Database

We used the Swedish Hip Arthroplasty Register (SHAR) to identify and collect data on patients who underwent elective primary THA due to osteoarthritis between 2005 and 2012. SHAR started in 1979 and is one of the oldest national quality registers. The register has been collecting patient-level data (eg, age, sex, diagnosis and type of implant) from all public and private orthopaedic departments in Sweden performing THA for over 25 years (ie, the degree of coverage is 100%). According to annual validations, the completeness is 97.0%–98.5%. Additionally, administrative data on these patients’ hospital inpatient stays related to the operation were collected from the National Patient Register (NPR) provided by the National Board of Health and Welfare. These data, including information on dates of admission and discharge, readmissions, diagnoses, procedures and diagnosis-related groups (DRGs), were linked to SHAR through personal identification numbers. The data were thereafter anonymised. The study and pooling of the data were approved by the Regional Ethical Review Board in Gothenburg, Sweden.

Selection of departments

All orthopaedic departments performing THA in Sweden from 2005 to 2012 (N=86) were eligible for inclusion in the study. However, as data from both SHAR and NPR were needed, one prerequisite for the inclusion of a department was the capability to match the data between the registers. Departments with no or low completeness in NPR (due to some under-reporting from private departments) were therefore excluded from the study. Furthermore, departments which opened during the last year or closed during the first year of the study period were excluded as data for at least 2 years were needed to be able to estimate any productivity changes. One department was further excluded as data were missing in NPR for half of the study period. Moreover, there were a few reorganisations involving changed ownership or managerial structure, mergers and splits over the time period. For simplicity, departments which merged or split over time were handled as one unit during the full study period. That is, if two departments merged after the beginning of the study period, we considered them to be one (the same) unit from the start. Similarly, if two departments split after the beginning of the study period, we considered them to be one (the same) unit after the split. Departments with changed ownership or managerial structure were also considered to be the same unit over time in the analysis. After these exclusions and reorganisations, a total of 65 orthopaedic departments remained in the study (figure 1).

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Figure 1

Department flow diagram. NPR, National Patient Register.

Input and output variables

To facilitate measurement of productivity development of THA, we initially specified inputs and outputs in the production process of the orthopaedic departments. Three different outputs based on the types of operations used for primary THAs in Sweden were defined; the number of non-cemented, hybrid and cemented THAs per department and year fulfilling the specific inclusion and exclusion criteria listed in Box 1. Patients who underwent bilateral THA or had a prior THA within 90 days of the operation were excluded due to a statistical merging problem. Moreover, patients with a missing or incorrect DRG code were excluded as we could not estimate their costs without a DRG code.

As a single input, the estimated department cost of THA was used. Following Iversen et al,10 we considered a fixed cost for the operation and a variable cost corresponding to the length of the hospital stay (LOS) in conjunction with the operation. These costs, presented in Supplementary Table 1, were based on national averages for the DRGs including THA and were provided by the National Board of Health and Welfare. It was not possible to differentiate the fixed cost between the three different types of operations (non-cemented, hybrid and cemented THAs). As a consequence, we had to use the same fixed cost for all three types of operations. The variable cost was derived by multiplying the cost per day with the LOS for each operation. According to Supplementary Table 1, the cost data seemed to be somewhat unstable during the first years of the study period. Both cost items decreased drastically from 2005 to 2006 and were followed by a considerable increase from 2006 to 2007. To address this issue, variations in the cost calculation were performed as sensitivity analyses.

In addition to the estimated cost of the surgical episode, costs of adverse events (AEs) within 90 days11 following THA were added, if there were any. By the concept, AEs implicate all forms of rehospitalisation that might have depended on the intervention that was carried out and, in that case, not only local complications but also general medical complications and death. Following SHAR’s definition of AEs within 90 days after THA,11 we included all forms of further surgery of the hip as well as cardiovascular, cerebrovascular and thromboembolic complications, pneumonia and ulcers if these complications resulted in hospitalisation as AEs. Costs for AEs were calculated using the DRG system. For each hospital stay with an AE, the corresponding DRG weight, provided by the National Board of Health and Welfare, was multiplied with the yearly specific estimated cost of DRG weight=1. To avoid double counting of costs, we excluded AEs which occurred during the same hospital stay as the operation. All costs were summarised per department and year and adjusted to 2012’s prices (in SEK) using the county council price index.12

Data analysis

The productivity development was measured by Malmquist Productivity Index, which was estimated following the approach developed by Färe et al.9 The methodology combines ideas from Farrell’s work on the measurement of efficiency,13 productivity measurement as expressed by Caves et al 14 and the use of distance functions as proposed by Malmquist.15 The index was calculated for each department by relating changes in their production from one period to the next, as well as by comparing their production to the best practice, that is, the departments which produces the most outputs from a given amount of input. The production of these departments creates the so-called production frontier, which accordingly shows the maximum possible production level of outputs from a specific amount of input. Due to innovation, for instance, the frontier shifts over time. Thus, the productivity development, measured by the Malmquist Productivity Index, can be split into two components: efficiency change (which relates to changes in the observed production relative to the maximum potential production, ie, the catch-up effect) and technical change (which relates to shifts in the production frontier, eg, because of innovation). As our input consisted of costs for THA, we took the approach of a cost-based index, which has previously been used by Färe et al.7 We assumed the managers have more control over the costs in the production process and might be able to reduce them while the number of operations is rather uncontrollable due to patient demand and referrals from doctors. Therefore, an input-oriented index was employed in the study. The mathematical expression of the index (Equation 1) was defined by Färe et al 9 as

(1)

where the index M measures the productivity change between the two periods t and t+1, D represents the Shephard16 distance functions used to calculate the productivity change from period t to t +1, x ^t denotes the input vector in period t, x ^{t + 1} denotes the input vector in period t +1, y ^t denotes the output vector in period t and y^t+1 denotes the output vector in period t+1. The distance functions were estimated using data envelopment analysis,13 17 and a constant returns to scale technology was further assumed, which means that increases in inputs and outputs are proportionate. The first ratio in the equation above represents the change in efficiency from period t to period t+1, whereas the ratio in the brackets measures the technical change between period t and t+1. To conform to standard interpretation in the productivity literature, we took the inverse of the index and its components. Thus, a value=1 indicates no change in production, a value <1 indicates regress and a value >1 indicates progress.9

To test the null hypothesis of no change in productivity, efficiency and technology between two consecutive years, we used a bootstrap methodology developed by Simar and Wilson18 19 to provide 95% CIs around the index and its components. If the CI includes unity (ie, 0% change in productivity, eg), the null hypothesis cannot be rejected and we say that the results are statistically insignificant. The calculations of the productivity development were performed using the FEAR package in the R software.20

Sensitivity analyses

To assess the robustness of the results, six different sensitivity analyses were performed (Supplementary Table 2). Because the productivity assessment is rather sensitive to the number of inputs and outputs, the three outputs were consolidated into one output (ie, the total number of THAs) in the first sensitivity analysis (S1). In the second analysis, costs for AEs were excluded (S2). To address the issue of unstable THA costs, two variations of the cost calculation were conducted in a third and fourth sensitivity analyses (S3 and S4). In S3, we used the department mean cost of THA to construct a model which we used to predict the cost of THA. These costs were collected from the cost per patient database provided by the Swedish Association of Local Authorities and Regions.21 The model included information on type of operation (non-cemented, hybrid and cemented THA), age group and LOS in conjunction with the operation. Costs for AEs were calculated using the DRG system in the same way as for the main model. In S4, following Iversen et al,10 costs for both the operation and AEs were estimated using the DRG system. For each DRG in the sample, we calculated the mean number of DRG points per day. Thereafter, we multiplied this mean with the LOS for each hospital stay to obtain the number of DRG points per stay. This number was then multiplied with the yearly specific value for DRG weight=1, which gave us the estimated cost for every individual hospital stay in the sample. In the fifth sensitivity analysis, we considered the LOS in conjunction with the operation, as well as the LOS with an AE diagnosis within 90 days following THA as the input (S5). Outliers were removed from the last sensitivity analysis (S6). Outliers were detected using the super-efficiency procedure with a screen level of 1.2.22 We identified 1–2 outliers per year.

Patient and public involvement

Patients and the public were not involved in the design and performance of the study. The study is based on administrative and public data and since the results are presented at department level, the patients included in the registers should not be caused by any type of discomfort or integrity infringement.