Cost-effectiveness of bone densitometry among Caucasian women and men without a prior fracture according to age and body weight

Abstract

Summary

We used a microsimulation model to estimate the threshold body weights at which screening bone densitometry is cost-effective. Among women aged 55–65 years and men aged 55–75 years without a prior fracture, body weight can be used to identify those for whom bone densitometry is cost-effective.

Introduction

Bone densitometry may be more cost-effective for those with lower body weight since the prevalence of osteoporosis is higher for those with low body weight. Our purpose was to estimate weight thresholds below which bone densitometry is cost-effective for women and men without a prior clinical fracture at ages 55, 60, 65, 75, and 80 years.

Methods

We used a microsimulation model to estimate the costs and health benefits of bone densitometry and 5 years of fracture prevention therapy for those without prior fracture but with femoral neck osteoporosis (T-score ≤ −2.5) and a 10-year hip fracture risk of ≥3%. Threshold pre-test probabilities of low BMD warranting drug therapy at which bone densitometry is cost-effective were calculated. Corresponding body weight thresholds were estimated using data from the Study of Osteoporotic Fractures (SOF), the Osteoporotic Fractures in Men (MrOS) study, and the National Health and Nutrition Examination Survey (NHANES) for 2005–2006.

Results

Assuming a willingness to pay of $75,000 per quality adjusted life year (QALY) and drug cost of $500/year, body weight thresholds below which bone densitometry is cost-effective for those without a prior fracture were 74, 90, and 100 kg, respectively, for women aged 55, 65, and 80 years; and were 67, 101, and 108 kg, respectively, for men aged 55, 75, and 80 years.

Conclusions

For women aged 55–65 years and men aged 55–75 years without a prior fracture, body weight can be used to select those for whom bone densitometry is cost-effective.

Appendix

This technical appendix describes in detail the derivation of a) the relative risks of fractures attributable to the absence of prior clinical fracture; b) the proportion of those without clinical fracture who have low bone mass warranting drug therapy; c) the relative risks of fractures attributable to low BMD warranting drug therapy; d) the pre-test probability cutpoints of low BMD below which bone densitometry followed by fracture prevention therapy is cost-effective; and e) the body weight thresholds below which the pre-test probability of low BMD warranting drug therapy is high enough such that bone densitometry is cost-effective.

Relative risk of fracture in those without prior fracture (RR_{NoPriorFracture vs All})

This relative risk is calculated from the following equation:

$$ {\text{R}}{{\text{R}}_{\text{NoPriorFracture vs All}}} = {1}/\left[ {{1} + \left( {{\text{R}}{{\text{R}}_{\text{PriorFx vs NoPrior Fx}}} - {1}} \right)*{\text{Pre}}{{\text{v}}_{\text{PriorFx}}}} \right] $$

(1)

[12]

We assumed the relative risk of incident clinical fracture in those with compared to those without prior fracture (RR_{PriorFx vs NoPrior Fx}) to be 1.73 and 2.04, respectively, for women and men [54].

The prevalence of prior clinical fracture at each age for each sex (Prev_PriorFx) was determined in three steps using unpublished second study visit data from the Study of Osteoporotic Fractures and baseline visit data from the Osteoporotic Fractures in Men (MrOS). First, prediction equations for the odds of prior clinical fracture as a function of age and BMD were derived using logistic regression, as described in a previous publication [6]. We used these same equations to extrapolate estimated prevalences of prior clinical fracture for those under age 65. Since SOF and MrOS only included women and men aged 65 and older, we did sensitivity analyses for 55-year-old men and women assuming prevalences of prior clinical fracture only half that predicted by these equations.

Second, the mean BMD for each age were obtained for Caucasian men and women from public use NHANES 2005–2006 data files [37]. Third, these mean BMD values were then entered into the prediction equations to obtain the estimated odds of a prior clinical fracture for each group defined by age and sex. These odds were converted to prevalences (Table 1) by the equation:

$$ {\text{Prevalence}} = {\text{Odds}}/\left( {{1} + {\text{Odds}}} \right). $$

(2)

Proportions of those without prior clinical fracture with bone density below treatment cutpoints

The prevalence of femoral neck BMD below the treatment cutpoints for each starting age in the female and male Caucasian US population was estimated from NHANES 2005–2006 data (labeled Prev_{BMD≤Cutpoint, All} in Eq. 3) [37]. This is then converted to an odds by the following equation:

$$ {\text{Odd}}{{\text{s}}_{{{\text{BMD}} \leqslant {\text{Cutpoint}},{\text{ All}}}}} = {\text{Pre}}{{\text{v}}_{{{\text{BMD}} \leqslant {\text{Cutpoint}},{\text{ All}}}}}/\left( {{1} - {\text{Pre}}{{\text{v}}_{{{\text{BMD}} \leqslant {\text{Cutpoint}},{\text{ All}}}}}} \right). $$

(3)

To estimate these proportions for the subsets without prior clinical fracture, we first estimated (using logistic regression models) the age-adjusted odds of femoral neck BMD below the treatment cutpoints in those with compared to those without prior clinical fracture (OR_{BMD≤Cutpoint, PriorFx vs NoPriorFx}) for women and men using unpublished second study visit data from SOF (7,927 women, mean age 73.7 years) and baseline visit data from MrOS (5,993 men, mean age 73.7 years).

The odds ratio (OR) for low BMD in those without prior clinical fracture compared to the entire subset of same age and sex is then

$$ {\text{O}}{{\text{R}}_{{{\text{BMD}} < {\text{Cutpoint}},{\text{ NO prior fracture vs all}}}}} = {1}/\left[ {{1} + \left( {{\text{O}}{{\text{R}}_{{{\text{BMD}} \leqslant {\text{Cutpoint}},{\text{ PriorFx vs NoPriorFx}}}}} - {1}} \right)*{\text{Pre}}{{\text{v}}_{\text{PriorFx}}}} \right], $$

(4)

where Prev_PriorFx is the prevalence of prior clinical fracture since age 50 for that age and sex, and OR_{BMD≤Cutpoint, PriorFx vs NoPriorFx} is 1.91 for men, 1.97 for women when the BMD T-score cutpoint is −2.5, and 2.10 for women when the BMD T-score cutpoint is −2.6 or lower.

The odds of BMD sufficiently low to warrant drug therapy is then given by the equation:

$$ {\text{Odd}}{{\text{s}}_{{{\text{BMD}} \leqslant {\text{Cutpoint}},{\text{\ NoPriorFx}}}}} = {\text{Odd}}{{\text{s}}_{{{\text{BMD}} \leqslant {\text{Cutpoint}},{\text{ All}}}}}*{\text{O}}{{\text{R}}_{{{\text{BMD}} < {\text{Cutpoint}},{\text{\ NO\ prior\ fracture\ vs\ all}}}}}. $$

(5)

The prevalence of femoral neck BMD below the treatment cutpoints for those in each subset defined by age and sex without prior clinical fracture (Prev_{BMD≤Cutpoint, NoPriorFx} ) is then calculated from the odds (Odds_{BMD≤Cutpoint, NoPriorFx}) using Eq. 2.

The Z-score cutpoint of low BMD (Z _cut) corresponding to this prevalence is then calculated from the normal distribution function.

Fracture risks attributable to low bone density

The mean Z-scores of those below the Z-score cutpoints were then calculated using the inverse Mills ratio (Table 1):

$$ {\text{Mean\ Z}} - {\text{score}} = - { \exp }\left[ { - \left( {{Z_{\text{cut}}}^{{2}}} \right)*0.{5}} \right]/\left[ {{\text{Normal}}\left( {{Z_{\text{cut}}}} \right)*{{\left( {{2}*{\text{pi}}} \right)}^{{0.{5}}}}} \right] $$

(6)

For each fracture type, the relative risk of incident fracture in those with a femoral neck BMD T-score below the treatment cutpoint was equal to a ^−Z, where Z is the mean Z-score for those with BMD below the treatment cutpoint (Table 1), and a is the relative risk of fracture per standard deviation (SD) decrease in femoral neck Z-score.

The relative risks of hip fracture for each SD decrease in femoral neck BMD, derived from a large meta-analysis of hip fracture predictors [55], were assumed to decrease with age from 3.29 and 3.92, respectively, for women and men aged 55 years to 2.24 and 2.67, respectively, for women and men aged 80 years (Table 2). The relative risks of hip fracture in those with compared to those without prior clinical fracture were assumed to decrease with age from 3.83 and 4.84 for women and men aged 55 years to 1.36 and 1.71 for women and men aged 80 years [54]. For women, we assumed relative risks for incident vertebral fracture of 1.32 in those with compared to those without prior fracture [56] and 1.9 per SD decrease in femoral neck BMD [57]. The relative risks of non-vertebral non-hip fractures per SD decrease in femoral neck BMD were assumed to be 1.34 and 1.44, respectively, in men [58] and women [57]. Using Rotterdam study data, for men we assumed relative risks for incident vertebral fractures of 1.8 per SD decrease of femoral neck BMD and 2.4 in those with compared to those without prior clinical fracture [59].

Estimation of weight thresholds below which bone densitometry is cost-effective

To calculate the weight threshold below which bone densitometry is cost-effective, we start with the prevalence (pre-test probability) of low bone density warranting drug therapy for the age-specific and sex-specific subgroup without prior fracture, and the threshold pre-test prevalence of low bone density at which bone densitometry becomes cost-effective for that subgroup (columns 2 and 3, Table 5 [women] and Table 6 [men]). These prevalences are converted to odds (columns 4 and 6) by the equation:

Table 5 Calculation of weight threshold at which bone densitometry becomes cost-effective for women

Table 6 Calculation of weight threshold at which bone densitometry becomes cost-effective for men

$$ {\text{Odds}} = {\text{Prevalence}}/\left( {{1} - {\text{Prevalence}}} \right) $$

(7)

Since the change of the odds of low BMD warranting drug therapy per change in body weight is linear in the natural logarithm scale, we then take the logs of these odds (columns 5 and 7). The difference in log(Odds) between these two = [log(Odds_threshold) − log(Odds_{age, sex})] (column 8).

The age-adjusted association between body weight and odds of femoral neck BMD below the treatment cutpoint among Caucasians (OR_{per10 kg weight change}) was estimated using unpublished data from the baseline visit of the MrOS study (for men) and the second study visit of the SOF visit (for women) with separate logistic regression models for each treatment cutpoint (column 9, Tables 5 and 6). These odds ratios were 0.30, 0.33, 0.39, and 0.42, respectively, for women aged 55, 60, 65, and 70 years and older, and were 0.40 and 0.44, respectively, for men younger than age 60 and age 65 and older (column 6, Tables 5 and 6).

The weight change (in kilogram, column 10) required for the odds of low bone density warranting drug therapy to change from the mean for that age-specific and sex-specific subgroup to the threshold for cost-effectiveness is equal to the difference in log-odds (column 8) times ten divided by the change in log(Odds) per 10-kg change in body weight (column 9):

$$ {\text{WeightChang}}{{\text{e}}_{{{\text{age}},{\text{\ sex}}}}} = \left[ {{\text{difference\ in\ log}}\left( {\text{Odds}} \right)} \right]*{1}0/\left[ {{ \ln }\left( {{\text{O}}{{\text{R}}_{{{\text{per1}}0{\text{\ kg\ weight\ change}}}}}} \right)} \right], $$

(9)

and

$$ {\text{Threshold\ Weight}} = {\text{MeanWeigh}}{{\text{t}}_{{{\text{age}},{\text{\ sex}}}}} + {\text{WeightChang}}{{\text{e}}_{{{\text{age}},{\text{\ sex}}}}}. $$

(10)

Probabilistic sensitivity analyses: distributions

Fracture costs were assumed to follow a log-normal distribution (Table 7), based on the distribution from the study of Gabriel and colleagues [39]. The proportion of individuals requiring long-term care beyond the first year after hip fracture was estimated to be 12% (38 out of 312 individuals), and this was assumed to follow a binomial distribution. A normal approximation to this yields a point estimate for long-term care costs of $9,057 (2010 US dollars) per year with a standard deviation of $1,103.

Table 7 Distributions for parameters allowed to vary in probabilistic sensitivity analyses

We constructed distributions for fracture rates by first assuming that the distributions of the proportions of individuals at risk who have a first distal forearm, clinical vertebral, or hip fracture within each specified age range [27] are binomial. The 95% confidence intervals can be calculated using an exact method appropriate for proportions close to zero [60]. If a normal approximation to these distributions is then assumed, the standard deviation for these proportions ranges from 30% for vertebral fracture between ages 65 and 69 to 10.9% for hip fracture after age 85. For the probabilistic sensitivity analysis, an additional normally distributed variable was created with mean value of 1.0 and standard deviation equal to 0.22. This is then multiplied by all of the fracture rates, so that fracture rates vary together over a normal distribution with the means equal to the point estimates rendered by the fracture risk equations.

Because of significant uncertainty regarding disutility from fractures, we assumed a uniform distribution for these to vary from between 50% and 150% of the base case disutility. The relative risks for hip, non-spine non-hip, and vertebral fractures attributable to osteoporosis or prior clinical fracture were assumed to be log-normal (since hazard ratios and odds ratios are linear in the logarithmic scale), as were the relative risks of fractures on oral bisphosphonates compared to no drug therapy.

Performance of probabilistic sensitivity analyses

The analyses were done with 500 simulations, with 10,000 trials per simulation. For each simulation, the parameter values are selected randomly from the above distributions. These analyses were repeated over a wide range of assumed prevalences of low bone density warranting drug therapy. We then determined, by linear interpolation, the threshold cost-effective low BMD prevalences (assuming a willingness to pay of $75,000 per QALY gained and a yearly drug cost of $500) using the 25th and 75th percentiles of costs per QALY gained. The corresponding weight thresholds were calculated for each of these two prevalences, and the proportion of the population of that age and sex below each of the two weight thresholds calculated as shown previously. The difference between these weight thresholds represents the inter-quartile range for the body weights at which bone densitometry is cost-effective for subgroup without prior fracture defined by age and sex.