59.0 (7.3) p < 0.001Weight (kg) 63.8 (12.6) 66.8 (12.0) NSHeight (m) 1.57 (0.08) 1.61 (0.10) p < 0.01BMI (kg/m2) 25.6 (3.7) 25.4 (3.8) NSTibia SOS (m/s) 3751 (157) 3818 (155) p < 0.01Radius SOS (m/s) 3922 (162) 4047 (128) p < 0.001Metatarsal SOS (m/s) 3366 (244) 3557 (190) p < 0.001Phalanx SOS (m/s) 3535 (143) 3872 (199) p < 0.001Spine BMD (g/cm2) 0.79 (0.15) 0.93 (0.14) p < 0.001Femoral neck BMD (g/cm2) 0.64 (0.11) 0.76 (0.12) p < 0.001Total hip BMD (g/cm2) 0.73 (0.14) 0.90 (0.12) p < 0.001

a For phalanx SOS, there were 49 fracture cases and 35 for metatarsal SOS.b For phalanx SOS, there were 128 control cases and 116 for metatarsal SOS.c NS, not significant.

Table 3Results for OR, Its 68% Confidence Limits, and Statistical Significance Obtained from Age-Adjusted Logistic Regression Analysis of Patients with Colles Fracture

Compared with Control Subjectsa

Mean fracture Variable OR (68% CI) p Value SD p Value risk (SEM)

Tibia SOS 1.22 (1.03–1.44) 0.234 1.02 0.845 1.03 (0.03)Radius SOS 1.49 (1.27–1.75) 0.015 1.27 0.027 1.28 (0.09)Metatarsal SOS 1.68 (1.35–2.09) 0.017 1.30 0.059 1.50 (0.16)Phalanx SOS 1.72 (1.36–2.18) 0.024 0.92 0.499 1.12 (0.09)Spine BMD 1.82 (1.52–2.18) 0.001 1.15 0.192 1.51 (0.17)Femoral neck BMD 2.13 (1.73–2.61) <0.001 0.86 0.169 1.58 (0.17)Total hip BMD 2.48 (2.01–3.05) <0.001 1.06 0.573 2.77 (0.52)

a The fourth and fifth columns give the SD of the Colles fracture patients in Z-score units and the statis-tical significance compared with the expected figure of unity obtained using the F test. The final column givesthe mean fracture risk and standard error for the Colles fracture group.

peripheral sites have RR values in the range of1.5–1.8 and are significantly poorer at predicting therisk of hip fracture (5,7,30).

The poor correlation among different devices hasalso made it difficult to devise a common scheme forinterpreting the results of different types of bonedensitometry investigation. Although it is usual tointerpret spine and femur DXA scans using the WHOdefinition of osteoporosis based on a T-score ≤–2.5(8,9), there is compelling evidence that it is not appro-priate to apply this simple rule to other techniquesbecause of the wide variation in the percentage of post-menopausal women who fulfill the WHO criterionwith different types of measurement (16–19). Thisdifficulty has prompted the search for new principlesof scan interpretation, and some investigators havesuggested that bone densitometry studies should bereported using thresholds (or equivalent T-scores)based on estimates of absolute fracture risk (4,22). Thepresent study has examined the basis for the interpre-tation of BMD and QUS variables in terms of absolutefracture risk. If the outcome of different types of mea-surement are to be compared in terms of quantitativeestimates of fracture risk, it is a necessary condition ofconsistency that similar results be obtained for thesame group of patients irrespective of the measure-ment technique used. While it is clear that the poorcorrelation among different types of bone densitome-try measurement precludes this rule from beingapplied to results from individual patients, it is reason-able to expect it to be applicable to results from largegroups of patients with established risk factors forosteoporosis.

We have tested this prediction both theoreticallyand in vivo by comparing quantitative estimates offracture risk derived from different types of bonedensitometry measurement for a group of patientswith existing osteoporotic fractures. The theoreticalanalysis assumed a Gaussian distribution of BMDvalues in the general population and a proportionalhazards model for the dependence of fracture risk onBMD. For RR values of 1.5, 2.0, and 2.5, the aver-age fracture risk of the fracture population wasfound to be 1.18, 1.62, and 2.32 times higher thanthe average risk for the whole population, respec-tively, thus showing that quantitative estimates offracture risk are a function of the RR value of thetechnique (Table 1). These theoretical findings were

compared with in vivo data based on seven differenttypes of BMD and SOS measurement in a group ofpatients with Colles fracture. The ORs obtained bylogistic regression analysis lay between 1.22 and2.48, and their wide range provided a suitable basisfor comparison with the findings of the theoreticalstudy. When the clinical data were used to deriveestimates of fracture risk in individual patients, thefindings of the in vivo and theoretical studies agreedwithin the expected statistical errors (Fig. 2).Although some mismatch is evident in Fig. 2, theseerrors principally reflect the random statistical devi-ations of the population SD values for the fracturegroup from the expected value of 1.0.

It was a limitation of the present study that the the-oretical analysis of fracture risk was necessarily basedon one specific mathematical model—a Gaussian dis-tribution of Z-score values and an exponential depen-dence of fracture risk on Z-score. This model waschosen because it is consistent with the proportionalhazards models widely applied to the interpretation ofprospective fracture studies (5–7,23–25). It also hasthe merit of leading to a simple analytical equation forfracture risk (Eq. 4). Although there is a case forreplacing the exponential dependence of fracture riskon Z-score with the logit function used in logisticregression analysis (28), Eq. 4 would be more com-plex, and the two approaches in any case give thesame result when p0 is much smaller than unity (29).More generally, it is evident from Fig. 1 that any sim-ilar model in which fracture risk increased progres-sively across a bell-shaped population distributionwould lead to a similar conclusion—that estimates ofabsolute fracture risk are dependent on the gradient ofthe fracture risk curve.

Another limitation of our study was the choice ofone particular subject population for the evaluationof absolute fracture risk: patients who had previ-ously suffered a low-trauma fracture. Although veryrelevant to the study of quantitative estimates of frac-ture risk, this choice leads to a particular predictionfor the mean Z-score of the patient group, Z = –β(Eq. 3). Other relations between the mean Z-scoresmeasured by different techniques are possible. Forexample, Frost et al. (31) reported that the meanBMD and QUS Z-scores were approximately equalin groups of patients with specific risk factors forosteoporosis. However, it is evident from Fig. 1 that

114 Blake et al.


the only way in which equal fracture risks could befound for measurements with different RR values isif systematically more negative Z-scores were mea-sured on devices with lower RR values.

In summary, our findings confirm that estimates ofabsolute fracture risk derived from bone densitometrymeasurements are a function of the RR index of themeasurement technique as well as the skeletal status ofthe patient. This conclusion is important given theaccumulating evidence for a clinically significant dif-ference in RR values between peripheral measure-ments and femur BMD. Thus, the concept ofinterpreting bone densitometry results based on evalu-ations of absolute fracture risk would seem to sufferthe same disadvantage as the WHO definition of osteo-porosis based on T-scores—that numerically equal val-ues obtained with different measurement techniquesdo not necessarily imply equivalent skeletal status.

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Fig. 2. Scatter plot showing mean fracture risk of a group of postmenopausal women with established Colles fractureplotted against OR obtained by logistic regression analysis for each of seven different types of BMD and SOS measure-ments measured by DXA and Sunlight Omnisense device. The fracture risk figures have been normalized to the mean frac-ture risk for an age-matched healthy population. The solid line is the theoretical curve of fracture risk against OR predictedfrom Eq. 4.

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