Mapping and Crosswalk of the Oxford Hip Score and Different Versions of the Hip Disability and Osteoarthritis Outcome Score

Abstract

Background

Patient-reported outcome measures such as the Oxford-12 Hip Score and Hip Disability and Osteoarthritis Outcome Score (HOOS) are used in daily orthopaedic practice to evaluate patients. Because different studies use different scores, it would be important to build conversion tables between scores (crosswalk) to compare the results of one study with those of another study. Various mapping methods can be used to develop crosswalk tables that convert Oxford-12 scores to the HOOS (and its derivatives, including the HOOS physical function short form, HOOS joint replacement, and HOOS-12) and vice versa. Although prior studies have investigated this issue, they are limited to short forms of the HOOS score. Consequently, they cannot be applied to hip preservation surgery and do not include quality-of-life items, whereas the Oxford-12 Hip Score is used for all hip evaluations.

Questions/purposes

We prospectively studied the Oxford-12 and HOOS and its derivatives to (1) determine which version of the HOOS has the best mapping with the Oxford-12, (2) define the most-appropriate mapping method using selected indicators, and (3) generate crosswalk tables between these two patient-reported outcome measures.

Methods

The study enrolled 500 adult patients before primary THA (59% men [294 of 500 patients]) with hip osteoarthritis or avascular necrosis of the femoral head who completed the HOOS and Oxford-12. Patients were recruited from January 2018 to September 2019 in a tertiary-care university hospital, and we included all primary THAs in patients older than 18 years with a BMI lower than 35 kg/m² and greater than 18 kg/m². After a minimum of 6 months of follow-up, 39% (195 of 500) of the patients were assessed using the same tools. To determine which version of the HOOS mapped best to the Oxford-12 and what the most-appropriate mapping method was, we used preoperative data from all 500 patients. Because there is no consensus on the method to establish crosswalk, various mapping methods (linear regression, tobit regression, and quantile regression) and equating methods (linear equating and equipercentile method) were applied along with cross-validation to determine which method was the most suitable and which form of the HOOS provided the best result according to different criteria (mean absolute error, r², and Kolmogorov-Smirnov distance).To generate crosswalk tables, we created a conversion table (between the Oxford-12 and the HOOS form that was chosen after answering our first research question and the method chosen after answering our second question) using preoperative and postoperative data (n = 695). This table was meant to be simple to use and allows easy conversions from one scoring system to another.

Results

The Oxford-12 and HOOS were strongly correlated (Pearson correlation coefficient range 0.586-0.842) for the HOOS subcategories and HOOS physical function, HOOS joint replacement, and HOOS-12. The correlation between the HOOS-12 and Oxford-12 was the strongest (r = 0.825). According to the three different criteria and five methods, the HOOS-12 was the best suited for mapping. The goal was to minimize the mean absolute error (perfect model = 0), have a Kolmogorov-Smirnov distance as close as possible to 0, and have the r² as close as possible to 1. Regarding the most-suitable method for the crosswalk mapping (research question 2), the five methods generated similar results for the r² (range 0.63-0.67) and mean absolute error (range 6-6.2). For the Kolmogorov-Smirnov distance, the equipercentile method was the best (Kolmogorov-Smirnov distance 0.04), with distance reduced by 43% relative to the regression methods (Kolmogorov-Smirnov distance 0.07). A graphical comparison of the predicted and observed scores showed that the equipercentile method provided perfect superposition of predicted and observed values after mapping. Finally, crosswalk tables were produced between the HOOS-12 and Oxford-12.

Conclusion

The HOOS-12 is the most complete and suitable form of the HOOS for mapping with the Oxford-12, while the equipercentile method is the most suitable for predicting values after mapping. This study provides clinicians with a reliable tool to crosswalk between these scores not only for joint arthroplasty but also for all types of hip surgeries while also assessing quality of life. Our findings should be confirmed in additional studies.

Clinical Relevance

The resulting crosswalk tables can be used in meta-analyses, systematic reviews, or clinical practice to compare clinical studies that did not include both outcome scores. In addition, with these tools, the clinician can collect only one score while still being able to compare his or her results with those obtained in other databases and registries, and to add his or her results to other databases and joint registries.

Introduction

Patient-reported outcome measures (PROMs) are used in daily orthopaedic practice to evaluate patients [2]. However, the lack of standardization of PROMs makes it difficult to compare studies and perform meta-analyses. One study, for example, found that more than 20 different PROMs were used in hip surgery [30]. Statistical methods (score mapping or crosswalk) have been developed in order to convert from one PROM to another [1, 11, 17, 22, 27]. These statistical methods can be used to predict the values of one PROM based on the responses to another PROM, while preserving its psychometric properties. These have been widely used with quality-of-life scores [3, 4]. Ghomrawi et al. [14] converted the University of California Los Angeles score to the Lower Extremity Activity Scales using the equipercentile method. Polascik et al. [28] used this same method to develop crosswalk tables between the abridged Hip Osteoarthritis Outcome Score (HOOS) Joint Replacement (JR) and Oxford-12 Hip Score.

However, there is no consensus on which mapping method should be used to convert one PROM to another when using only the data from the first PROM [11]. A number of methods apart from the equipercentile approach have been used for this purpose, including linear regression [4, 18]. Although the equipercentile method is easy to use, there is no proof that this method is suitable for all PROMs. We believe this method should be tested for each PROM and will depend on the score’s distribution. This is relevant to orthopaedic surgeons who might want, for example, to convert from the Oxford-12 to the HOOS [6, 7, 23, 25] or one of its derivatives (HOOS physical function short form [PS], HOOS JR, and HOOS-12) [5, 12, 13, 20]. While previous studies have investigated this issue, they are limited to short forms of the HOOS score (JR) [28], and consequently cannot be applied to hip preservation surgery. They also do not include quality-of-life items, whereas the Oxford-12 Hip Score is used for all types of hip evaluations [2, 6, 7].

We therefore performed a prospective study using the Oxford-12 and HOOS and its derivatives to (1) determine which version of the HOOS has the best mapping with the Oxford-12, (2) define the most-appropriate mapping method using selected indicators, and (3) generate crosswalk tables between these two patient-reported outcome measures.

Patients and Methods

This prospective study was performed at the Lille University Hospital, a university hospital tertiary-care center with a high volume of arthroplasty procedures (> 1000 per year), between January 2018 and May 2020.

Patients

During the inclusion period, every patient older than 18 years with hip osteoarthritis or avascular necrosis of the femoral head after nonresponse to medical treatment was invited to participate in the study. After providing written informed consent, they completed the HOOS and Oxford-12 questionnaires before undergoing primary THA. Patients were excluded if they were not covered by the health insurance scheme in France, were younger than 18 years, were unable to provide consent, were pregnant, or had a BMI greater than 35 kg/m² or less than 18 kg/m². After applying the selection criteria, of the 720 eligible patients, we enrolled 500 (294 men, 206 women); with a mean age of 61 ± 14 years (range, 22-89 years) before THA. The time scheduled for analysis was May 2020. At that time, 195 of the 500 patients had a postoperative evaluation completed by postal survey using the same tools, with no missing data for these 195 responders. There were no missing data when the questionnaire was completed. There was no floor or ceiling effect to the Oxford-12 and HOOS or its derivatives preoperatively (Fig. 1). A ceiling effect (greater than 15% of the maximum scores) was found in the postoperative dataset of the Oxford-12 (Fig. 1). Given this ceiling effect, the preoperative dataset was used to analyze and select the best-suited HOOS variant, along with the most-appropriate method, because it had the largest variation, was unimodal, and had a homogenous distribution.

Fig.1.

These graphs show the Oxford-12 score (A) before and (B) after surgery. There is a ceiling effect in the Oxford-12 scores, with saturation of the maximum scores.

Outcome Scores

The HOOS [23] is self-administrated and includes 40 items with five possible responses, graded from 0 to 4 (0 points = worst possible score; 100 points = best possible score). This score has five subcategories: pain (10 items), symptoms and stiffness (five items), activities of daily living (17 items), function in sports and recreational activities (four items), and quality of life (four items). Other versions of the HOOS have been developed based on the original 40-question questionnaire, such as the HOOS PS (five items) [5] and HOOS JR (six items) [20]. In 2019, the team that developed the original HOOS simplified it to 12 items, calling it the HOOS-12 [12, 13]. In our study, we also analyzed the total HOOS as the mean of the five HOOS subcategories (HOOS global). All HOOS domain scores and derivative scores ranged from 0 (worst score) to 100 (best score).The minimum clinically important difference for the HOOS score, defined by Lyman et al. [21] using the anchor method, was 36 points for HOOS pain, 20 points for HOOS symptom, 14 points for HOOS activities of daily living, 13 points for HOOS quality of life, and 18 for HOOS JR.

The Oxford-12 [6] is self-administrated and consists of 12 questions with five possible responses, graded from 0 to 4. These scores are added to calculate the final score of 48 points (0 = worse possible score; 48 = best score with no symptoms). Both PROMs have been validated and have undergone transcultural adaptation for the French-speaking population [7, 25, 26]. The minimum clinically important difference for the Oxford Hip Score defined by Beard et al. [2] was at least 5.

Objectives of the Study

The primary objective was to determine which form of the HOOS score was the most suitable for mapping with the Oxford-12 score. The nine forms of the HOOS score were mapped with the Oxford-12 using five mapping methods (equipercentile, linear equating, tobit regression, quantile regression, and linear regression), and each was assessed based on three quality criteria (the mean absolute error [MAE], r², and the Kolmogorov-Smirnov distance). The goal was to minimize the MAE (perfect model = 0), have a Kolmogorov-Smirnov distance as close as possible to 0, and have the r² as close as possible to 1.

After choosing the most appropriate HOOS form, our second objectives were to determine the most suitable mapping method for this form (using the five mapping methods and three quality criteria listed above) and to generate crosswalk tables between these two PROMs.

Addressing Potential Sources of Bias

This study was prospective, with consecutive inclusion of eligible patients. The patients were seen at a tertiary-care university hospital with a high volume of arthroplasty procedures (> 1000 per year). There is no accepted method to define how many participants are needed for a mapping study. Thus, we determined the number of participants based on a study by Rouquette and Falissard [31], who recommended having at least 300 participants to validate a PROM. We used PROMs whose French translations have been validated [7, 25, 26].

Statistical Methods

The statistical analysis was performed at the biostatistics department of Lille University Hospital using the software R (R Foundation for Statistical Computing).

Except when specified, the analysis was performed using the preoperative dataset. The Pearson correlation coefficient was calculated for the Oxford-12 and HOOS. Dorans [8, 9] recommends having a correlation coefficient of at least 0.3 between two PROMs before starting the mapping procedure.

Two broad types of methods can be used: equating methods and regression methods. We used five of the most common methods: linear regression, quantile regression, tobit regression, linear equating method, and equipercentile method [4, 16, 18, 19, 29].These methods were evaluated based on three criteria: the MAE, r², and the Kolmogorov-Smirnov distance [33].

Selecting the HOOS That Maps the Best to the Oxford-12

For a given method and PROM, a single value calculated based on the study sample provides no information about uncertainty in the criterion’s estimate and cannot be used to directly compare the mapping quality using the different HOOS questionnaires. To estimate the distribution of the criteria, we used the bootstrap method with replacement [10]. We performed 100 bootstrap iterations with n ≤ 500 individuals who were randomly drawn (with replacement) among the 500 individuals in the study cohort. To determine variations in the distribution of the criteria because of sample size, we repeated the analysis by changing the number from 50 to 500 in increments of 50. We would expect dispersion of the criterion’s distribution to be reduced and then stabilized when the number increases. For each bootstrap iteration, the nine HOOS versions were mapped with the five methods; the three mapping quality criteria were calculated for each of these methods. The criterion calculated with the sample on which the method was developed was affected by optimism bias (the same sample that was used to predict a score’s value and judge the quality of this prediction). To account for this bias, we estimated the criteria for each bootstrap iteration using leave-one-out cross-validation [15].

Lastly, we created a graphical representation of each method (linear regression, quantile regression, tobit regression, linear equating method, and equipercentile method) and one given criterion (MAE, r², and Kolmogorov-Smirnov distance) to visualize the criterion’s distribution for the nine HOOS versions relative to the size of the sample (mean values and 95% CIs). This resulted in 15 charts that were used to identify which HOOS version was the best suited for mapping with the Oxford-12.

Selecting the Most Suitable Mapping Method

For the chosen HOOS, the procedure described above was used to compare the mapping methods. We created a graphical representation of how effective the mapping was for the chosen HOOS using all five methods with a fixed criterion. The most suitable method was then selected based on the three criteria (MAE, r², and Kolmogorov-Smirnov distance). The observed density and estimated density after mapping of the chosen HOOS were determined for the full sample with each method using a non-parametric procedure involving a Gaussian kernel [32].

Creating the Crosswalk Tables

To generate a larger distribution of the minimum PROM values toward the maximum values, we produced the crosswalk tables using both the preoperative and postoperative datasets (n = 695), as described by Ghomrawi et al. [14].

Ethical Approval

This study was approved by our local institutional review board (approval number: AC 2017-A01911-52). This study was registered in Clinicaltrials.gov (NCT04057651).

Results

Which Version of the HOOS had the Best Mapping with the Oxford-12?

The HOOS-12 had the best mapping with the Oxford-12. The correlation between the Oxford-12 and HOOS versions was above the 0.3 threshold defined by Dorans [8] and ranged from 0.59 for the HOOS quality of life to 0.84 for the HOOS global (Table 1). Based on the 15 charts used to compare the mapping of the nine HOOS versions by method (linear regression, quantile regression, tobit regression, linear equating method, and equipercentile method) and criterion (MAE, r², and Kolmogorov-Smirnov distance), the HOOS-12 and HOOS global appeared to have the best mapping (Table 2). The HOOS-12 and HOOS global had the lowest MAE for the equipercentile method (Fig. 2). The HOOS-12 was created by the group that created the HOOS and was intended to be used as an overall score [12, 13], while the same group did not recommend using the HOOS global as an overall score. Thus, the HOOS-12 was used for mapping purposes to generate the crosswalk tables.

Table 1.

Pearson correlation coefficient between the HOOS and Oxford-12

Score	HOOS symptoms	HOOS pain	HOOS ADL	HOOS sports	HOOS QOL	HOOS global	HOOS PS	HOOS JR	HOOS-12
Oxford-12	0.649a	0.787a	0.835a	0.661a	0.586a	0.842a	0.775a	0.795a	0.825a

^ap < 0.001. ADL = activities of daily living; QOL = quality of life; PS = physical function short form; JR = joint replacement.

Table 2.

HOOS scores that provide the best mapping with the Oxford-12 based on different criteria and different methods

Parameter	Linear regression	Quantile regression	Tobit regression	Linear equating	Equipercentile method
MAE	HOOS-12 / HOOS global	HOOS-12 / HOOS global	HOOS-12 / HOOS global	HOOS-12 / HOOS global	HOOS-12 / HOOS global
KS	HOOS ADL/ HOOS global	HOOS ADL/ HOOS global	HOOS ADL	HOOS global/ HOOS ADL	HOOS PS / HOOS JR / HOOS Sport / HOOS QOL
r2	HOOS 12 / HOOS global / HOOS ADL	HOOS 12 / HOOS global / HOOS ADL	HOOS 12 / HOOS global / HOOS ADL	HOOS 12 / HOOS global / HOOS ADL	HOOS 12 / HOOS global / HOOS ADL

The HOOS-12 was identified in 10 of the 15 combinations. Only the HOOS global was found more often (13 of 15), but the authors of the HOOS recommend that the HOOS global should not be used to summarize all subscales. ADL = activities of daily living; PS = physical function short form; global = mean of the five HOOS domains; MAE = mean absolute error; KS = Kolmogorov-Smirnov distance.

Fig. 2.

The HOOS was based on the MAE criterion; the points are the mean value calculated on 100 bootstrap iterations of size n (n = 50 up to 500 by increments of 50). The bars correspond to 95% CIs. The HOOS-12 and HOOS global had the lowest MAE criteria for the equipercentile method. JR = joint replacement; PS = physical function short form; QOL = quality of life; ADL = activities of daily living. A color image accompanies the online version of this article.

What is the Most-appropriate Mapping Method for the Chosen HOOS Form?

The equipercentile method was the most-suitable method for mapping between the HOOS-12 and Oxford-12. The five methods were compared based on the three criteria by using bootstrap estimates (mean and 95% CI) as a function of the sample size for the HOOS-12 mapping (Fig. 3). The methods generated similar results for the r² (range 0.63-0.67) and MAE (range 6-6.2) (Table 3). For the Kolmogorov-Smirnov distance, the equipercentile method was the best by far, with distance reduced by 43% relative to the regression methods and by a factor of 2.5 relative to the linear equating method (Table 3). Finally, only the equipercentile method resulted in very similar observed and estimated densities (Fig. 4). Consequently, we selected the equipercentile method to generate the crosswalk tables. When we examined how the HOOS-12 mapping performed for the five methods based on the three selection criteria, as a function of sample size, the three criteria stabilized starting at 300 individuals (Fig. 3).

Fig. 3.

These graphs show the three criteria for the HOOS-12 selection with the five methods; the points are the mean value calculated on 100 bootstrap iterations of size n (n = 50 up to 500 by increments of 50). (A) Shows the MAE for the HOOS-12 with the five methods, (B) shows the r² for the HOOS-12 with the five methods, and (C) shows the KS distance for the HOOS-12 with the five methods. The equipercentile method had the lowest KS distance. The bars correspond to 95% CIs. MAE = mean absolute error; KS = Kolmogorov-Smirnov. A color image accompanies the online version of this article.

Table 3.

Results of the different methods based on the predefined criteria for mapping between the HOOS-12 and Oxford-12

Method	MAE	r2	KS
Linear regression	6.0	0.67	0.07
Tobit regression	6.0	0.67	0.07
Quantile regression	6.0	0.67	0.07
Linear equating	6.2	0.64	0.11
Equipercentile method	6.2	0.63	0.04

The goal was to minimize the MAE (perfect model = 0), have a Kolmogorov-Smirnov distance as close as possible to 0, and have the r² as close as possible to 1. The methods generated similar results for the r² (range 0.63-0.67) and MAE. The KS distance was best with the equating methods (linear equating and equipercentile methods). MAE = mean absolute error; KS = Kolmogorov-Smirnov distance.

Fig. 4.

These graphs show the observed density of the HOOS-12 for the entire patient cohort (n = 500) and the density of the HOOS-12 after mapping for the Oxford-12. The densities were estimated for each method using the Gaussian kernel method. (A) Shows the density of the HOOS-12 with linear regression, (B) shows the density of the HOOS-12 with quantile regression, (C) shows the density of the HOOS-12 with tobit regression, (D) shows the density of the HOOS-12 with linear equating, and (E) shows the density of the HOOS-12 with the equipercentile method. The predicted distribution using the equipercentile method was the closest to the observed distribution. A color image accompanies the online version of this article.

Generation of a Crosswalk Table

Using the equipercentile method, we created crosswalk tables in both directions: Oxford-12 to HOOS-12 (Table 4) and HOOS-12 to Oxford-12 (Table 5).

Table 4.

Crosswalk table for the Oxford-12 to HOOS-12

Oxford-12 →	HOOS-12	Oxford-12 →	HOOS-12
0	0	25	42
2	2	26	44
3	4	27	48
4	6	28	52
5	8	29	52
6	10	30	54
7	15	31	56
8	15	32	58
9	17	33	60
10	19	34	65
11	21	35	67
12	21	36	67
13	25	37	71
14	27	38	73
15	29	39	75
16	29	40	77
17	31	41	79
18	31	42	81
19	33	43	83
20	35	44	86
21	35	45	90
22	38	46	92
23	40	47	96
24	40	48	100

Table 5.

Crosswalk table for the HOOS-12 to the Oxford-12

HOOS-12→	Oxford-12	HOOS-12→	Oxford-12	HOOS-12→	Oxford-12	HOOS-12→	Oxford-12
0	2	26	14	51	28	76	39
1	2	27	14	52	28	77	39
2	2	28	15	53	30	78	41
3	3	29	15	54	30	79	41
4	3	30	17	55	31	80	42
5	5	31	17	56	31	81	42
6	5	32	18	57	32	82	43
7	5	33	18	58	32	83	43
8	5	34	20	59	33	84	44
9	6	35	20	60	33	85	44
10	6	36	22	61	34	86	44
11	7	37	23	62	34	87	44
12	7	38	23	63	34	88	45
13	7	39	23	64	34	89	45
14	7	40	25	65	35	90	45
15	9	41	25	66	35	91	45
16	9	42	26	67	36	92	47
17	10	43	26	68	36	93	47
18	10	44	27	69	37	94	47
19	11	45	27	70	37	95	48
20	11	46	27	71	37	96	48
21	13	47	27	72	37	97	48
22	13	48	28	73	39	98	48
23	13	49	28	74	39	99	48
24	13	50	28	75	39	100	48
25	14

Discussion

An accurate method is needed to perform the crosswalk necessary to compare studies reporting different PROM scores. The Oxford-12 and HOOS are some of the most frequently used scores in clinical practice [6, 7, 20, 21, 23, 25, 26, 28]. Previous studies have reported crosswalk between the Oxford-12 and short forms of the HOOS score (JR), which is useful for comparing different hip arthroplasty studies [28]. However, they cannot be used to compare studies of hip preservation surgery and assess how treatment alters a patient’s quality of life [20, 28]. This study demonstrated that the HOOS-12 is the most-suitable questionnaire to crosswalk with the Oxford-12 while assessing quality of life for all patients undergoing hip surgery [12, 13]. This study also demonstrated the refinements that are required to investigate different crosswalk methods and determine the most accurate one; in our study, the equipercentile was chosen among the five methods. Our study is clinically relevant because it yielded reliable crosswalk tables between the Oxford-12 Hip Score and HOOS-12 and vice versa. The resulting crosswalk tables can be used in meta-analyses or in clinical practice when a study uses only one of these two PROMs. These tables allow the patient to complete only one PROM while still permitting the clinician to obtain the result of both PROMs.

Limitations

Our study has certain limitations. First, although the size of our sample (500 individuals) may seem small, 300 patients appears to be sufficient to validate a subjective evaluation scale, as others have suggested [31]. A review of mapping studies [4] found that the number of patients varied greatly, from 48 to more than 30,000. A graphical evaluation of the number of participants showed the methods were stable, with 300 patients being sufficient, although this is not definite proof. Second, the single-center nature of our study (tertiary-care university hospital with a high volume of arthroplasty procedures) is also a limitation, although the indications for primary THA were consistent across a contemporary population. Third, although restricting the sample to patients who were scheduled for THA and not for all hip surgery indications could be perceived as a limitation, it provided us with a population that has similar indications. Fourth, we needed to use preoperative and postoperative data to generate the crosswalk tables. Some authors also used preoperative and postoperative data to generate their crosswalk tables because using the preoperative or postoperative datasets alone did not provide a complete score distribution [14]. Using the preoperative dataset to validate the data may be questionable; however, the absence of ceiling or floor effects [34] in this dataset compared with the postoperative dataset validates these data for the selection step of the method and score with a unimodal distribution and a large sample, whereas the postoperative cohort was limited to 195 patients with a ceiling effect.

Which Version of the HOOS had the Best Mapping with the Oxford-12?

We demonstrated that the HOOS-12 is the most suitable form to crosswalk with the Oxford-12, allowing an assessment of quality of life and the outcomes of preservation surgery of the hip. Verification of the prerequisites (correlation) as recommended by Oppe et al. [24] is vital before mapping. For equating methods, Dorans [8] set a threshold of 0.3, although this is a relatively low value for correlations. We believe it is important to evaluate clinical relevance along with the degree of the correlation. If the PROMs of interest are not widely used by healthcare professionals in their practice, the mapping process is useless. Polascik et al. [28] used the HOOS JR, although the correlation was not as good as that of the HOOS-12 in our study. Moreover, this form of the HOOS is only recommended to assess joint replacement, not to investigate quality of life. Because the HOOS-12 was created recently by the original authors of the HOOS and resembles the HOOS global [12, 13], the HOOS-12 allowed us to achieve satisfactory mapping from the Oxford-12. The 12-question format facilitated the mapping procedure and enabled us to generate a crosswalk table. Certain HOOS subcategories (especially the domains of function in sports and recreational activities and quality of life) were less correlated with the Oxford-12 (Table 1). The activities of daily living subcategory had the highest but not the best correlation to the Oxford-12. With these two PROMs, we felt justified in selecting the HOOS-12 from a clinical perspective because this instrument better captures the various parameters of the HOOS than other PROMs do.

What is the Most-appropriate Mapping Method for the Chosen HOOS Form?

The equipercentile approach was the most-suitable method to perform the crosswalk between the HOOS-12 and Oxford-12. Various mapping methods exist without a consensus about which methods and assessment criteria are the most appropriate. In a review of economic studies, Dakin [4] found that regression methods were used the most often to develop health economics studies, without identifying the reference method (linear, tobit, or quantile regression). In fact, regression methods—particularly linear regression, which is often used for mapping—have the drawback of using the mean value, which does not always correspond to the score’s distribution. Consequently, tobit regression, quantile regression, and mixed models are preferred [4]. Other tested methods, such as equating methods, were mainly developed in the context of classical test theory. Some authors have proposed supplementing regression methods with the equating method for evaluating economic models [11, 35]. Equating methods were used in a study in which the University of California Los Angeles score was mapped with the Lower Extremity Activity Scales [14], as well as by Polascik et al. [28]. However, Lee et al. [18] showed that each method has limitations when used for mapping. There is no universal method; consequently, we think the method should be selected based on the distribution and structure of the PROM being investigated. Therefore, we proposed a method based on statistical procedures to determine the most-suitable method. Because the choice of the crosswalk method depends on the assessment criterion, we investigated the three criteria that were used the most (r², MAE, and Kolmogorov-Smirnov distance). The MAE criterion is mainly used with regression methods and appears to be the most suitable for these methods. A less-specific Kolmogorov-Smirnov distance [33], evaluating the distance between the predicted model and the observed model, produces better results with equating methods than with other methods. It is still relevant when comparing methods that do not use regression, such as the equipercentile method, which we observed graphically.

Generation of the Crosswalk Table

Crosswalk tables were created between the Oxford-12 and the HOOS-12 (Table 4) and between the HOOS-12 and Oxford-12 (Table 5) using the equipercentile method. These tables are simple to use clinically, making it easy to convert from one PROM to another [9]. These tables allow the patient to complete only one PROM instead of two, which saves time and simplifies the patient follow-up procedure, while still allowing the clinician to compare his or her patients’ results with the results of studies that used the other score. Likewise, the clinician can collect only one score, making it easier to build and maintain databases and joint registries.

Conclusion

The HOOS-12 is the most complete and suitable form of the HOOS for mapping with the Oxford-12. For this mapping, the equipercentile method is the most-suitable method. This study provides clinicians with a reliable tool to crosswalk between these scores, not only for joint arthroplasties but also for all types of hip surgery, and to do so in a way that also allows for an assessment of quality of life. The crosswalk tables we derived can be used in meta-analyses or clinical practice to compare clinical studies that did not include both outcome scores and compare the results of one study with those of another. Additionally, these tables can be used for clinical assessment because patients would not need to complete both PROMs. Future studies might seek to replicate our work, which would add to its external validity.