Estimation of lean body weight in older women with hip fracture

Abstract

Objective

Lean body weight (LBW) decreases with age while total body fat increases, resulting in altered drug pharmacokinetics. A semi-mechanistic equation estimating LBW using height, weight and sex has been developed for potential use across a wide range of body compositions. The aim of this study was to determine the ability of the LBW equation to estimate dual energy x-ray absorptiometry-derived fat free mass (FFM_DXA) in a population of older women with recent hip fracture.

Methods

Baseline, four and 12 month data obtained from 23 women enrolled in the Sarcopenia and Hip Fracture study were pooled to give 58 measurements. LBW was estimated using the equation:

$$LBW\left(\mathrm{k}\mathrm{g}\right)=\frac{9270\times Wr}{8780+(244\times BMI)}$$

Body composition was classified as: ‘normal' (BMI <25kg/m² and not sarcopenic), ‘overweight-obese' (BMI >25kg/m² and not sarcopenic), ‘sarcopenic' (sarcopenic and BMI <25kg/m²), or ‘sarcopenic-obese' (sarcopenic and BMI >25kg/m²). The ability of the LBW equation to predict FFM_DXA was determined graphically using Bland-Altman plots and quantitatively using the method of Sheiner and Beal.

Results

The mean ± SD age of female participants women was 83±7 years (n=23). Sarcopenia was frequently observed (65.2%). Bland-Altman plots demonstrated an underestimation by the LBW equation compared to FFM_DXA. The bias (95% CI) and precision (95% CI) calculated using the method of Sheiner and Beal was 0.5kg (−0.7, 1.66kg) and 4.4kg (−3.7, 12.4kg) respectively for pooled data.

Conclusion

This equation can be used to easily calculate LBW. When compared to FFM_DXA, the LBW equation resulted in a small underestimation on average in this population of women with recent hip fracture. The degree of bias may not be clinically important although further studies of larger heterogeneous cohorts are needed to investigate and potentially improve the accuracy of this predictive equation in larger clinical cohorts.

Introduction

Increasing age after mid-life is associated with decreases in lean body weight (LBW) and increases in total body fat (1). Sarcopenia, defined as an involuntary loss of muscle mass and strength that occurs with ageing, contributes to a loss of functional status, increased risk of illness and increased mortality (2, 3), however there is still no consensus for any standardized definition of sarcopenia (4). Age-related sarcopenia is a contributor to frailty, a biologic syndrome of decreased reserve and resistance to stressors (5). LBW is a predictor of the functional capacity of the body for drug elimination (6) as over 99% of metabolic processes (including drug clearance) take place in lean tissue (7). Age-related changes in body composition also affect drug pharmacokinetics, particularly volume of distribution and clearance (8).

Body composition can be assessed using multiple methods including bioelectrical impedance, total body nitrogen, skin fold thickness measurements and multi-compartmental models (9, 10). Dual energy x-ray absorptiometry (DXA) offers a relatively low-cost alternative method of body-composition assessment that involves minimal radiation exposure and is becoming increasingly common in clinical and research applications (11). DXA-derived fat free mass (FFM_dxa) can be calculated from the analysed scan output by summing total bone mineral content (BMC) and fat free soft tissue (FFST) (9). clinically, the terms LBW and FFM can be used interchangeably. While LBW includes the lipids in cellular membranes, the central nervous system and in bone marrow and FFM does not, this is considered to be a negligible fraction of total body weight (approximately 3% in males and 5% in females) (10). It would be of significant clinical value to have an accurate method of estimating LBW that relies on easily measured subject characteristics (e.g. body weight, height) (10) in cases where DXA is unavailable or impractical.

Recently, a semi-mechanistic gender specific equation for estimating LBW based on height and weight terms was described (10, 12). This equation was developed using a population of relatively healthy men (n=168) and women (n=205) aged 18-82 years, with bodyweights of 40.7-216.5kg and body mass index (BMI) values of 17.1-69.9 kg/m² (10). The predictive equation was externally evaluated in a separate population of subjects (BMI 18.7-38.4 kg/m²) and was compared to a reference method, FFM_DXA (10). The prediction error for the LBW equation compared to FFM_dxa for female participants, was acceptably small indicated by a mean error (95% confidence interval (CI)) of 1.14kg (0.07, 2.20kg) and root mean square error (95% CI) of 3.90kg (2.55, 4.88kg) (10). The LBW equation was based on the biologically plausible Ohms Law developed using knowledge of the interaction between variables and not from an empirical relationship derived from the data (10) such as regression of variables, therefore the LBW equation has theoretical applicability to all body types (10). However further evaluation of the LBW equation as a tool for estimating LBW is required, particularly in older women who have altered body composition.

The aim of this study was to determine the transportability of the LBW equation to predict dual energy x-ray absorptiometry derived fat free mass in older women with recent hip fracture as an alternative method to estimate LBW using the easily obtainable participant characteristics of height, weight and sex.

Methods

De-identified data were obtained from baseline, four month and 1 2 month measures on 23 women enrolled in the Sarcopenia and Hip Fracture (SHIP) study, a cohort study of community-dwelling older persons admitted for surgical repair of hip fracture to three acute care hospitals in Sydney, Australia: Royal North Shore Hospital (RNSH), Royal prince Alfred Hospital, and St. George Hospital (13). These women were part of a pre-planned sub-study of in-depth body composition analysis within the SHIP cohort, and included all those who agreed to DXA scanning from among the RNSH recruitment site where the scanner was located (13). The SHIP study was approved by each hospitals human ethics committee and the University of Sydney Human Ethics committee. Permission to access the SHiP study database was approved by the Northern Sydney central coast Health Area Health Service Human Ethics committee and by Professor Fiatarone Singh, chief investigator.

Lean Body Weight (LBW) and Fat Free Mass (FFM)

LBW was calculated according to the LBW equation for females (10, 12):

Females

$LBW\left(\mathrm{k}\mathrm{g}\right)=\frac{9270\times Wt}{8780+(244\times BMI)}$

Where WT is weight (kg) and BMI is body mass index (kg/m2)

DXA measurements were performed on a Norland (Fort Atkinson, Wi, USA) Model XR36 instrument as described previously (9, 14). FFM_DXA was calculated from the analysed scan output by summing total BMc and FFST. Precision of total BMC, FFM_DXA and FFST measurements were 1.4%, 2% and 2%, respectively (9). The same researcher (RH) analysed all scans. It has been reported that metal implants can affect DXA scans resulting in underestimation of fat mass and bone area (15, 16). Participants who had metal implants had their scans corrected as suggested by Di Monaco et al (17, 18).

Body Composition

Body mass index (BMI) was defined as: underweight BMI < 18.5 kg/m², normal BMI 18.5-25 kg/m², overweight 25-30 kg/m², and obese BMI >30 kg/m² (19). The female classification for sarcopenia was defined as a skeletal muscle index (SMi) of <7.0 kg.m² (20). Body composition was classified as follows: “normal “ (BMI <25 kg/m² and not sarcopenic), “overweight-obese “ (BMI >25 kg/m² and not sarcopenic), “sarcopenic” (sarcopenic and BMI < 25 kg/m²), or “sarcopenic-obesity” (sarcopenic and BMi >25 kg/m²) (13).

Predictive performance of the LBW equation compared to DXA-derived FFM

The method of Bland and Altman (21) was used to assess graphically the bias and limits of agreement between FFM_DXA and the LBW equation (10, 12). The limits of agreement were defined as the mean difference between the two methods (DXA and the LBW equation) ± 2 standard deviations of the difference (21). The predictive performance was assessed quantitatively in terms of the mean error (ME) and root mean square error (RMSE) calculated according to the method of Sheiner and Beal with 95% CI (22). The ME is an estimate of the bias in the prediction and should include zero for a non- biased model (22). The RMSE is a measure of the precision of the model predictions (22).

Data Analysis

one hundred and ninety three participants (72% female) were enrolled into the SHiP study at baseline and DXA data were available for 23 female participants. Data from baseline, four and 12 months were pooled to give a total number of 58 DXA measurements. Data from participants enrolled in the SHiP study who did not have a DXA measurement were excluded from analysis. All data are presented as mean ± standard deviation (SD) or number (percent) as specified. Subgroup analysis was performed based on body composition and BMi as defined above. The Kruskal-Wallis Analysis of ranks was used to determine differences between participant characteristics at baseline, four month and 12 months. The Mann-Whitney U test was used to determine differences in the ME at baseline compared to four and 12 months following hip fracture. A p value of < 0.05 was considered statistically significant. SPSS version 16.0 for Windows (SPSS, inc, chicago, IL) was used for all data analysis.

Results

Participant characteristics

The characteristics of participants are shown in Table 1. DXA data were available for 23 women at baseline, 16 at four months and 19 at 12 months yielding a total of 58 DXA measurements. Twelve women had measurements at all three time periods, eight at two time periods (n=1 baseline and four months; n=4 at baseline and 12 months; n=3 at four and 12 months) and six women had only baseline measurements.

Table 1.

characteristics of female SHip participants at baseline, four months and 12 months following hip fracture

	Baseline	Four months following hip fracture	12 months following hip fracture	Pooled data	p*
N	23	16	19	58
Age (years)	83.0 ± 8.7	84.6 ± 7.3	83.3 ± 9.2	83.5 ± 8.4	0.98
Weight (kg)	56.5 ± 15.6	57.0 ± 9.5	60.1 ± 14.4	57.8 ± 13.6	0.49
Height (m)	1.56 ± 0.09	1.55 ± 0.09	1.55 ± 0.09	1.55 ± 0.09	0.94
BMI# (kg/m2)	23.2 ± 5. 5	23.7 ± 3.3	24.9 ± 5.0	23.9 ± 4.8	0.33
FFMDXA† (kg)	35.4 ± 8.8	36.6 ± 5.7	37.5 ± 7.2	36.9 ± 6.5	0.89
LBW‡ (kg)	35.8 ± 6.6	36.1 ± 4.8	37.1 ± 6.24	36.1 ± 5.9	0.73

^*p comparing baseline, 4 month and 12 month participant groups using Kruskal-Wallis Analysis of ranks; BMI#: Body Mass index; FFM_DXA†: Dual energy x-ray absorptiometry- derived fat free mass; LBW‡: Lean body weight (kg) calculated using the LBW Equation (10,12)

The mean ± SD age of participants was 83 ± 7 years (baseline, n=23). Sixty five percent of women were sarcopenic. Age, weight, height and BMI were not significantly different across time points for participants (Table 1).

Predictive performance of the LBW equation compared to ffm_dxa

DXA data were analysed by time point (Figure 1A), across body composition sub-groups of normal, overweight-obese, sarcopenic, and sarcopenic-obese (Figure 1B) and by BMI (Figure 1C).

Figure 1.

Bland-Altman plots for female SHIp participants showing pooled DXA data with the mean difference (solid line) and limits of agreement (dashed line). Data points are stratified by data collection time (A), body composition category (B) and by body mass index category (C)

Bland-Altman plots demonstrated an underestimation by the LBW equation compared to FFM_DXA with a mean difference of 0.59 kg and limits of agreement of -8.11kg to 9.29kg. The mean difference was small however the individual differences ranged from a 12.3kg underestimation by the LBW equation compared to FFM_DXA, up to a 6.7kg overestimation by the LBW equation compared to FFM_DXA. Subgroup analysis of body composition (Figure 1B) and BMI categories (Figure 1C) revealed trends towards non-random distribution of data points around the line of identity, with more underestimation by the LBW equation compared to FFM_DXA at higher values of LBW.

The predictive performance (22) was assessed quantitatively with the ME and RMSE with 95% CI shown in Table 2. There was a trend towards a smaller ME (95% CI) at four months 0.5kg (-1.6, 2.6kg; p=0.92) and 12 months following hip fracture 0.4kg (-1.8, 2.6kg; p=0.70) compared to baseline 0.8kg (-1.2, 2.8kg) values. The ME (95% CI) expressed as a percentage of total FFM_DXA for pooled data was small 0.4% (2.5, 3.4%). The RMSE was smaller at four and 12 months compared to baseline.

Table 2.

Precision and bias calculated according to the methods of Sheiner and Beal (22) comparing FFM_DXA† to the LBW‡ equation for female SHIP (13) participants. DXA data is shown stratified by collection time and by body composition

	ME*	%ME#	RMSE∞
	(95% CI)	(95% CI)	(95% CI)
Pooled data (n=58)	0.5	0.4	4.4
	(−0.7, 1.6)	(−2.5, 3.4)	(−3.7, 12.4)
Baseline (n=23)	0.8	1.4	4.6
	(−1.2, 2.8)	(−3.8, 6.6)	(−11.3, 20.5)
Four months following	0.5	0.6	3.9
hip fracture (n=16)	(−1.6, 2.6)	(−6.3, 5.0)	(−5.1, 12.3)
12 months following	0.4	0.2	4.4
hip fracture (n=19)	(−1.8, 2.6)	(−5.0, 5.4)	(−11.3, 20.1)
Sarcopenic (n=33)	0.2	0.4	3.2
	(−0.9, 1.4)	(−3.0, 3.7)	(−3.8, 10.1)
Sarcopenic-obese (n=15)	−1.2	−3.8	4.3
	(−3.5, 1.2)	(−10.3, 2.7)	(−4.0, 12.5)
Overweight-Obese (n=10)	4.5	9.2	7.1
	(0.3, 8.6)	(0.9, 17.5)	(−31.1, 45.3)

^*ME : Mean Error (kg). A measure of bias; %ME#: Mean Error (bias) expressed as a percentage of DXA derived-FFM; RMSE∞: Root Mean Square Error (kg). A measure of precision; FFMdxa† Dual Energy X-ray Absorptiometry-derived fat free mass; LBW‡: Lean body weight (kg) calculated using the LBW Equation (10, 12)

Sub-group analysis of body composition revealed an underestimation by the LBW equation for sarcopenic and obese women while the equation overestimated DXA for sarcopenic- obese (Table 2). The ME for sarcopenic women (n=33) was 0.2 kg (-0.9, 1.4 kg), -1.2 kg (-3.5, 1.2 kg) for sarcopenic-obese women (n=15), and 4.5kg (-0.3, 8.6 kg) for obese women (n=10). The ME as a percentage of total FFM_DXA was highly variable and was larger for obese women. There was relatively more imprecision and bias for obese participants compared to sarcopenic or sarcopenic-obese.

Discussion

This study examined the ability of the LBW equation to estimate FFM_DXA in women following recent hip fracture. The SHIP population had high quality body composition data including DXA (11), and presented an excellent opportunity for evaluating the predictive ability of the equation in this difficult to study population. We observed an underestimation of FFM_DXA by the LBW equation with a ME (95% CI) of approximately 0.5kg (-0.7, 1.6 kg). The precision was poorest, indicated by a larger RMSE value, at baseline but improved at four and 12 months following hip fracture. consistent with our study, Janmahasatian et al, reported an underestimation by the LBW equation for female participants with a ME (95% cI) of 1.1kg (0.07 kg, 2.20kg) (10). Despite the smaller mean error observed in our study compared to Janmahasatian and colleagues, on subgroup analysis the ME was highly variable ranging from 0.2kg for sarcopenic participants, to 4.5kg for overweight-obese, non-sarcopenic participants. The larger degree of variability in our data may be due to the highly variable characteristics of our population, our smaller sample size or a combination of both. The SHIP study participants were older, frail and primarily sarcopenic (11) while the population used to develop and evaluate the LBW equation were relatively healthy despite being largely overweight and obese (10). Furthermore the proportion of older people used to develop the equation was small (10) which could lead to inconsistencies in the equation to predict LBW at the extremes of the age spectrum. Recently the LBW equation was found to over estimate FFM_DXA in a large population of older Australian men with a ME of 5.5kg (23). While the direction of the effect is different for men and women (10), the degree of variability in that study (23) and in our study is consistent. Furthermore the SHIP participants were recovering from hip fracture surgery at baseline, and suffered from multiple co-morbidities, including poor nutrition, depression, heart disease, respiratory disease, and osteoarthritis (13). The effect of acute illness on the precision and bias, although small, may be the cause of the non-significantly smaller values for four and 1 2 month estimates compared to baseline values.

The Bland-Altman plots demonstrated a non-random distribution of differences between methods, with the LBW equation more likely to underestimate FFM_DXA at higher values of LBW and, therefore, higher values of body weight. This was consistent with precision and bias analysis where obese participants’ FFM_DXA was underestimated by the LBW equation by approximately 4 kg which equated to approximately 10% of the total FFM_DXA. This may be due in part to the relatively small number of obese participants (n=10), combined with co- morbidities and an age-related decrease in total body water (24) resulting in poorer hydration of FFM, which may have contributed to errors in the LBW equation and DXA techniques. We also acknowledge that there are difficulties with DXA in optimally modelling fat distribution, particularly in the trunk, in older women (9) and that there may have been another factor which was unable to be quantified. It is impossible to determine if one or all of these factors are causative of the observed bias and variability.

Numerous equations exist to predict fat mass and percentage fat mass using bioelectrical impedance, BMI and other terms (25., 26., 27.). However, these equations are often specific to their development population and have little external evaluation, especially in the Australian population, and particularly in older people. Here we have assessed the ability of the LBW equation to estimate DXA derived FFM in this population of older women recently recovering from hip fracture. This small sub- study analysed the predictive performance of the LBW equation and was therefore limited to a small proportion of the total SHIP participants as DXA measurements were only available at one recruitment site (RNSH). However, those included were representative of the total study population as reported previously (11). Therefore our findings may be cautiously generalised to older female community-dwelling hip fracture cohorts.

Despite the variability of the LBW equation to predict FFM_DXA in this small study, the LBW equation has the potential to be of significant clinical value. The use of LBW instead of total body weight or ideal body weight in conventional weight based dosing regimes (i.e. milligrams per kilogram) may improve the dosing of drugs as biological functions are not directly proportional to total body weight (12). Increasing age, frailty and changes in body composition affect the pharmacokinetics of drugs leading to a greater risk of adverse drug reactions (8, 28). Hence, it is increasingly important to calculate drug dosage optimally. However we do acknowledge that the relationship between body composition and clearance accounts for only a portion of the predictable aspects of interindividual variability in drug clearance (12). Indeed for most drugs the remaining inter-individual variability after the inclusion of body composition is still >20% for the majority of the drugs. We strongly recommend that these hypotheses require confirmatory testing in clinical cohorts to establish their validity.

The SHIP study excluded nursing home residents and those with severe cognitive impairment or terminal illness (13). As we did not have enough male DXA data (n=5 at baseline, n=4 at 4 months, n=2 at 12 months) for analysis, males were excluded from this study so findings are applicable only to females. Body composition was determined based on both BMI and sarcopenic index, as it is now recognized that weight gain can mask sarcopenia (29), and that sarcopenic-obesity is distinct from sarcopenia and from obesity (30). The SHIP study was novel in that sarcopenia was pre-defined and the prevalence was high (65%). This allowed us to examine the predictive ability of the LBW equation in sarcopenic compared to non-sarcopenic participants. The validity of the LBW equation in older people may have been influenced by sarcopenia, which increases with age so would not have been as prevalent in the initial studies (10) of the equation.

Future studies need to evaluate the ability of the LBW equation to accurately predict DXA-derived FFM in other older populations, people living in residential aged care, those with terminal illness and cognitive impairment as well as in larger cohorts of hospitalised patients such as the SHIp cohort. More importantly, studies on the use of LBW in drug-dosing equations need to be performed to determine its clinical utility in older people to improve pharmacologic efficacy and safety profiles.

Conclusion

Lean body weight can be easily calculated using this simple equation of height and weight terms. When compared to DXA estimates of FFM, the LBW equation resulted in a small underestimation on average, but large differences in individuals, and non-uniform errors across individuals at the extremes of body weight in elderly women with recent hip fracture. Further studies need to investigate and potentially improve the utility of this predictive equation in larger and more heterogeneous clinical cohorts.

Declaration of sources of funding

The Sarcopenia and Hip Fracture Study was funded by the Australian National Health and Medical Research council (project grant 107472) and supported by the University of Sydney.

Conflicts of interest

the authors declare no conflicts of interest.