3.1. Data
The analyzed dataset contains the records of patients who were subjected to revision total hip replacement (re-THR) in the period of 2000–2020. The patient records were collected in two different ways.
The first part of the disease histories was taken from the archives. The corresponding patient group is named ‘the retrospective group’. Initially the group contained 603 patients with PJI. The collection of information was started by personal examination and questioning of patients in the polyclinic of the Vreden’s Russian Scientific Research Institute of Traumatology and Orthopedics (25 (4.1%) patients). Patients who did not have the opportunity to come for examination were interviewed by phone (356 (59.03%) cases). In a number of observations, information about the condition of patients was obtained as a result of correspondence by mail (53 (8.8%) observations). In 169 (28.02%) cases, it was not possible to establish the results of PJI treatment and they were excluded from the study. The final list of patients in the retrospective part contained 434 patients with chronic PJI.
The prospective group of records included 166 patients with chronic PJI who were treated in the Department of Purulent Surgery of Vreden’s Russian Scientific Research Institute of Traumatology and Orthopedics in the period from 2016 to 2020. The record list contains those patients who were not subjected to exclusion from the study. Among the criteria of the latter were the following:
Systemic inflammatory response syndrome, sepsis;
Infectious inflammation of soft tissues of an unlimited form (phlegmon) or extensive purulent streaks to the neurovascular bundles;
A soft tissue defect that does not allow the wound to be sutured;
Implant-associated osteomyelitis IV (diffuse) anatomical type, patient’s physiological class C (Cierny-Mader classification);
Recurrent course of PJI, when the number of reEP with implantation of an antibacterial spacer was equal of more than 3;
Defects of the acetabulum not less than 3B and of the femur not less than 4 according to Paprosky classification, which were identified before surgery or formed as a result of surgical treatment.
All the patients were being observed for the possible PJI relapse till the end of 2020. In the retrospective group, the following treatment methods were applied: resection arthroplasty (RA), revision operation with the preservation of endoprosthesis (re-THR-PE) and two-stage revision total hip replacement with the two consecutive interventions separated by more than 2 months.
In the prospective group, new treatment methods were presented, namely, one-stage re-THR and partial re-THR (both 1-stage and 2-stage). The patients in the prospective group who underwent two-stage re-THR were divided into two subgroups based on their waiting time: 2–3 weeks and 6–8 weeks correspondingly.
The quantities of groups of patients of a certain age and gender in the records database are presented in
Table 1. The description of treatment methods regarded in this study is presented in
Table 2. As it can be seen the group ‘1-stage retro’ has extremely small sample size. Due to that reason it was excluded from this study.
Each patient record in the dataset contains their ID, birthdate, dates of registered health issues (manifestation dates), operation dates, types, and costs, the resulting state of the patient measured during his/her last attendance to healthcare services (PJI relapse or no PJI), and death date, if the patient died.
In case of the optimal treatment outcome, the resulting number of operations performed on each patient is defined solely by the PJI treatment method (for instance, two-stage re-THR assumes two interventions, with the installation of antibiotic-impregnated cement spacer and its subsequent removal, whereas the one-stage method is a single surgery). However, in many cases additional operations are required due to the relapse of PJI or other issues (postoperative wound hematomas, spacer dislocations, etc.). The recorded data we worked with contain 15 different types of operations, which were divided into three groups: operations which have no connection with PJI, first case of PJI, or PJI relapse. The full list of operations is presented in
Table 3.
3.4. Cost-Effectiveness Analysis
To assess and compare the cost-effectiveness of different treatment methods, we implemented algorithms to calculate the statistics of expenses and the overall QALY (quality-adjusted life-years, a generic measure of disease burden), related to different treatment stages. Since the decision trees and the Markov models have different structures, the calculation algorithms, although conceptually similar, differ in some details. The resulting value to measure cost-effectiveness, which is used as an output of the framework, is average cost per QALY for the particular PJI treatment method.
3.4.1. Decision Trees
Since, in a decision tree, each state matches exactly with the particular intervention from the patient record, the intervention costs could be assessed in an easy and straightforward way. At the same time, the time is not tracked in this model type, which makes it complicated to compare time-dependent costs. As it was described in [
31], the framework supports the assignments of parameters, related to the impact of the intervention, to each branch of the tree. To assess the cost-effectiveness of the treatment methods, we measured intervention costs in rubles and measured utility of the patient calculated in QALY units. The quantitative outcomes of the treatment in terms of healthcare costs and QALY units gained by the patient might be derived from the decision tree using the following formula:
where
is the probability of selecting the branch, obtained by cross-validation,
is the impact measured in either of the two units. The interval assessment of
C can be calculated using the same formula with left and right boundaries for
used instead of their mean assessments.
The resulting values of
and
are used to calculate the costs of one QALY unit and analyze them for different treatment strategies. To calculate QALY units and costs for particular tree branches, we relied on the data provided by Russian Scientific Research Institute of Traumatology and Orthopedics named after R.R. Vreden. The operation costs were taken from the disease histories, and the QALY units were assessed based on the EQ-5D indices for each particular patient measured between the subsequent operations according to the methodology described in [
32].
3.4.2. Markov Models
The treatment impact for a fixed individual patient trajectory is calculated according to the formula
where
are the monthly costs or QALY units associated with the patient state
i in the model, and
is the expected average patient’s time of staying in a state
i (the number of months). Due to the fact that in the Markov model we use generalized patient conditions which are not tied to particular intervention types, the accurate values for
(both in rubles and QALY units) cannot be found in records. The expenses for every model state were assessed by averaging the costs of all possible interventions associated with that particular state, and the QALY units gained were found based on the experts’ opinion. We assumed that the patient gains maximum QALY units when he is in the ‘Observation’ status. The lowest QALY values correspond to ‘PJI’. The quality of life of a patient waiting for the second stage or additional surgeries is higher than in case of PJI, but lower than in the ‘Observation’ state due to corresponding health issues (particularly, the patients waiting for the second stage of the treatment have limited mobility due to spacer installation which badly affects their QALY count). Under the expert assumption, we assumed the QALY for the ‘PJI’ state equal to 0.35, for ‘Second stage’ equal to 0.7, for ‘Non-PJI operation’ equal to 0.5, for ‘Observation’ equal to 0.85, and for ‘Death’ equal to 0.
As an example, we consider a patient who undergoes a two-stage therapy with a three-month interval between stages. The model presents the chain of states ‘Waiting for surgery related to PJI (month 1)’, ‘Waiting for the second stage of therapy’ (month 2), ‘Waiting for the second stage of therapy’ (month 3), ‘Waiting for the second stage of therapy’ (month 4), and ‘Observation’ (month 5). When searching for the average QALY values obtained with various methods of therapy, based on the Markov model, the length of stay in each state is multiplied by the QALY units characteristic of it. In our example, we have to sum 1 × 0.35 (QALY for PJI condition, 1 month duration), 3 × 0.7 (QALY for the period of waiting for the second stage, 3 months duration) and 1 × 0.85 (observation, 1 month duration).
For calculating costs, along with the cost of staying in a model state during a certain amount of time (as in QALY calculation), the cost of operations should also be considered. In the setting of generalized Markov model operations are attributed to transitions between states. For instance, a transition from ‘Waiting for the second stage of therapy’ to ‘Observation’ implies a performed operation with spacer removal and endoprosthesis installation. Consequentially, in the above example, the total cost will consist of the following terms:
The cost of a month of inpatient stay awaiting surgery related to PJI (state of the model);
Cost of the PJI operation (the transition of the model from “Waiting for surgery with PJI” to “Waiting for the second stage of therapy with PJI”);
Cost of three months of waiting for the second stage of therapy (state of the model);
Cost of the operation of the second stage of therapy with PJI (transition of the model from “Waiting for the second stage of therapy with PJI” to “Observation”);
The cost of a month in the “Observation” state.
The results of assessing cost-effectiveness of PJI treatment using two described modeling approaches are presented in the following section.