Osteoporosis International

Screening for and Treatment of Osteoporosis: Construction and Validation of a State-Transition Microsimulation Cost-effectiveness Model

Lei Si1,2, MSc. MSc. • Tania M. Winzenberg1,3, PhD • Qicheng Jiang2, PhD • Andrew J. Palmer1, B Med Sci, MBBS.

1 Menzies Research Institute Tasmania, University of Tasmania, Hobart, Tasmania 7000, Australia

2School of Health Administration Anhui Medical University, Meishanlu 81, Hefei, Anhui, China

3 School of Medicine, University of Tasmania, Hobart, Tasmania 7000, Australia

Correspondence to: Lei Si, Menzies Research Institute Tasmania, University of Tasmania,

Medical Science 1 Building, 17 Liverpool St (Private Bag 23),

Hobart, Tasmania 7000, Australia

E-mail:

Tel.: +61-3-62264252

Fax: +61-3-62267704

Appendix 2. Internal and external validation

Internal validation

For internal validity, the results generated by our model werecompared with those reportedfrom studies used in creating the model. Specifically, we compared age-specific hip, vertebral and wrist fracture incidence rates from model outputs against those from the reference studies. Goodness of fit was evaluated by plotting the model predictions versus observed data reported in the reference studies, fitting a linear curve through the points with the intercept of zero. The squared linear correlation coefficient (R2), which isan index of the degree to which the paired measures co-vary was provided using linear regression.

In total, we performed 27 internal validations by comparing model prediction of age-specific hip, clinical vertebral and wrist fracture incidence rateagainst those usedas model inputs (Table 1).

Table 1. Annual fracture rates, per 10,000 person-years from model reproduction and model inputs

Age (years) / Annual fracture rates, per 10,000 person-years from model prediction / Annual fracture rates, per 10,000 person-years from literature
Hip fracture
50-54 / 3.4 / 3.3
55-59 / 4.6 / 4.6
60-64 / 5.3 / 5.4
65-69 / 9.7 / 9.6
70-74 / 23.2 / 23.3
75-79 / 42.8 / 40.8
80-84 / 61 / 64.4
85-89 / 63.2 / 65.9
90+ / 84 / 86.7
Clinical vertebral fracture
50-54 / 23.2 / 21.9
55-59 / 32.1 / 31.3
60-64 / 53.3 / 51.6
65-69 / 58.7 / 56.4
70-74 / 91.1 / 87.4
75-79 / 124.9 / 120.5
80-84 / 218.2 / 211.9
85-89 / 267.7 / 268.9
90+ / 268.2 / 268.9
Wrist fracture
50-54 / 34.3 / 34.272
55-59 / 55.6 / 52.704
60-64 / 79.55 / 80.352
65-69 / 93.9 / 93.24
70-74 / 94.95 / 94.824
75-79 / 102.05 / 99.864
80-84 / 107.8 / 108.072
85-89 / 104.8 / 108.72
90+ / 97.15 / 100.584

According to the values in Table 1, goodness-of-fit test is illustrated in Figure 1, by plotting the model predictions versus observed data, the regression line slope was 0.996 which was close to 1.00 and the R2 was 0.99 which indicated that the model faithfully reproduced the published data.


Figure 1. Goodness-of-fit test for model internal validation

External validation

Similar to the internal validation, goodness-of-fit test was performed using linear regression. We compared the model’s predictions of life expectancy (LE) and osteoporosis prevalence rates at specific ages, lifetime osteoporotic hip, clinical vertebral and all main (hip, clinical vertebral and wrist fracture combined) osteoporotic fracture risks, and 10-year fracture risks for all main osteoporotic fractures against the corresponding reported data (Table 2).

According to the values in Table 2, goodness-of-fit test is illustrated in Figure 2. The regression line slope was 0.952, which was close to 1.00, and the R2 was 0.994.

Table 2. External validation: comparison of model predictions to the published data

Parameters / Model predictions / Data from literature
Life expectancy for age 65-69, years / 17.15 / 17.38
Prevalence of osteoporosis ,%
60-69 years / 14.2 / 14.4
70-79 years / 26.8 / 26.3
80+ years / 39.2 / 39.9
Lifetime osteoporotic fracture risk at age 50 years, %
Hip fracture / 12.3 / 7.85
Wrist fracture / 21.7 / 18.68
Any major fracture (Hip, clinical vertebral and wrist fractures) / 59.5 / 56.31
10-year risk of any major osteoporotic fractures (Hip, clinical vertebral and wrist fractures), % / 17 / 13.69

Figure 2. Goodness-of-fit test for model external validation

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