Normal ranges for bone loss rates

Bone and Mineral 26 (1994) 169-180

ELSEVIER

Normal ranges for bone loss rates Philip D. Ross *a, Yi-Fan He a, James W. Davis a, Robert S. Epstein b, Richard D. Wasnich a aHawaii Osteoporosis Center, 401 Kamakee Street, Honolulu, HI 96814, USA bMerck Research Laboratories, Epidemiology Department, West Point, PA 19486, USA

Received 29 November 1993; revision received 9 May 1994; accepted 17 May 1994

Abstract We reported previously that the variability in bone loss rates among postmenopausal women decreases dramatically during the first few years of followup. In this paper, we have examined the distributions of bone loss rates measured at the calcaneus, distal radius and proximal radius. The incidence of physical impairment was five times greater among women with bone loss rates faster than 2 S.D. below the mean. Because the rate of change in bone density was skewed at the lower end of the distribution (representing rapid bone loss), the influence of values at the extreme ends of the distribution were statistically removed in order to estimate the normal distribution of bone loss rates. For the convenience of clinicians, the upper and lower limits of the 90 and 70% normal ranges are presented. Because average bone loss rates vary with age, normal ranges are provided separately by age group. The width of each normal range decreased by at least half after 3 or 4 years of foUowup, compared to less than 1 year. Consequently, measured loss rates which were well within the normal range at l year were sometimes far outside the normal range for longer followup times. We conclude that followup duration has a profound effect on estimates of the normal range, and must be considered when interpreting the clinical significance of measured loss rates. Keywords." Bone density; Bone loss rate; Longitudinal study; Population study; Reference data

1. Introduction Until recently, most information about the rate o f decrease in bone density with age was based on cross-sectional data. More recent reports, such as this paper, provide loss rates based on longitudinal measurements. Measurement errors can lead to * Corresponding author. 0169-6009/94/$07.00 9 1994 Elsevier Science Ireland Ltd. All rights reserved SSDI 0169-6009(94)00726-W

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P.D. Ross et al. / Bone Mineral. 26 (1994) 169-180

errors in estimating the rate of change in bone density. Furthermore, biologic fluctuations in bone density may occur over periods of less than one year (as well as over longer periods). These fluctuations in bone density and measurement errors could be interpreted as large rates of change when observed over short time intervals, but such trends often may not per.sist over longer periods. We recently reported that variability in the rates of change decreases dramatically with followup time [1]. That report estimated the magnitudes of contributions to this trend which were separately attributable to measurement errors and actual changes in bone density. The interpretation of bone density change rates might depend on how well the variability between individuals follows a normal distribution, and to what extent rates of change and their variances are influenced by age. To address these issues, we have examined the distribution of bone density change rates by age group, after correcting for the influence of abnormal cases. For the convenience of clinicians, we have summarized the findings as normal ranges and percentiles.

2. Methods

2.1. Population and measurements Data for the analyses here were obtained from the female subjects of the Hawaii Osteoporosis Study (HOS). These women are the wives of a 30% sample of men born between 1900 and 1920 who previously participated in the Honolulu Heart Program, selected at random. Additional details of the original population have been published [1-3]. All men and their wives (age range 43-80) were of Japanese ancestry. The women in this analysis are a subset (n -- 495) of the original cohort of 1098 women. Inclusion criteria for these analyses were postmenopausal women who had bone density measurements at two or more examinations, and who did not report using estrogens, thiazides, or corticosteroids at any study examination. The average age at the first examination was 64 years (range, 43-80). Bone density was measured at the calcaneus, and the distal and proximal radius, using a custom-made singlephoton densitometer, based on a design developed for the NASA space program [2,4]. Calibration was performed daily, and the 125I radiation source was changed every 6-8 weeks. Measurements were repeated at approximately 1-2 year intervals. The average number of bone density measurements was five for the calcaneus and four for the radius sites, with a mean followup of 5.3 years at each measurement site [I]. The reproducibility (coefficient of variation) of this technique is approximately 1.5% for postmenopausal women [5]. Bone density is expressed here as bone mineral density (BMD; mg/cm 2) for the calcaneus, and bone mineral content (BMC; g/cm) for the radius sites. The mean bone density for ages less than 60, 60-69 and greater than 69 years old, respectively, were 320, 300 and 274 mg/cm 2 for the calcaneus, 0.74, 0.65 and 0.62 g/cm for the distal radius, and 0.77, 0.70 and 0.65 g/cm for the proximal radius [6]. To investigate the potential effects on bone loss rates, physical impairment (disability/poor health) was defined as being bedridden or requiring use of a wheelchair or other aid for at least 8 weeks after the baseline examination, based on the subject's response to a standardized questionnaire.

P.D. Ross et al./ Bone Mineral. 26 (1994) 169-180

171

2.2. Statistics The rate of change in bone density was calculated as the later value minus the earlier value, divided by the time interval between them. This approach was used because it is the most generalizable application of serial bone density measurements; it depends only on the total time interval, and not on how many measurements might have been made between the beginning and end. For each subject, up to 21 values for rate of change in bone density were calculated, using all available combinations of two sequential measurements (a total of up to seven measurements for the calcaneus yields 21 temporally unique combinations; first and last, second and last, first and second, and so on). After calculating all combinations, the loss rates were stratified by the time interval separating each pair of measurements. Age strata were based on the individual's age at the beginning of each pair of observations; thus, one individual could contribute observations to more than one age group. On the average, bone loss rates differ between age groups. At the radius, especially, the mean rate of bone loss decreases substantially with time after the menopause [6]. In order to explore the influence of age, but still preserve adequate sample sizes in each category, subjects were stratified into three age groups; < 60, 60-69 and 70+ years. The average rate of change in bone density for each age group was calculated as the mean, weighted by the inverse of the standard deviation for each followup interval; this gives greater influence to longer followup times, which have less uncertainty compared to short time intervals. The observed distributions of bone density change rates were visibly skewed at the lower end (more rapid loss rates). Because this skewness could influence standard deviations (S.D.), and therefore the normal ranges calculated from S.D., the effects of skewness were removed statistically using the following technique, which has been applied in removing skewness from distributions of vertebral dimensions [7]. Plotting the observed change rates against the observed Z-score quantile (based on the overall distribution) yields a straight line with slope equal to the S.D. for Gaussian distributions. Potential effects of skewness were eliminated by performing least squares regression analysis to estimate the slope after excluding 10% of values at the extremes of this distribution. Percentiles corresponding to the 70% and 90% normal ranges were calculated from the means and S.D.s described above, assuming a normal Gaussian distribution. 3. Results

Quantile-quantile (Q-Q) plots of bone density change rate against Z-score indicated that the relationship was linear over most of the range of values, confirming that most of the observed distribution conforms to a true Gaussian distribution. A representative plot is shown for the calcaneus in Fig. l; similar results were found for the radius sites. The end representing rapid bone loss was visibly skewed away from the normal distribution. We hypothesized that this skewness might be related to rapid bone loss among women with disability or other health problems. To investigate this issue, we compared the incidence of physical impairment after stratifying women into two groups based on their fastest rate of bone loss at the calcaneus.

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P.D. Ross et aL / Bone Mineral 26 (1994) 169-180

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Fig. 1. Plot of observed rates of change in calcaneus bone density by quantile. Individual rates of change in caicaneus bone density among women aged 60-69 with followup intervals between 3.0 and 3.9 years are plotted against Z-scores calculated from the overall distribution. The slope of this plot (excluding the extreme 10% of values at each end) estimates the true standard deviation of the Gaussian distribution for this age, indicated by the solid line. The 80% of values used in calculating the slope lie approximately between Z-scores o f - i . 3 and 1.3. It is apparent from this plot that skewness (deviation from the normal Gaussian distribution) is restricted to extreme values of bone loss.

Table 1 Standard deviations calculated from Q-Q regressions of calcaneus change rates Time interval (mean (S.D.))

0.78 (0.11) 1.49 (0.28) 2.51 (0.26) 3.53 (0.21) 4.59 (0.22) 5.45 (0.30) 6.28 (0.23)

Standard deviation of bone density change rate (mg/cm 2 per year) Age < 60 (n)

Age 60-69 (n)

Age 70 + (n)

14.88 (157) 9.07 (183) 6.67 (143) 4.72 (82) 4.62 (45) 5.09 (67) 3.52 (60)

12.80 (616) 7.73 (686) 5.35 (601) 4.43 (351) 3.20 (213) 3.10 (239) 2.89 (168)

13.31 7.83 4.82 3.77 3.73 2,71 2.60

(166) (173) (158) (96) (61) (49) (30)

Weighted-mean change rates were -5.60 mg/cm 2 per year for age <60, -4.31 mg/cm 2 per year for age 60-69 and -4.15 mg/cm 2 per year for age 70+. Values in the Table indicate the standard deviation of the distribution calculated as the slope of the Q-Q plot. The number in parentheses next to each S.D. value indicates the number of observations used in the Q-Q plot.

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P.D. Ross et al. / Bone Mineral. 26 (1994) 169-180

Table 2 Standard deviations calculated from Q-Q regressions of distal radius change rates Time interval (mean (S.D.))

0.89 (0.1i) !.40 (0.27) 2.43 (0.26) 3.53 (0.21) 4.60 (0.22) 5.52 (0.33) 6.27 (0.23)

Standard deviation of bone density change rate (g/cm per year) Age <60 (n)

Age 60-69 (n)

Age 70 + (n)

0.0350 (28) 0.0287 (132) 0.0212 (105) 0.0150 (83) 0.0102 (42) 0.0113 (23) 0.0109 (56)

0.0412 (166) 0.0267 (496) 0.0177 (450) 0.0126 (342) 0.0101 (196) 0.0094 (78) 0.0085 (148)

0.0435 (66) 0.0261 (129) 0.0168 (126) 0.0126 (92) 0.0086 (56) 0.0069 (17) 0.0076 (25)

Weighted-mean change rates were -0.01297 g/cm per year for age <60, -0.00723 g/cm per year for age 60-69 and -0.00502 g/cm per year for age 70 +. Values in the Table indicate the standard deviation of the distribution calculated as the slope of the Q-Q plot. The number in parentheses next to each S.D. value indicates the number of observations used in the Q-Q plot.

A m o n g the 429 w o m e n w h o a p p e a r e d to be gaining bone, or h a d loss rates slower than 2 S.D. below the mean, only eight women, or 1.9% (95% CI = 0.6, 3.1%), h a d r e p o r t e d physical i m p a i r m e n t d u r i n g the study. However, the prevalence (10.6%, 95% CI = 3.2, 18.0%) was a b o u t five times greater a m o n g w o m e n with extremely r a p i d bone loss (seven out o f 66 w o m e n with loss rates m o r e than 2 S.D. below the mean). These d a t a are consistent with the hypothesis t h a t the skewed distribution is p r o b a b l y caused in p a r t by r a p i d b o n e loss a m o n g w o m e n with physical impairments or o t h e r health problems.

Table 3 Standard deviations calculated from Q-Q regressions of proximal radius change rates Time interval (mean (S.D.))

0.89 (0.11) i.40 (0.27) 2.43 (0.26) 3.53 (0.21) 4.60 (0.22) 5.52 (0.33) 6.27 (0.23)

Standard deviation of bone density change rate (g/cm per year) Age < 60 (n)

Age 60-69 (n)

Age 70 + (n)

0.0351 (28) 0.0210 (132) 0.0158 (105) 0.0114 (83) 0.0107 (42) 0.0109 (23) 0.0089 (56)

0,0300 (166) 0.0198 (496) 0.0126 (450) 0.0093 (342) 0.0073 (196) 0.0065 (78) 0.0067 (148)

0.0278 (66) 0.0191 (129) 0.0119 (126) 0.0093 (92) 0.0081 (56) 0.0067 (17) 0.0058 (25)

Weighted-mean change rates were -0.01203 g/cm per year for age < 60, -0.00665 g/cm per year for age 60-69 and -0.00602 g/cm per year for age 70 +. Values in the Table indicate the standard deviation of the distribution calculated as the slope of the Q-Q plot. The number in parentheses next to each S.D. value indicates the number of observations used in the Q-Q plot.

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P.D. Ross et aL / Bone Mineral. 26 (1994) 169-180

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P.D. Ross et al./ Bone Mineral. 26 (1994) 169-180

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TIME (yr) Fig. 3. Predicted percentiles of distal radius bone density rate of change, by age group and fo|lowup interval. The mean loss rate (50th percentile) is indicated by the horizontal solid line for each age group. The 5th and 95th percentiles (lower and upper 90% normal range limits) are shown as dotted lines, and the dashed lines indicate the 15th and 85th percentiles (lower and upper 70% normal range limits) predicted by a Gauss/an distribution. The reproducibility of the technique used for the bone density measurements was 0.0216 g/cm [5]. Ranges should be adjusted for instruments with better, or worse reproducibility (see text).

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P.D. Ross et al. / Bone Mineral. 26 (1994) 169-180

The standard deviations (S.D.) of bone loss rate distributions calculated from the Q-Q plots are provided in Tables 1-3, together with the mean bone loss rates for each age group. The values of S.D. declined substantially with increasing time intervals. On the average, the S.D. calculated from the regressions of the Q-Q plots (Tables 1-3) were 89 4- 7% (mean 4- S.D.) as large as the S.D. values calculated from the overall distributions (not shown), suggesting that abnormal loss rates resulted in about an 11% upward bias in the unadjusted S.D. values. The means and percentiles corresponding to 70 and 90% normal ranges of bone density change rates, stratified by age group and time interval, are illustrated in Figs. 2-4 for the three bone measurement sites. The 90% normal range includes 90% of the expected values; therefore, 5% are outside this range at either end, and the limits of this range correspond to the 5th and 95th percentiles predicted from the Gaussian distribution. By definition, an estimated 5% of women have change rate values below the 5th percentile, and 95% have values below the 95th percentile. Similar reasoning leads to 15th and 85th percentile limits for the 70% normal range. The bone loss rate means were essentially identical at the distal and proximal radius sites for women of similar age, but the normal ranges were consistently wider for the distal radius than the proximal radius for all time intervals of the 60-69 age group, and up to about 4.5 years of followup for the other age groups, except for the first time interval of the age < 60 group (Figs. 3 and 4). 4. Discussion

Longitudinal measurements of changes in bone density are preferable to estimates based on cross-sectional data, which fail to consider possible cohort effects [6]. For example, women who are currently older than eighty years had different lifestyles than their daughters, who are 20-40 years younger. Attempting to estimate average loss rates from the slope of bone density plotted against age would fail to consider possible effects of these lifestyle differences on peak bone density and subsequent losses. An example of this was reported earlier for our cohort, where longitudinal rates of change for the radius were found to be much slower at older ages than predicted from the cross-sectional data [6]. Another limitation of cross-sectional data is that it is not possible to estimate the degree of variability in bone loss rates between people. To overcome these limitations, we present results here that are based on longitudinal measurements. We reported previously how to calculate normal ranges for individual bone loss rates. However, deciding what rate of bone loss should be cause for concern remains controversial, and somewhat arbitrary. In this paper, we report normal ranges for the distribution of loss rates between individuals. One potential use of this approach would be to help select individuals with abnormal loss rates who should be studied in greater detail for possible underlying conditions. Among the Hawaii Osteoporosis Study (HOS) women, the average rate of bone loss declined with age at the radius sites, but remained relatively constant at the calcaneus [6]. We report here that age also appears to influence the variance in change rates. Because the average rates of change vary with age group, and the variance in change rates varies with both age

177

P.D. Ross et aL / Bone Mineral 26 (1994) 169-180

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P.D. Ross et al. / Bone Mineral. 26 (1994) 169-180

and followup interval, we have summarized mean change rates and their normal ranges by age group and followup interval. The variance of loss rate distributions and the estimates of sample size required to detect specified differences in loss rate between groups of subjects should be greater for followup periods less than 5 years, and smaller for more than 5 years followup, compared to our earlier reports, which were based on the average followup interval of 5.3 years [5,8,9]. The data presented here suggest that the large majority of bone density change rate data for our population are consistent with a Gaussian distribution. Hui and Berger [10] also reported that bone density change rates were normally distributed. Knowing that the variability in change rates follows a predictable distribution greatly simplifies interpretation of the results. We also present evidence that at least some of the outlying values which cause skewness in the 'uncorrected' distribution appear to be related to health problems such as disability. Our population was restricted to subjects who were not using drugs which are known to strongly influence bone loss rate, but were not restricted on other health variables because we wanted the results to be as generalizable as possible. If we were to exclude subjects with any health problem (history of diabetes, stroke, MI, etc.), the sample size might be too small, and the results difficult to generalize, because many elderly people have some health disorders. The greater variance at shorter followup time appears to be related partly to actual (biological) fluctuations in the rate of change in bone density which do not persist for more than a few years [1]. Similar results were reported by Hui et al. [11]. They found that bone loss rates during the first 5 years of observation correlated poorly with loss rates during the subsequent 5 years. In this paper, we describe normal ranges which include the influences of both (1) biological fluctuations in bone density over time and (2) instrument precision errors. The normal ranges would be narrower for densitometers with better precision, and wider if precision is worse. The effect of changes in precision can be calculated using estimates of the true variance and error contributions published previously [1] by altering the magnitude of the error term in the equation: observed variance = (variance due to error) + (true variance), where variance = S.D. 2. For example, if the precision was 2.0% (instead of the 1.5% in this study), both the 70 and 90% normal ranges at 0.8 year would be approximately 15% wider than shown in Fig. 2. If the precision were 1.0% (instead of 1.5%), both the 70% and 90% normal ranges at 0.8 year would be about 13% narrower than shown in Fig. 2. Because the influence of measurement error decreases profoundly with followup time, with 6 years followup the effects of changing instrument precision to 2.0 or 1.0% (instead of 1.5%) would only increase or decrease the width of the normal ranges by 4 or 3%, respectively, compared to Fig. 2. The effect of increasing the number of measurements can also be estimated, using the equations provided in reference [9]. Increasing the number of measurement points might reduce the variability of measured loss rates by helping to reduce the effects of measurement errors. From the information in Ref. 9 and Table 1, we estimate that the S.D. of the calcaneus loss rate distribution for 5 years of followup would be reduced by 2.6, 5.2 and 7.8%, respectively, if the number of measurements

P.D. Ross et al. / Bone Mineral. 26 (1994) 169-180

179

were increased to four, five or six (instead of two measurements). Thus, increasing the number of measurements has much less effect on the loss rate S.D., compared to increasing the time interval. This is partly because measurement errors only account for part of the variability in measured loss rates, and because uncertainties in bone loss rates are influenced by the duration of observation to a much greater degree than by the number of points [9]. There is currently no consensus regarding how to interpret bone loss rates. What rate of loss should be cause for concern? To illustrate the implications of our findings, consider a situation where a loss rate twice as fast as the mean would signal a need for intervention. Among women aged 60-69, more than 15% of women have greater than double the average calcaneus loss rate with 2 years followup, and an even larger percentage at 1 year (37% at 0.8 years). However, with 4-5 years of followup, only about 5% of women fall into this category (Fig. 2). A rate of change which is well within the limits for measurements made one year apart may be far outside the limits for longer intervals. For example, a change rate of -20 mg/cm 2 per year at the calcaneus (corresponding to about 7% per year, based on the mean bone density of about 300 mg/cm2 of women at age 65 years) is only about 1 S.D. below the mean if the interval between measurements was 1 year, almost 2 S.D. below the mean for an interval of 2 years, and about 5 S.D. below the mean for intervals greater than 4 years. For the calcaneus and proximal radius, the greatest decrease in width of the normal range occurs during the first 3 years of followup. However, the magnitude of decline in variability was less for the youngest age group, at all three bone measurement sites, suggesting that biological differences in change rates may persist for longer periods in this age group. Decreases in width of the normal range with followup time were almost identical (proportionately) comparing the distal radius and calcaneus. The wider range for distal radius compared to the proximal radius does not mean that the distal radius would be less useful clinically. It indicates that there may be more variation between individuals at the distal radius. This variation may in fact make it easier to categorize, or distinguish between people based on rates of change in bone density. It is difficult to estimate the generalizability of the results presented here, because there are few longitudinal data with which to compare our loss rates. Harris and Dawson Hughes [12] reported loss rates o f - 1 . 8 % per year at the calcaneus and -0.68% per year at the proximal radius for approximately 100 women at 11-20 years postmenopause (adjusted for calcium intake, treatment, smoking and body mass index). Although the rates are not directly comparable, these values are very similar to our estimates of -1.4% per year at the calcaneus and -1.0% per year at the proximal radius for women ages 60-69, based on Tables 1-3, and bone mass for this age group. Thus, our loss rate data appear to be consistent with those reported for postmenopausal Caucasian women. In summary, we have presented normal ranges for the distribution of bone density change rates among postmenopausal women in the HOS. It is our hope that comparison of measured rates of change in bone density to the population distribution will help physicians to understand and interpret changes in bone density over time.

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Acknowledgements The authors thank the staff of the Hawaii Osteoporosis Center for excellent technical and logistic support. This study was supported in part by a grant from Merck Research Laboratories, by PHS grant R01 AG10412-01 under the auspices of the Pacific Health Research Institute, and by the Hawaii Osteoporosis Foundation.

References [1] He Y-F, Davis JW, Ross PD, Wasnich RD. Declining bone loss rate variability with increasing follow-up time. Bone Mineral 1993;21:119-128. [2] Yano K, Heilbrun LK, Wasnich RD, Hankin JH, Vogel JM. The relationship between diet and bone mineral content of multiple skeletal sites in elderly Japanese-American men and women living in Hawaii. Am J Clin Nutr 1985;42:877-888. [3] Heilbrun LK, Ross PD, Wasnich RD, Vogel JM, Yano KY. Characteristics of respondents and nonrespondents in a prospective study of osteoporosis. J Clin Epidemiol. 1991;44(3):233-239. [4] Vogel JM. Application principles and technical considerations in SPA. In: HK Genant (ed), Osteoporosis Update, University Press, Berkeley. 1987;219-231. [5] Ross PD, Davis JM, Wasnich RD, Vogel JM: The clinical application of serial bone mass measurements. Bone Mineral 1991;12:189-199. [6] Davis JW, Ross PD, Wasnich RD, MacLean CJ, Vogel JM: Comparison of cross-sectional and longitudinal measurements of age-related changes in bone mass. J Bone Mineral Res 1989;4(3):351-357. [7] Black D, Cummings SR, Stone K, Hudes E, Palermo L, Steiger P. A new approach to defining normal vertebral dimensions. J Bone Mineral Res 1991;6:883-891. [81 Wasnich RD, Ross PD, Vogel JM, Davis JW: Osteoporosis. Critique and Practicum. Banyan Press, Honolulu, 1989. [9] Davis JW, Ross PD, Wasnich RD, MacLean CJ, Vogel JM. The long-term precision of bone loss rate measurements among postmenopausal women. Calcif Tissue Int 1991;48(5):311-318. [10] Hui SL, Berger JO. Empirical Bayes estimation of rates in longitudinal studies. J Am Stat Assoc 1983;78:753-760. [11] Hui SL, Slemenda CW, Johnston CC Jr. The contribution of bone loss to postmenopausal osteoporosis. Osteoporosis lnt 1990;1:30-34. [12] Harris S, Dawson-Hughes B: Rates of change in bone mineral density of the spine, heel, femoral neck and radius in healthy postmenopausal women. Bone Mineral 1992;17:87-95.