In a recent article, Cummings et al. (1) appliedthe concept of regression to the mean to the moni-toring of osteoporosis therapy using bone mineraldensity (BMD) measured by dual X-ray absorp-tiometry (DXA). As applied to bone densitometry,the principle of regression to the mean is observedwhen individuals who have BMD measurementsthat differ from the mean for a population haverepeat BMD measurements that are closer to thatmean (1). Because regression to the mean wasobserved in their analysis of the FractureIntervention Trial (FIT) with alendronate and theMultiple Outcomes of Raloxifene Evaluation(MORE) trial with raloxifene, Cummings and col-leagues concluded that “treatments for osteoporo-sis should not be changed because of loss of BMDduring the first year of use” (1). This articleprompted much-needed discussion about the valueof monitoring BMD changes. Application of theconcepts presented in that article to the use of ser-ial bone density measurements in clinical practicerequires further consideration.

Cummings and colleagues examined the BMDchange in the treated patients from the alendronateFracture Intervention Trials (FIT) (2,3). For theiranalysis, they divided the patients into eight groupsbased on the 1-yr change in BMD (see legend forFig. 1 for group assignments). Their Table 1 (see

Table 1 in this article) shows that the group who hadthe greatest increase in BMD (10.4%) during year 1,had the greatest decrease in BMD (1.0%) duringyear 2. Likewise, the group that had the greatestdecrease in BMD (6.6%) during year 1, had thegreatest increase in BMD (4.8%) during year 2 (1).Clearly, the principle of regression to the mean ispresent. However, their figure (see our Fig. 1A) sug-gests that the patients whose BMD was above thebaseline at year 1 were below the baseline at year 2and vice versa. This display of data is misleadingbecause their own data (see Table 1) show that thegroups with extreme changes in BMD during year 1do not cross baseline during year 2. The manner inwhich the data are presented has a profound impacton the reader’s interpretation. Although Cummingsand colleagues convincingly showed the principle ofregression to the mean in their article, their figuremight mislead the reader into thinking that patientswith extreme changes in BMD during year 1 hadeven more dramatic changes (in the opposite direc-tion) during year 2. When Cummings’ data are plot-ted beginning with the baseline values, the impressionis much different (Table 2 and Fig. 1B). The phe-nomenon of regression to the mean is still seen, butthe effect is much less dramatic.

The use of BMD for monitoring osteoporosistherapy in clinical practice is different from its use inclinical trials. In clinical trials, the use of BMD formonitoring is intended to show a difference betweenthe treatment group and a placebo group. In clinicalpractice the use of BMD for monitoring is intended

Regression to the Mean: What Does it Mean?Using Bone Density Results to Monitor Treatment of Osteoporosis

Leon Lenchik, MD1 and Nelson B. Watts, MD2

1Assistant Professor of Radiology, Wake Forest University School of Medicine, Winston-Salem NC, and 2Professor ofMedicine, Emory University School of Medicine, Atlanta GA

1

Editorial

Journal of Clinical Densitometry, vol. 4, no. 1, 1–4, Spring 2001 © Copyright 2001 by Humana Press Inc. All rights of any nature whatsoever reserved. 0169-4194/01/4:1–4/$11.00

Received 08/07/00; Revised 11/27/00; Accepted 12/05/00.

to identify individual patients who are not compliantwith therapy as well as those who do not respond tothat therapy. In clinical practice, it is customary to

1. monitor the PA spine rather than the total hip (thesite used by Cummings et al.),

2. use the concept of least significant change (LSC)to distinguish biologic change from that attribut-able to instrument error,

3. compare the results of a follow-up measurementto the baseline measurement as well as to the lastmeasurement, and

4. monitor after 2 yr rather than 1.

Therefore, it is instructive to consider the effect ofthese principles of use of serial BMD in clinicalpractice on the conclusions of Cummings and col-leagues, which were drawn from clinical trial data.

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Fig. 1 (A) Percentage change in total hip BMD with alendronate treatment in the Fracture Intervention Trial (FIT).Symbols reflect groups based on BMD change at year 1: open squares, >8% gain; open diamonds, 6–8% gain; open tri-angles, 4–6% gain; open circles, 2–4% gain; closed circles, 0–2% gain; closed triangles, 0–2% loss; closed diamonds,2–4% loss; closed squares, >4% loss. From Cummings et al. (1), American Medical Association, used with permission.(B) Percentage change from baseline in total hip BMD with alendronate treatment. Symbols reflect groups based on BMDchange at year 1: open squares, >8% gain; open diamonds, 6–8% gain; open triangles, 4–6% gain; open circles, 2–4%gain; closed circles, 0–2% gain; closed triangles, 0–2% loss; closed diamonds, 2–4% loss; closed squares, >4% loss.Based on data from Cummings et al. (1) (reprinted with permission). (Copyright © 2000, American Medical Association.)

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Quantitative measurements including BMD aresubject to a statistical variation. In bone densitome-try, precision is defined as the reproducibility of ser-ial measurements. When monitoring therapy, knowingthe precision error allows clinicians to distinguishdifferences that are due to statistical variations inher-ent in the instrument from changes that are due totherapeutic effects. Because osteoporosis therapyusually leads to greater increases in BMD at the spinethan at the hip, and the precision error for measure-ment is lower at the spine, most clinicians use mea-surements at the spine for monitoring therapy. Inaddition, the FDA-approved dose of alendronate fortreatment of postmenopausal osteoporosis, 10 mg pd,produces greater gains in BMD than the 5-mg doseused in the Cummings study. Although the principleof regression to the mean applies to spine measure-ments as well as any others, the impact is likely to beless when the biological change is greater.

In clinical practice, knowing the least significantchange (LSC) is essential for proper interpretation offollow-up bone density measurements (4). To deter-mine the least significant change at the 95% confi-dence level, the precision error is multiplied by 2.77(5). When monitoring therapy, a change in BMD thatexceeds the LSC indicates to the clinician that he orshe can be 95% confident that that change in BMDis due to the effect of treatment and not due to statis-tical variation. Because precision errors in clinicalpractice are typically 1.5–2 times worse than that of

clinical trials, it is common to require a 3–5%change in BMD at the spine and 4–6% at the totalhip before it can be considered to be real. Whenmonitoring osteoporosis therapy, BMD changes thatare less than the LSC should be reported as “nochange” and should not lead to changes in patientmanagement.

Table 2 demonstrates how the concept of LSCaffects the Cummings analysis. The critical questionis how many individuals would “lose” bone (i.e.,more than the LSC) at year 1 compared with baselineand at year 2 compared with baseline. Unfortunately,because the data from Cummings’ analysis are forgroups rather than individuals, the full impact of thiscannot be calculated. Most of the group means arewithin or above the clinical LSC (i.e., improved orunchanged), where therapy would not be changed.For this reason, both the principle of regression to themean and the principle of LSC should lead cliniciansto the same conclusion: Small differences in BMD inpatients receiving osteoporosis therapy should notresult in changes to that therapy.

Looking at the group data, Cummings’ analysisshows that 37 patients out of 2,634, or 1.4%, wouldbe labeled as “losing” bone at 1 yr. At 2 yr, the meanfor this group is within the LSC; however, some indi-viduals in this group might have changes that exceedthe LSC (i.e., would be “losing” at both the 1-yr and

Table 1From Table 1 in Cummings et al. (1)

Mean Mean Percentage percentage percentage

change change change during during during year 1 year 1 year 2

<-4 (loss) -6.6 4.8-4 to <-2 -2.9 1.8-2 to 0 -0.9 1.70 to <2 1.0 1.02 to <4 3.0 0.84 to <6 4.9 0.56 to < 8 6.8 0.1> 8 gain 10.4 -1.0

Table 2Percentage change from baseline in total hip bone

mineral density (BMD)a

Number of Category Subjects Year 1 Year 2

A 61 10.4* 9.4*B 133 6.8* 6.7*C 406 4.9 4.4D 759 3.0 2.2E 791 1.0 0.0F 345 -0.9 0.7G 102 -2.9 -1.1H 37 -6.6* -1.8

aCategories based on BMD change at Year 1: Category A,>8% gain; B, 6–8% gain; C, 4–6% gain; D, 2–4% gain; E, 0–2%gain; F, 0–2% loss; G, 2–4% loss; H, >4% loss. From data inCummings et al. (1). Asterisks (*) indicate differences thatexceed the least significant change (LSC).

2-yr measurements) and some whose change fellwithin the LSC might actually be losing. Deciding toinvestigate these patients further based on an appar-ent decrease in BMD after 1 yr of treatment does notseem like a radical mistake.

There are no studies that provide guidance in themanagement of patients who truly lose BMD while ontreatment for osteoporosis. Many of these patients areconsidered “nonresponders,” and their medicationsare discontinued or changed. The principles of regres-sion to the mean and least significant change suggestcaution in following this approach. However, it islikely that different patients would be in the “loss”group in clinical practice than in the Cummings’study. In clinical practice, there are many patients whoare not adherent to therapy; it is likely that many ofthese patients would be in the “loss” group. There arefew of these patients in clinical trials, and those fewpatients in FIT were excluded from Cummings’analysis. Technical factors may also explain the “loss”of BMD in some patients: inconsistent patient posi-tioning, inconsistent scan analysis, or even change inequipment. This was adjusted for in the analysis of theFIT data. These should be done in clinical practice,but this may not always be the case.

Because clinicians are interested in the cumulativeeffect of osteoporosis therapy, follow-up DXA exam-inations are usually compared with baseline as wellas with the most recent measurement. Table 2 showsthe effect of comparing year 2 with baseline ratherthan with year 1. In most instances, group means arein the same categories (i.e., significant increase, nochange, or significant decrease) at year 1 and year 2.

Monitoring of BMD at 2 yr rather than 1 yr afterinitiating osteoporosis therapy is becoming com-mon in clinical practice. This makes sense consid-ering that the magnitude of treatment effect and theleast significant change are often very close. Whenmonitoring patients on osteoporosis therapy, BMDchanges are more likely to exceed the LSC aftertwo years of therapy rather than after one year. Itwould be instructive to evaluate how the principle

of regression to the mean would apply if year 2 ofalendronate therapy was to be compared to year 4.Because of the way the FIT trial was designed,Cummings and colleagues were not able to analyzethe data in this manner.

Regression to the mean occurs in serial monitor-ing of BMD as it does in other serial biological mea-surements. The impact of this on clinical practiceshould be considered when interpreting results.Nevertheless, regression to the mean does not renderserial BMD measurements useless. Appropriateattention should be paid to acquisition and analysisof data. The precision error of the measurement mustbe known and used to calculate the least significantchange (LSC). Serial results within the bounds ofLSC should be reported as “no change.” If there is anapparent decrease in BMD, more than the LSC, thedata should be reexamined, the scan should berepeated if necessary, changes at other sites shouldbe considered, and other indicators of response totherapy (e.g., biochemical markers of bone turnover)should be measured. If, after considering all of thesefactors, it is felt that the patient is not responding totreatment, and a careful investigation for underlyingdiseases or conditions yields nothing, then a changein treatment seems appropriate.

References1. Cummings SR, Palermo L, Browner W, et al. 2000 Monitoring

osteoporosis therapy with bone densitometry - Misleadingchanges and regression to the man. JAMA 283(10):1318–1321.

2. Black DM, Cummings SR, Karpf DB, et al. 1996 Randomizedtrial of effect of alendronate on risk of fracture in women withexisting vertebral fractures. Lancet 348:1535–1541.

3. Cummings SR, Black DM, Thompson DE, et al. 1998 Effectof alendronate on risk of fracture in women with low bonedensity but without vertebral fractures—Results from thefracture intervention trial. JAMA 280(24):2077–2082.

4. Glüer CC, Blake G, Lu Y, et al. 1995 Accurate assessment ofprecision errors: how to measure the reproducibility of bonedensitometry techniques. Osteoporos Int 5:262–270.

5. Yao L, Sayre JW. 1994 Statistical concepts in the interpreta-tion of serial bone densitometry. Invest Radiol 29:928–932.

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