As mentioned earlier, the paramount aim of this paper is to support a DM in studying, analyzing and comparing available exercise therapies by considering various (conﬂicting) objectives simultaneously. Besides a DM, the consideration involves an analyst whose responsibility is generating information, modeling, identifying a suitable solution method and taking care of all mathematical parts. An analyst can be a human, a computer program or their combination.
Information of diﬀerent exercise modalities can be collected from previous meta-analyses of RCTs. This data has to be pre-processed based on clinical objectives that are set by a DM. Based on this information, a relevant multiobjective optimization problem can be formulated. We suggest using an interactive multiobjective optimization method to support the DM in ﬁnding the compromise solutions that best reﬂects the DM’s preference information (see, e.g.,[10, 13, 24] and references therein for the basic features of interactive methods). This means that the DM augments the available data with one’s domain expertise and iteratively provides one’s preference information and sees what kinds of therapies reﬂect the preferences best and what kinds of trade-oﬀs exist. At the same time, the iterative nature reduces the cognitive load since the DM can concentrate on therapies that satisfy the preferences best. Furthermore, the DM can modify the preferences based on the insight gained and eventually identify the most preferred exercise therapy considering the patient’s needs and health status. One should note that we are not providing a global answer or recommendation. The DM involved can analyze the suggested therapies by the proposed approach and prescribe the most appropriate one based on the individual patient characteristics.
Figure 1 describes an overall view of the proposed decision support approach for ﬁnding the most preferred exercise therapy in knee OA, where the DM and an analyst participate. Diﬀerent phases of the proposed approach (i.e., boxes in the ﬁgure) are described as follows.
Inclusion Criteria and Data Extraction (Phases 1 and 2)
As a starting point, we consider RCTs selected in the meta-analysis in Goh et al. that evaluated the eﬃcacy of exercise therapies in knee OA, hip OA, and knee and hip OA. The authors made a literature search systematically from “the dates of inception” to December 2017. They included papers reporting trials, where a comparison was made between an exercise intervention with a non-exercise one in the knee and hip OA treatment. They also established speciﬁc eligibility criteria after the literature search. They included trials if participants; 1) had not undergone knee or hip joint replacement surgery, 2) had only exercise therapy without additional treatment and 3) were assigned to usual care in the control group. The reported outcomes were pain, function, performance and quality of life (QoL).
In Goh et al., 77 RCTs were selected for the meta-analysis based on the literature search and the speciﬁc eligibility criteria. We used the same inclusion criteria for the exercise therapy studies as Goh et al., except that we included the studies with the patients of knee OA only and where the data of the WOMAC (Western Ontario and McMaster Universities) scale had been used as an outcome measure for pain and function. Besides, we ruled out the studies where the patients underwent an exercise therapy program before knee replacement surgery. The WOMAC was chosen as it is recommended and most commonly used as a disease-specific outcome instrument in OA patients, whereas the KOOS (Knee injury and Osteoarthritis Outcome Score) is intended to be used particularly for knee injuries that can result for a variety of reasons, including OA. Preoperative exercise programs were excluded in turn, because people waiting for knee replacement surgeries often have mobility restrictions due to the pain and disabilities, and we do not know how much physical activity is safe and feasible for people with severe knee OA. Apart from these, for performance outcomes, several testing types and results were listed. This heterogeneity makes a comparison between the outcomes of diﬀerent therapies challenging in a quantitative way. In addition, QoL outcomes were not measured in a majority of the RCTs (33 papers). Therefore, in this paper, we do not consider outcomes for performance and QoL measurements. Figure 2 summarizes the papers (and therapies) meeting our inclusion criteria mentioned above.
According to the reasoning above, we collected data from the selected papers (see Table 1 in supplementary material A). We listed the therapies, the outcomes for pain and function in the WOMAC scale, the number of supervised sessions and the lengths of the therapies. We also adjusted the ranges of the WOMAC scale into the same range (0-20 for pain, 0-68 for function), if the reported outcomes had diﬀerent ranges for the WOMAC scale. It should be noted that the values we collected from the papers are average scores since the individualized data is not given in these papers.
Multiobjective Optimization for Knee OA (Phase 3)
As mentioned earlier, the focus of this study is in ﬁnding the most preferred exercise therapy for a patient with knee OA. To characterize the goodness of an exercise therapy, we consider ﬁve conﬂicting objectives: minimizing cost, maximizing pain reduction and function improvement, minimizing the number of supervised exercise sessions and the length of the treatment period and we want to optimize all of them simultaneously. As they are conﬂicting, there does not exist any therapy that can have the best performance in all objectives, but there exist compromises with tradeoﬀs, as mentioned in the introduction. With the help of multiobjective optimization methods, we can support the DM to identify the most preferred exercise therapy among the compromises, and them make the final choice based on the patient’s characteristics.
One should note that the objectives considered could also be selected diﬀerently if some other aspects characterize the goodness of therapies better. For example, some more objective functions, such as improvement in performance and QoL, can be added. As mentioned, our selection of objectives is explained by the data available. Since no information about combinations of exercise therapies was available, only one therapy can be chosen as the ﬁnal decision. In what follows, we discuss the objectives in some more detail.
Minimize the Cost of Therapy
We estimate the cost of each exercise therapy based on personal expenses, such as the number of supervised or unsupervised training sessions, length of each session, number of trainees in each group, types of equipment and possible checkpoint calls. Moreover, cost is measured from the time between the baseline and end-point of the outcome measure (later follow-ups are not included). Cost is estimated with the current prices (early 2020) in Finland. However, this can simply be adapted for any time in any other country. Details of cost estimation can be found in the supplementary material D.
Maximize Pain Reduction
As mentioned before, we have only average values of WOMAC scores for pain reduction. We do not have individual data for the patients in exercise and control groups in each exercise therapy. Therefore, we consider the diﬀerences between the mean of the WOMAC pain scores pre- and post-intervention as the pain reduction. Furthermore, to take into account the control groups and to be able to measure clinically important change or improvement, we consider the expected net change in pain as the pain reduction objective. We deﬁne the net change as the diﬀerence between the mean change in exercise and control groups.
Maximize Improvement in Physical Function
Similar to pain, we consider the expected net change in WOMAC score for physical function as the disability improvement objective.
Minimize the Number of Supervised Training Sessions
Organizing the supervised training sessions is always challenging. Besides, some patients (e.g., because of disability, additional time and expenses, pollution, travel distances, quarantine limitations causing by an epidemic or pandemic such as COVID-19) or physicians (e.g., due to lack of time and other duties) prefer to have as few (physical) supervised sessions as possible. We consider this as the fourth objective.
Minimize the Length of Treatment
Finally, the ﬁfth objective is minimizing the length of treatment, which often is of concern for both patients and healthcare professionals.
Proposed Multiobjective Optimization Problem
With the objectives discussed so far, we formulate a multiobjective optimization problem to support decision making and analysis of diﬀerent therapies to ﬁnd the most preferred one. (Mathematical formulations are given in equation (1) in the supplementary material B):
minimize cost of therapy
maximize expected net improvement in pain reduction
maximize expected net improvement in physical function
minimize number of supervised training sessions
minimize length of treatment
subject to one therapy is selected from a list of options.
The Proposed Interactive Method (Phases 4-6)
In this section, we propose a new interactive multiobjective optimization method to be applied to solve the problem formulated. The interaction means that the preferences of the DM are taken iteratively into account in the solution process in ﬁnding the most preferred therapy. The proposed interactive method is inspired by the NIMBUS method in which multiple solutions reﬂecting the preferences as well as possible are generated and shown to the DM in each iteration. However, in NIMBUS, the DM’s preferences are expressed by classifying the objective functions into pre-deﬁned classes, which is not the case in this study. Our method diﬀers from NIMBUS in two perspectives; 1) preference type, 2) way of showing solutions to the DM.
As preferences, we use desirable upper and lower bounds for the possible outcomes of our five objectives (also called objective values), since they are meaningful and understandable for the DM. They form a so-called preferred range. Accordingly, we propose a novel interactive method incorporating the preferred ranges in the solution process. Then we generate diﬀerent compromise solutions reﬂecting these DM’s preferences as well as possible. In this, we introduce two kinds of solutions since it may not be possible to ﬁnd a solution that meets all the DM’s preferences. The ﬁrst kind of solutions (group I) meets all the desired preferred ranges, while the second kind of solutions (group II) only meets some preferred ranges. Even though solutions in the latter group violate some preferred ranges, the DM gets more insight of the trade-oﬀs in the compromise solutions. In this way, the DM can learn what is achievable and what is not. Diﬀerent visualizations have been utilized to illustrate solutions in the multiobjective optimization literature[27, 28]. In this paper, we visualize the solutions with parallel coordinate plots which are able to represent several objectives and solutions at once.
In diﬀerent iterations, the DM can update one’s preferences based on the increasing understanding of the available therapies and the existing trade-oﬀs between the objectives. The solution process continues until the DM is satisﬁed and has found the most preferred therapy.
Figure 3 depicts the iterative steps together with some other steps of the interactive method to support decision making in knee OA. The steps are explained below. The technical details of the proposed interactive method are given in the supplementary material C.
Step 1. The best and the worst values of each objective function are identiﬁed and shown to the DM to give an overview of what is feasible. Then, the DM provides his/her preference information as a preferred range for each objective.
Step 2. The multiobjective optimization problem is solved and a desired number of compromise therapies reﬂecting the preferences as well as possible is shown to the DM. In the visualization, the group I solutions are highlighted while the others (group II) are represented in shading, meaning that some sacriﬁcing in some preferred ranges are needed to get the higher values oﬀering by these solutions in some other objectives. Note that if the objective values exceed the DM’s desired values, the relevant solutions are still counted as group I solutions.
Step 3 (optional). The DM can compare and analyze the compromise exercise therapies in more detail e.g., checking the exercises from the clinical aspects, if so desires.
Step 4. If the DM wants to continue and provide diﬀerent preferences, the solution process continues from Step 2. Alternatively, if the DM is satisﬁed with the current compromise exercise therapies, the process continues with Step 5.
Step 5. Finally, after analyzing the compromise therapies, the DM prescribes the most preferred and suitable exercise therapy according to the patient’s needs and clinical status. This ends the solution process.