Scientific Papers

Cost-effectiveness analysis of surgical proximal femur fracture prevention in elderly: a Markov cohort simulation model | Cost Effectiveness and Resource Allocation


We created a model with cohort simulation, which means that a cohort of identical individuals was simulated and had during any model cycle to be in one of the defined health states [28] (Healthy, Recovery with complications, Recovery without complications, and Death) (Fig. 1). The model is from a societal perspective with a lifetime time horizon. A decision tree with Markov nodes can be found within the supplementary material 1 accompanying the manuscript. Due to the availability of literature, the model is based on data from the United States. However, it can apply comparatively to any industrial country with a high life expectancy. The model’s cycle length was defined as one year. Complications are modeled to occur within one cycle of the initial fracture, and the surgery’s length is less than one cycle. Therefore, the health state “Surgery” is a transitional health state, which denotes that individuals in this health state never stay in it for a complete cycle. A CEA has three core components: costs, utilities, and transition probabilities. Costs were calculated in United States dollars (US$). Utilities allow the comparison of health effects and changes in quality of life. We measured them as quality-adjusted life years (QALYs).

Fig. 1
figure 1

Model design for models A & B showing the health states (Ellipses) and the transition probabilities (Arrows). A cohort of identical individuals enters the Markov model and transitions through different health states with their correlated costs and QALYs

The result of a CEA is the additional investment of resources needed for each additional unit of health improvement expected to result from investing in the new treatment. It is the incremental cost-effectiveness ratio (ICER) with the unit dollars per QALY ($/QALY). $50,000 – $100,000/QALY is the most common range for the willingness to pay (WTP) [31]. WTP is the threshold for the ICER, and we defined it as $100,000/QALY. The WHO advised that the WTP should be one to three times the country’s GDP per capita [29]. Hence, we considered an ICER less than $50,000/QALY definitely cost-effective and an ICER less than $100,000/QALY likely cost-effective. Calculations were performed using TreeAge software (TreeAge Pro Healthcare 2020, TreeAge Software, LLC, Massachusetts, USA).

A CEA using a Markov model is commonly employed in medicine to compare two treatment strategies [32]. This study compares the current medical practices without prevention treatments with a strategy where a low-cost mini-invasive prophylactic procedure (femoroplasty) is steadily employed. Two key target groups for which such a scenario could be cost-effective were defined. Target Group 1: Patients who already suffered from a femoral neck fracture on one side as they have a 5- to 10-fold higher risk of breaking the contralateral side [33,34,35]. Target Group 2: Patients presented with high fracture risk factors, such as osteoporosis (T-score of -2.5), glucocorticoids, tobacco and alcohol use, female sex, or parent fractured hip but with no fracture history. We carried out a CEA that evaluated only these two target groups. To do so, we created two models, model A, in which we assumed that 100% of the healthy population had already suffered from a fracture in the hip. Model B assumes that all individuals who enter the model belong to a high fracture risk group. Although both models have the same structure (Fig. 1), they differ in costs, transition probabilities, and utility scores. The baseline patient age was 60 years, and we also assessed patients aged 60 to 90 years, as they are most prone to hip fractures.

Transition probabilities

Transition probability is the likelihood of transitioning from one health state to another. We acquired the age-dependent model probabilities from the available literature, as shown in Table 1. Given that the literature scope is limited for older age groups, transition probabilities for ages over 90 years were extrapolated from past trends assuming linearity. An exception is the general all-cause mortality rate, which we adapted online for all ages from a website that calculated it for life insurance purposes [36]. All probabilities were considered equal with and without prophylaxis, except for the risk of sustaining a hip fracture. Due to the mentioned biomechanical findings, it is safe to assume that surgical prophylaxis will reduce fracture probability [19]. Therefore, we predicted a 10% relative reduction in fracture probability in the baseline analysis due to prophylactic surgery. This assumption is based on expert approximation, as it is impossible to translate biomechanical values into probabilities. Different percentages from 1 to 50% were also assessed in the sensitivity analysis.

Table 1 Model’s age-dependent transition probabilities. The low and high parameter ranges were estimated as 60–120% of the base value shown

For model A, the contralateral fracture probability was acquired from three sources [16, 17, 37]. As every source considers different factors to estimate this probability, we performed the calculations three times using each source. Regarding model B, we used two references that estimated the probability of the first hip fracture for a high-risk group [17, 37]. The FRAX® [37] tool was used as one of the sources for both models. FRAX® is a prognostic tool created by the WHO to preview the individual risk of femoral neck fracture in 10 years. When calculating this risk from the FRAX® [37] tool, we used the USA’s average body mass index (BMI) of 29.6 [39]. A T-score of -2.5 was incorporated during the calculations. The risk factors assumed for model B were parent fractured hip, current smoking, glucocorticoids, rheumatoid arthritis, secondary osteoporosis, and heavy alcohol use. When calculating the one-year risk, we presumed a linear probability distribution. Supplementary pharmacologic fracture prevention therapy was disregarded in both models.

Implementing all types of preoperative complications in the model would cause it to be inexplicable and may reduce its accuracy. Therefore, we assumed that simulated patients could only sustain one preoperative complication regardless of its type. An article from Roche et al. followed 2448 hip fracture patients for four years. It concluded that 498 patients developed complications, representing approximately 20% of the total study subjects [38]. Alternatively, another study conducted by Pugely et al. followed 4331 patients undergoing hip fracture surgery. It established a total complication rate of 30% [6]. We used both articles and the article by Jiang et al. [16] to estimate the age-dependent risk of complications. After sustaining one preoperative complication, the excess mortality rate was calculated as an average from two papers [16, 38]. It was applied only for the first five years after the fracture complication.

The study by Tosteson et al. found that even if the patient recovers without complications, the mortality rate is elevated in the first six months [8]. Consequently, we assigned an elevated mortality rate only for individuals spending their first cycle in the health state “Recovery without complications” to simulate patients who died during the surgery (Table 2). After that, the mortality rates for this health state were considered equal to the general all-cause mortality rate. For model A, we assumed that the prophylactic procedure was performed during the contralateral side’s surgery. Thus, we assigned the same elevated mortality rate to individuals in the health state “Healthy” in the first cycle in model A. We estimated the low and high parameter ranges for transition probabilities as 60–120% of the base value.

Table 2 Model’s fixed variables


We defined all costs from the payer’s perspective and discounted them by 3% per year. The discount rate was varied between 0% and 8% in the sensitivity analysis. Since the simulated cohort is older than 60, we did not consider productivity gains due to improved health. We regarded no new costs if no complications were present one year after the fracture. We based our estimates of equipment and surgeon costs on the Healthcare Common Procedure Coding System (HCPCS) code 27495 (Reinforce thigh) [40] and on the expert’s approximation. Consequently, it was assumed that all hip fractures were treated using fracture fixation rather than total hip arthroplasty with code 27130, as only proximal femur fractures in the pertrochanteric area were considered. Varying the costs in the sensitivity analysis should eliminate the difference introduced by that assumption.

In model A, we assumed the prophylactic procedure was performed during the contralateral side surgery. Therefore, the null set of model A is the surgery performed during which the prophylactic treatment was executed. This means that the additional cost of prophylaxis is only the cost of the equipment used and the cost of the extra time needed for the surgeon to perform it (Table 3). We did not assume that it would increase the length of hospitalization as it is a mini-invasive procedure with negligible effect on morbidity. Meanwhile, from the payer’s perspective, all costs were considered in model B, as the patient had to be admitted to the hospital specifically to perform the surgery (Table 3). For explicitness in model B, it was assumed that the prophylactic procedure was performed only on the most fragile proximal femur.

All other costs were collected from the American Federal Government website managed by the Centers for Medicare & Medicaid Services. It included the Inpatient Prospective Payment System (IPPS) Provider Summary for All Diagnosis-Related Groups (DRG) – FY2017 [41] and the Medicare 2020 Physician Fee Schedule [40]. We obtained hospital costs from average Medicare payments for DRG codes 481 and 482 (hip and femur procedures except major joint with or without a complication or comorbidity (CC) or major complication or comorbidity (MCC)) [41]. Facility and nonfacility fees from the Medicare 2020 Physician Fee Schedule with their respective HCPCS codes and all other costs are shown in Table 3. We derived the average cost per day for the skilled nursing facility (SNF) from a report by the U.S. Department of Health and Human Services [42]. The length of stay in the SNF for hip fracture was based on available literature and expert approximation [16, 43, 44]. The low and high parameter ranges were estimated as 66–340% of the base value obtained [16].


QALY is the product of a utility score and the time spent in a health state. It combines morbidity and mortality. The utility score is a value from 0 to 1, where 1 is perfect health and 0 is death. The only difference between models A and B is the normative utility for the health state “Healthy”. The age-specific normative utilities used in model B are shown in Table 4 [17]. In model A, it was considered constant for all ages, as it is challenging to obtain age-specific utilities for hip fracture patients (Table 5) [7]. Disutility was assigned for the fracture year and each year for the first five years after fracture complication (Table 5) [16]. Naturally, the quality of life deteriorates after surgery and then improves gradually as the patient recovers. Therefore, the utility score for patients spending their first cycle in the health state “Recovery without Complications” was presumed to be 0.48 and for the cycles afterward 0.63 [7] (Table 5). No disutility was assumed after prophylaxis, as no mobility loss or pain is expected from such a procedure.

Table 4 Age-specific normative utilities for model B [17]
Table 5 Model’s fixed utility/disutility scores


Before running the models and investigating the data collected, fracture treatment costs 9.5 times the prophylaxis cost on the contralateral side (model A) and 6.6 times the prophylaxis cost as a preventive procedure (model B). Therefore, it is economically advantageous to perform a prophylactic procedure on the contralateral side on almost ten patients to prevent just one fracture. Furthermore, considering QALYs, even if the cost of fracture treatment is ignored (set to zero), prophylaxis is definitely cost-effective if it improves the QALYs by 0.034 for model A and 0.049 for model B. We included three different sources for the fracture risk in an attempt to simulate all possible scenarios.

In model A, the risks and their age distributions varied drastically between the different sources. Regarding model B, the two sources from which the probability of fracture was obtained were significantly different. Since we considered all risk factors simultaneously while using the FRAX® tool, it resulted in very high fracture risk (Table 1). Bearing in mind that we did not explicitly define the high-risk group, both sources were regarded as a range subject to the surgeon’s evaluation of the risk factors. Additionally, a sensitivity analysis was performed on both sources to assess how different probability trends affect cost-effectiveness variability. The baseline analysis was defined as a 10% reduction in fracture risk after prophylaxis in the 60-year-old simulated cohort.

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