Potential cost-effective use of spine radiographs to detect vertebral deformity and select osteopenic post-menopausal women for amino-bisphosphonate therapy

Abstract

Prevalent vertebral deformities are predictive of future clinical fractures independent of bone density. We used a Markov model with eight health states to estimate from the societal perspective the cost-effectiveness of using spine radiographs to identify postmenopausal women age 60 or older with one or more vertebral deformities and then treat them with anti-resorptive drug therapy to prevent fractures. We compared three strategies: 5 years of amino-bisphosphonate (alendronate) therapy for all, 5 years of alendronate therapy for only those with prevalent a radiographic vertebral deformity or no initial alendronate treatment. Lifetime direct medical and indirect costs, quality adjusted life years (QALYs) and incremental cost-effectiveness ratios (ICERs) were tracked. For women with one or more prevalent vertebral deformities, the costs per QALY gained ranged from $5,084 (for an 80 year old with a T-score of −2.4) to $61,192 (for a 60 year old with a T-score of −1.0). For women without prevalent vertebral deformity, the costs per QALY gained ranged from $41,897 (for a 60 year old with a T-score of −2.4) to $166,219 (for an 80 year old with a T-score of −1.0). These results were modestly sensitive to reasonable changes in fracture rates, disutility, discount rates and assumptions about the accuracy of spinal radiographs for detecting vertebral deformity. Assuming a societal willingness to pay per QALY gained of $50,000, the strategy of performing spine radiographs in post-menopausal osteopenic women with T-scores at or below –1.5 and treating those with 1 or more prevalent vertebral deformities is likely to be cost-effective. However, further research on the accuracy of vertebral deformity ascertainment from routine clinical radiographs and on the efficacy of amino-bisphosphonate drugs for reducing the risk of non-vertebral fractures in osteopenic women is needed to define more precisely the subset of osteopenic post-menopausal women in whom use of spinal radiographs is most cost-effective.

Appendix

Derivation of age- and BMD-specific fracture risk equations

Adjustment of the age-specific fracture risk functions for BMD, which apply to a population with a mean Z-score of 0, were done in the following manner[23, 24]. Because the relationship between bone mineral density and incident fractures is exponential, to estimate the risk for a specific fracture for individuals with a Z-score equal to a specific value, the risk equation needs to be divided by a correction factor:

$$ {\text{C = }}{\int {\text{1}} }{\text{/}}{\left( {{\sqrt {{\text{2}}\Pi } }} \right)} * {\left( {{\text{e $ \hat{} $ }} - {\text{0}}{\text{.5z}}^{{\text{2}}} } \right)} * {\left( {{\text{a $ \hat{} $ }} - {\text{z}}} \right)} * {\text{dz}}{\text{,}} $$

(1)

where z is the actual Z-score and a is the relative risk of that fracture for each Z-score change of 1. For example, assuming a relative risk of 2.6 for incident hip fracture per Z-score change [62], this correction factor equals 1.57854 for an individual with a Z-score equal to 0.

The Z-score at any age stage of the model was derived from the starting T-score by the following equations. Mean BMD (Z-score =0) for any age was estimated from the regression line of mean bone density (in gm/cm²) as a function of ages 50 to 90 [25],

$$ {\text{Mean BMD for Age}} = {\text{1}}{\text{.075}} - {\left( {{\text{0}}{\text{.00554*Age}}} \right)}{\text{ gm/cm}}^{{\text{2}}} {\text{.}} $$

(2)

The starting T-score was converted to absolute gm/cm² by the equation:

$$ {\text{Starting BMD}}{\left( {{\text{gm/cm}}^{{\text{2}}} } \right)} = {\text{0}}{\text{.858}} + {\left( {{\text{Starting T - score}}} \right)} * {\text{0}}{\text{.12}}{\text{,}} $$

(3)

and therefore BMD at any given age is:

$$ \begin{aligned} & {\text{Current BMD}} = {\left[ {{\text{0}}{\text{.858}} + {\left( {{\text{Starting T - score}}} \right)} * {\text{0}}{\text{.12}}} \right]} - {\text{0}}{\text{.00554}} * {\text{Age}}{\text{, and}} \\ & {\text{Current Z - score}} = {\left[ {{\left( {{\text{Current BMD}}} \right)} - {\left( {{\text{Mean BMD for age}}} \right)}} \right]}{\text{ / 0}}{\text{.114}}{\text{,}} \\ \end{aligned} $$

(4)

where 0.114 equals the pooled standard deviation of femoral neck BMD for Caucasian women aged 50 to 90 [25].

Estimation of radiographic vertebral deformity prevalence for combinations of age and BMD

For each starting age, the prevalence (Prev_age) of radiographic vertebral deformity was estimated from the population-based study of Melton and colleagues [19], which apply to age-specific groups of women with a mean Z-score equal to zero. We estimated the odds ratio of one or more prevalent vertebral deformities for each Z-score change of 1 to be 1.5 [53, 63, 64].

Therefore, for women with a Z-score equal to zero,

$$ {\text{Prev}}_{{{\text{Z}} = {\text{0}}}} = {\text{Prev}}_{{{\text{age}}}} {\text{/}}{\int {\text{1}} }{\text{/}}{\left( {{\sqrt {{\text{2}}\Pi } }} \right)} * {\left( {{\text{e $ \hat{} $ }} - {\text{0}}{\text{.5z}}^{{\text{2}}} } \right)} * {\left( {{\text{1}}{\text{.5 $ \hat{} $ }} - {\text{z}}} \right)} * {\text{dz}} = {\text{Prev}}_{{{\text{age}}}} {\text{/1}}{\text{.0857}} $$

(5)

Therefore, for any Z-score,

$$ {\left[ {{\text{Prev}}_{{{\text{Age}}{\text{,Z}}}} {\text{/}}{\left( {{\text{1 - Prev}}_{{{\text{Age}}{\text{,Z}}}} } \right)}} \right]}{\text{/}}{\left[ {{\text{Prev}}_{{{\text{Z}} = {\text{0}}}} {\text{/}}{\left( {{\text{1 - Prev}}_{{{\text{Z}} = {\text{0}}}} } \right)}} \right]} = {\text{1}}{\text{.5}}^{{ - {\text{Z}}}} {\text{,}} $$

(6)

with starting Z-score = [(starting BMD) – (1.0375 – 0.00554*Age)]/0.114.

The prevalence of one or more radiographic vertebral deformities for any combination of starting age and T-score is therefore given by solving equations 5 and 6 for Prev_Age,Z.

However, we estimated that 30% of these vertebral deformities represented clinical vertebral fractures, discovered at the time of their occurrence. Therefore, the final prevalence of clinically unapparent radiographic vertebral deformities (Prev_final) for any starting age and Z-score (Table 1) is:

$$ {\text{Prev}}_{{{\text{final}}}} = {\left( {{\text{Prev}}_{{{\text{Age}}{\text{,Z}}}} - {\text{ 0}}{\text{.3}} * {\text{Prev}}_{{{\text{Age}}{\text{,Z}}}} } \right)}{\text{/}}{\left( {{\text{1}} - {\text{0}}{\text{.3}} * {\text{Prev}}_{{{\text{Age}}{\text{,Z}}}} } \right)}. $$

(7)