Assessing quality of life : reducing the items of a survey used for hip patients by item-reduction techniques

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Bachelor Thesis

Econometrics

Assessing Quality of Life

Reducing the items of a survey used for hip patients by item-reduction techniques Author:

Sharon Schotman

10795014 Supervisor: Dr K.J. van Garderen Date: June 26, 2018

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Statement of Originality

This document is written by student Sharon Schotman who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Introduction

Total hip replacement (THR) is a common procedure for patients suffering from osteoarthritis. During this surgery, the hip joint is replaced by a hip prosthesis. The goal of this surgery is to relieve pain and to improve mobility for the patient. In 2010, 109 patients per 100,000 persons in Europe underwent this surgery (Organisation for Economic Co-operation and Development [OECD] as cited in Hofstede, Gademan, Stijnen, Nelissen, & Marang-van de Mheen, 2018). THR is considered a successful surgery, but there are also various risks - like infections - and dissatisfied patients involved (Anakwe, Jenkins, & Moran, 2011). Aalund, Glassou and Hansen (2017) for instance state that approximately “approximately 10% of patients report some degree of dissatisfaction after surgery” (p. 1952).

This illustrates one of the reasons why it can be interesting to know how well the patient’s quality of life improved after surgery and therefore determine the success rate. Insights in such improvements contribute to the development of a prediction model that can help doctors make more realistic prognoses of the improvements to be expected after surgery (given the patient’s preoperative quality of life score and other preoperative characteristics). Such a prediction model can also help doctors to decide whether to operate at all (taking the above mentioned risks into account) easier. Another reason comes from a health economics’ point of view, where (economic) comparison between clinical interventions is desired for budgetting. Analyzing the quality of life improvements contributes to determining a certain value that makes these comparisons possible. In determining the actual success rate of clinical interventions in terms of quality of life improvements, patient-reported outcome data (or measures, then abbreviated to PROMs) resulting from questionnaires have become more favorable as outcome measure over the years (Ostendorf et al., 2004). These PROMs can be of great importance for the evaluation, since quality of life is actually an unobservable variable. Before such an instrument can be used, it

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needs to satisfy a few psychometric criteria, like whether the PROM actually measures what it is intended to measure (this is called validity).

Besides standard psychometric criteria, it is preferable that a PROM isn’t too long, mean-ing it doesn’t contain too many questions. The most obvious downside of lengthy questionnaires is the excessive time it takes to complete or administer it. One can also imagine the risk of biased responses increasing with the number of questions the patient has to answer. The same negative effect could result from situations where patients are requested to fill in not one, but multiple (lengthy) questionnaires. So, to improve feasibility and compliance of these type of PROMs, there is a need for shorter but still all-covering versions.

One such PROM that could benefit from item-reduction is the Hip disability and Os-teoarthritis Outcome Score (HOOS) (Kl¨assbo, Larsson, & Mannevik, 2003), which includes 40 questions regarding the quality of life of hip patients. Previous studies have been performed on finding a shorter version (Davis et al., 2008; Lyman et al., 2016), but those are limited to Item Response Theory only, while Factor Analysis is another broadly used method for item-reduction. Therefore, this thesis examines to what extent factor analysis can be used to reduce the HOOS to a shorter version that is relevant for measuring the effect of THR surgery.

In trying to answer this question, previous studies on the development of short versions of existing PROMs have been reviewed. This review has focused on what statistical techniques were used and why. Afterwards, when a solid method for item-reduction was determined, ex-ploratory factor analysis has been performed on data from the Bergman clinic in the Netherlands. These data contain (besides personal and health-related characteristics) completed surveys of the HOOS and two other PROMs of 1596 hip-patients, answered 6 weeks before surgery and 3 and 12 months after.

This thesis is organized as follows: the next chapter (2) reviews existing literature on the ongoing development and evaluation of the HOOS-questionnaire and previously developed short-forms. In chapter 3 the data and methodology for the analysis are explained. Then, in chapter 4, the results of the proposed factor analysis are presented and discussed. Chapter 5 concludes with a summary of this study and recommendations for further research on this topic.

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Chapter 2

Literature review

This section reviews existing literature on development of short-form PROMs. First, the PROM analysed in this thesis is introduced. Then, previous studies on the reduction of the HOOS are presented in section 2.2. Section 2.3 offers an introduction to factor analysis, the proposed methodology for the item-reduction of this thesis.

2.1 The Hip disability and Osteoarthritis Outcome Score (HOOS)

The Hip disability and Osteoarthritis Outcome Score, from now on abbreviated to HOOS, is a disease-specific PROM. Kl¨assbo, Larsson and Mannevik (2003) developed this score as an extension of the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC). This was done for mainly two reasons: Firstly, with this new instrument, they aimed at assessing hip disability for a wider range of patients, and secondly, this same procedure had shown to improve responsiveness for the knee-equivalent of the HOOS (the Knee injury and Osteoarthritis Outcome Score). It was namely considered that the WOMAC didn’t evaluate (enough) aspects for young and active patients (De Groot et al., 2007), resulting in the extension of questions revolving around (for example) sports in the HOOS.

The authors tested the added items for validity and reliability. This resulted in the HOOS with 40 items, divided over 5 different domains: pain, symptoms, activity of daily living, sport and recreation functioning and hip related quality of life (Kl¨assbo et al., 2003). All items can be answered on a scale from 0 (no problems) to 4 (severe problems). All five subscales get their own summary score, by adding up the different items and transforming them to a 0 (worst outcome) - 100 (best outcome) scale (Kl¨assbo et al., 2003). The full questionnaire can be found in Appendix A.1.

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Nilsdotter et al. (2003) point out that “many of the WOMAC items did not meet the criteria chosen and could have been removed to form a shorter questionnaire”, but they also mention their own reasons not to pursue this (namely by stating that the WOMAC is used worldwide and that it would be beneficial to calculate the WOMAC out the HOOS). Specifically, problems with the domain symptoms are pointed out. Another study (De Groot et al., 2007) also refers to redundancy in the HOOS, because some of their Cronbach’s alphas (used for measuring internal consistency) were above 0.90.

2.2 Previous studies on developing a short-form HOOS

Two studies have been performed on reducing the HOOS to a smaller questionnaire (Davis et al., 2008; Lyman et al., 2016). These studies show similarities in the methodologies used (they both used Rasch modelling, a form of Item Response Theory [IRT]). However, when comparing their results, only one HOOS item remains in both short-forms. Both short-forms can be found in Appendix A.1.

Davis et al. (2008) aimed to develop a short-form PROM, derived from the HOOS, that focuses on the physical function in people with all kinds of osteoarthritis severities. For their methodology, the authors refer to a similar study by Cole et al. (2003), in which another disease-specific short-form PROM was derived. Following this study, Davis et al. (2008) relied on the so-called partial-credit Rasch model to reduce the 21 HOOS-items of the two function domains activities of daily living (17) and sport and recreation (5). The other three domains were not included in the analysis, because this short-form was intended just to measure physical function. This resulted in the HOOS-PS of five remaining items, as can be found in Appendix A.1.

The other study on this subject is the one by Lyman et al. (2016). They aimed to develop a nonproprietary short-form hip-specific PROM that would specifically focus on outcomes after THR. Lyman et al. (2016) refer to the study by Davis et al. (2008) and the HOOS-PS, but point out that this new PROM unfairly excludes the pain domain. By stating that “[pain] is the dominant reason for which patients undergo THA (=THR)” (Lyman et al., 2016, p. 1473), they judge that the Physical Shortform cannot be used for the evaluation of THR surgery.

As stated before, their methodology is somewhat the same as [the one by] Davis et al. (2008), the difference being the exclusion criteria used before the actual Rasch based item-reduction. Where the HOOS-PS was derived from just two domains (21 items), Lyman et al. (2016) started off with the full HOOS (40 items). However, not all 40 items were directly

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evaluated with the use of Rasch models. Before this statistical analysis, they performed a more qualitative method to select the items suited for the Rasch analysis. For instance, they a priori excluded the four questions of the QoL-domain. They also carried out a so-called relevance study under a group of their patient-sample. This relevance study was among other used for pointing out redundant items in the activity of daily living and pain domains, because some activities are questioned twice in the original HOOS (even if in a different format). The item-reduction of the remaining 30 HOOS-items was based on bootstrapped Rasch and afterwards iterative manual Rasch on the remaining 12 items. The resulting six-items HOOS, JR (Joint Replacement) can be found in Appendix A.1.

Although the resulting HOOS, JR was considered to have good psychometric criteria, they point out the limitation of not being able to compare the new score with other (good) short PROMs such as the Oxford Hip Score (12 items), because their dataset lacked these other scores, and state that cross-validation should be done (Lyman et al., 2016).

Both the HOOS-PS and HOOS, JR form good examples of short-form questionnaires that are derived from the HOOS. Nevertheless, more research is needed to validate both these studies. Validation is desired for two things: the psychometric criteria for the short-forms (the questionnaire themself) and the methodology.

As described, both studies have used Item Response Theory - or partial-credit Rasch modelling to be precise - in order to derive their short-forms. The fact that neither of them explains or justifies the reason why they have applied this methodology is remarkable, considering the fact that there are other common and favorable statistical procedures for item-reduction. Factor analysis is such a broadly used method to describe multivariate data in fewer ‘factors’, while retaining approximately the same information.

Coste et al. (1997) reviewed 42 studies that shortened composite measurement scales, in order to propose some recommendations. Factor analysis is mentioned as one of the four statistical methods (the others being correlation between long/short form scores, cronbach’s alpha and correlation item/composite score), which turns out to be the most frequently (40%, n=42) used one (potentially in combination with one of the other statistical methods) in this subset of studies. A similar (follow-up) review article (Goetz et al., 2013) found that from the 91 reviewed studies shortening a composite measurement scale (between 1995 and 2009), still 52% performed factor analysis. In this more recent review, Item Response Theory (Rasch model) makes it debute with 11%. They conclude that they “lack published recommendations integrating these [IRT] methods” (p. 711).

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So, according to the literature, there seem to be two groups of methods that can be used for deriving a short-form PROM: Classical methods like factor analysis and principal component analysis and the more “modern” Item Response Theory-method, including the (partial-credit) Rasch model. These two different methods are further explained in the next section, after which other studies on comparing these two methods are reviewed.

2.3 Item Reduction Methods

Factor analysis is a technique that tries to describe a large set of variables (in this case: items of a questionnaire) by a smaller set of unobservable variables. Especially for PROMs, in which a set of questions is intended to assess the broad concept health-related quality of life, it is expected that answers to the items are actually determined by a few underlying constructs that together make up someone’s quality of life.

(Exploratory) factor analysis can then be used to uncover the underlying structure of the variables and identify which variables ‘go together’. Once the underlying structure of the variables is known, it can be used to reveal redundant items. However, item-reduction is not the main purpose of factor analysis. This section explains the basic principles of factor analysis and examines the way it can be used for item-reduction.

2.3.1 Factor Analysis

The idea of factor analysis, often assigned to C. Spearman and R. Cattell, is that all p observable random variables (i.e. the p items of a questionnaire), in vector x, are in fact a linear combination of m (m < p) latent variables, called “(common) factors” (f1, . . . , fm), and an error term

(also called the specific factor, since these are unique for all p variables). In this research, the observable variables x1, ..., xp would consist of the HOOS-questions that are being analyzed.

So in the original setting, p = 40.

This research employs exploratory1 factor analysis, meaning, as the name suggests, that the dataset is being explored. This means that there is no real hypothesis on the factor structure that is being tested: all options (on which factor and how many factors) are still open. However, the researcher can of course have some expectations on the underlying factor structure. For instance: The factors (latent variables) could be the five domains that the HOOS covers (see section A.1). The real factor structure can only be determined after the analysis.

1

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The model takes on the following form: x1 = λ11f1+ λ12f2+ ... + λ1mfm+ ε1 x2 = λ21f1+ λ22f2+ ... + λ2mfm+ ε2 .. . xp = λp1f1+ λp2f2+ ... + λpmfm+ εp (2.1)

Here the λjk are called the factor loadings. These are the coefficients you try to estimate.

They do not vary per observation, where x and f do. The factor loadings represent the strength of the correlation between the variable and the factor. The vectors x and f represent the scores on the p items, and the m factors, respectively. Note that x contains scores the patients actually give, whereas f (the factor scores) can only be estimated via factor analysis. For item-reduction, the determination of these factor scores is not particularly of interest.

The matrix notation with dimensions xp×1, Λp×m, fm×1, ep×1 is given by:

x = Λf + e (2.2)

Note that the variable xj actually is a vector of n observations (the n answers to the jth

HOOS question). When including the sample in the model, we can also write:

Xn×p= Fn×mΛ0m×p+ en×p (2.3)

The model assumes that the error terms are uncorrelated (therefore the name specific fac-tors). Furthermore, it assumes that the factor scores f and the specific scores e are independent. The common factors f1, ..., fm can either be pairwise uncorrelated, making them orthogonal, or

correlated, making them oblique.

As can be seen, the factor analysis model (2.1) resembles a standard linear regression model. But there is a sufficient difference: neither Λ nor f are known. This requires different estimation methods. The procedure start with estimating Λ. Afterwards, f can be derived. But, as stated before, that is not particularly of interest for this thesis.

You can show that taking the covariance on both sides results in: Σ = Cov(X) = Cov(Λf + e)

= Λ Cov(f) Λ0+ Cov(e) = ΛΛ0+ Cov(e)

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So, we try to find Λ and Ψ that fits the sample covariance matrix S the best.

Estimation is done in two steps. First, an initial solution for Λ is found by Maximam Likelihood or Principal Axis Factoring and then rotation is applied. Rotation (i.e., orthogonal or oblique projection) is used because there is no unique solution, and you can argue that some other solutions may be preferred for interpretation. The fact that rotation offers multiple solutions, can be derived as follows. Take Q to be an orthogonal matrix and take Λ∗ = Λ1Q. Suppose {Λ1_{, Ψ} is found to be the initial solution, then, by the properties of an orthogonal}

matrix, it follows that {Λ∗, Ψ} also is a solution:

Λ∗Λ∗0= (Λ1Q)(Λ1Q)0 = Λ1QQ0Λ10 = Λ1Λ10

Although estimation proceeds in two steps, one other analysis is needed beforehand. The functions that computes the factor analysis output namely needs an initial number of factors to extract. So, in order to perform factor analysis, one needs to determine which techniques are best suitable for the following three steps: (1) determining the number of factors, (2) extracting the initial factors and (3) rotating these initial results. These steps are briefly discussed below.

1. Determining the number of factors

There are a plethora of methods available for determining the number of factors (Yong & Pearce, 2015). Basically, all methods revolve around the eigenvalues of the correlationmatrix, since that is the one being analysed. The methods used in this thesis are discussed in the next chapter.

2. Extraction of the factors

As illustrated above, to find estimates of Λ, the covariance matrix - or in most cases the cor-relation matrix - is factor analyzed. Over the years, a lot of factor solution methods have been derived. For example, Harman (1967) summarizes his mathematical derivations with a table (p. 108) covering eleven different factor solution methods. Rummel (1970) shows a similar table (p. 348) which covers eight “factor analysis approaches and techniques”. Some of the methods discussed by these authors are outdated and have been abandoned with the development of modern computers. Nowadays, we can identify two popular streams of methods: Principal Axis Factoring (PAF) and Maximum Likelihood (ML) (Izenman, 2008).

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Maximum Likelihood For estimating Λ with Maximum Likelihood (ML), we need the as-sumption that x is multinormally distributed. Under this asas-sumption, the loglikelihood can be derived.

xi = Λfi+ e ∼ N (0, Σ)

For the individual:

L(xi; Σ) = (2π)−p/2∗ |Σ|− 1 2 ∗ exp( −1 2 x 0 iΣ −1 xi)

For all n individuals, we can take the product of this likelihood, resulting in: L(x1, x2, ..., xn; Σ) = (2π)−n∗p/2∗ |Σ|−n/2∗ exp( n X i=1 −1 2 x 0 i Σ−1xi)

With ML, we want to find Σ such that the (log)likelihood is maximized. The loglikelihood is given by. ` = log(L) = −np 2 log(2π) − n 2log|Σ| − 1 2 n i=1x 0 iΣ −1 xi

In stead of maximizing this function, the so-called fitting function is minimized. This is explained by Izenman in section 15.4.2 (2008).

Principal Axis Factoring Another common method for factor extraction is Principal Axis Factoring (PAF). PAF originates from principal component factor analysis. In order to under-stand the estimation process of PAF, one needs to be familiar with principal component analysis and how this technique is used for factor analysis. Mark that principal component analysis is something different than principal component factor analysis, but that the latter uses tech-niques of the former, to serve a different purpose. In factor analysis, the technique aims to find underlying factors in stead of principal components. The exact differences between princi-pal component analysis and principrinci-pal component factor analysis are not extensively explained here, because it is not relevant enough for this study. The interested reader can consult other literature on principal component analysis, for instance Jolliffe (2002, Chapter 7).

To fully understand the mathematical derivations of the PAF-estimates for Λ, one should be familiar with the method of principal components applied to factor analysis (as introduced above). The interested reader can consult other literature on this subject, for instance Harman (1967) or Rummel (1970).

Since we know that ΣXX = ΛΛ0 + Ψ, we also know that the ith diagonal entry of the

correlation matrix equals 1 = h2_i + ψii, with h2i =

P

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commu-nalities and stand for the amount of variance of the variable that is explained by the common factors.

In the principal-factor method (i.e., the principal axis factoring), the correlation matrix ΣXX, with ones along the main diagonal, is replaced by the reduced correlation matrix ΣXX−Ψ.

This matrix thus has the communalities on the diagonal. In the principal-component factor analysis ΣXX is replaced by bΣXX. But, since we also do not know Ψ, here the communalities

need to be estimated.

One of the advantages of PAF is that, in contrast to ML, there are no distributional assumptions needed.

Besides ML and PAF, there are even more methods for extraction of the factors. These are not taken into account in this thesis, because these are not commonly used in recent literature (Yong & Pearce, 2015).

3. Rotation

Rotation serves to make the outcome as interpretable as possible, by seeking to load all the variables to the least factors as possible. There are general two forms of rotation:

• Orthogonal

• Oblique: this one allows the factors to be correlated, which is very likely the case for the subscales of quality of life in hip patients

Concluding remarks

Based on all the literature that is reviewed above, the following can be stated about the HOOS. There is an aspiration for a short version of the HOOS. Two previous studies have been performed aiming the same and they resulted in two possible short-form PROMs that can be used for the evaluation of THR surgery and for patients of the broad spectrum of osteoarthritis. The HOOS, JR is the preferred one for evaluating the THR surgery, because this one didn’t a priori exclude the pain domain, as had been done when finding the (other short-form) HOOS-PS. Although the relevant studies did test the psychometric qualities of the new PROMs, there are some uncertainties and shortages before the HOOS, JR (or the HOOS-PS if preferred) can be adopted for practical use by clinics. This includes applying the other common technique

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for item-reduction - exploratory factor analysis - and comparing the two different outcomes (as described in section 2.3.3), in aiming to conclude on which technique, and thus which short-form HOOS, is the best one to use. Above that, when it turns out that Rasch analysis actually is the prefered technique, the HOOS, JR could be validated further by comparison to the Oxford Hip Score and other forms of cross-validation.

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Chapter 3

Research design

Chapter 2 has given an overview of the methodology used by other researchers for the develop-ment of short-form PROMs. This included an introduction to exploratory factor analysis. This chapter now explains how exploratory factor analysis was conducted for the goal of this thesis. The exact steps followed for the statistical analysis can be found in section 3.2. But first, in section 3.1, the dataset used for the analysis is described.

3.1 Data

Data were received from the Bergman clinic in the Netherlands. The Bergman clinic performs total hip replacement surgery on patients with different severities of osteoarthritis and keeps track of the QoL improvements of the patients by the use of three different surveys: the HOOS, Oxford Hip Score (OHS) and the generic EuroQol-5 Dimensions (EQ-5D). The dataset contains 1596 individual patients who answered the surveys (between 31-03-2015 and 13-04-2018). Of those 1596, approximately 85% actually underwent THR surgery.

The patients were asked to fill in the surveys multiple times: approximately six weeks before their surgery (t0), three months after (t1) and 12 months after (t2). That is why the

PROM-dataset initially contained 2266 observations..

The first 61 observations did not include answers to all 40 questions of the HOOS, so they were removed from the dataset. Of the remaining 2205 observations (1581 individuals), almost all observations included answers to all the questions (40 HOOS, 10 OHS and 6 EQ-5D). It was chosen to not remove any other observations, because missing values only appeared in the answers of the OHS or EQ-5D.

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The 40 questions of the HOOS, with the sample mean scores and standard deviations (in brackets) are given in table A.1. The table shows the mean scores of the 1397 observations at t0 and those of the 388 individuals who answered the follow-up surveys at t1. It shows that, as

expected, the mean scores of all 40 questions have decreased (meaning on a 0 [no problems] to 4 [severe problems] scale that the concept has improved) after surgery.

3.2 Methods

Exploratory factor analysis was introduced in section 2.3.1. Implementing this technique for item-reduction requires a few decisions to be made. This section explains all the decisions that were made in this research and what criteria were obtained.

First, as noted in the previous chapter, EFA should only be carried out on a dataset that contains items with relevant pairwise correlations. Among other things, this means that inter-item-correlations (r) should be high enough (the rule of thumb is > 0.3), but also not too high (Yong & Pearce, 2013). So before the statistical analysis was conducted, the questionnaire and the dataset were critically reviewed on which items were eligible for the factor analysis. I therefore split this section into two paragraphs: item eligibility process and factor analysis.

3.2.1 Item eligibility process

Since the goal of this thesis is to find a short version of the HOOS that can be used for evaluating the THR surgery (as described in chapter 1), some items were first of all removed based on their content. The quality of life domain questions were considered not relevant for the analysis and were therefore excluded a priori. This was decided, based on the consideration that the PROM itself can be used to assess the patient’s quality of life improvements (under the assumption that the relief of pain and improved mobility directly contribute to quality of life improvements). This is in line with the research by Lyman et al. (2016).

The questions of the HOOS (see Appendix A.1) were furthermore checked for obvious redundancies between the different domains and were then compared with the correlation matrix (see Appendix). If two (or more) items appeared to be measuring the same activity or concept and showed high pairwise correlations (> 0.75), it was chosen to select one of these duplicate questions for the factor analysis. This selection was based on mean item difficulties, meaning the question with the higher sample mean could stay. If the mean scores were (almost) the same, the difference in mean scores between t0 and t1 (of the same group of individuals, so n = 388)

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were compared (where the highest difference could stay).

The items were then checked for low intercorrelations. When more than half of the correlation coefficients from one item were < 0.30, the item was removed.

3.2.2 Factor analysis

The number of factors

Once it was determined which items of the HOOS could be excluded from the analysis, the first step in the actual factor analysis could be made. The basic concept of factor analysis has been explained in section 2.3.1. There, it is mentioned that the first step of factor analysis is determining how many factor to extract and that there are a plethora of methods widely used in relevant research to do this. Here, I describe the techniques that I have used and what they rely on. Essentially, all methods are based on the eigenvalues of the factors. This is argumentative since we know that principal axis factoring is in fact an eigenvalue-decomposition.

Kaiser’s criterion This method is the default method in many statistical packages and is often attributed to Kaiser (1960). The criterion states that the eigenvalues of the factors should be greater than 1. In essence, this means that a factor should extract at least as much variance as the original variables. To determine this number, all p possible factors are extracted and they are ordered in the size of their eigenvalues.

Scree test The scree test (Cattell, 1966) is a visual method similar to Kaiser’s criterion. The eigenvalues of the factors are plotted against the factor number. Instead of the harsch line that is drawn with Kaiser’s criterion, the researcher must look for those factors that together account for the most variance. In the so-called scree plot, this is visible as a twist or break, after which the downward slope stays somewhat constant.

Parallel analysis Parallel Analysis also focuses on the eigenvalues. Only this method com-pares the eigenvalues of the extracted factors of X to those from a random generated sample matrix of the same size. Therefore, the researcher can determine (using this method) whether the high eigenvalues can be attributed to factors, or are just random. Simply stated, we want factors to account for more variance than factors that are derived from random data.

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Because it is evident from the literature that multiple techniques might lead to a different suggestion, all above mentioned techniques have been used, hoping that the different approaches corroborate each other. If this is not the case, subjective measures are needed. Therefore, once the loading matrices of all the possible factor numbers were determined, the factor structure was interpreted, aiming to exclude some of the proposed number of factors (and ultimately end up with one final factor structure). This was subjectively done based on what made the most sense.

Extraction of the factors & Rotation

For all possible number of factors, both principal axis factoring and maximum likelihood were used to extract the factors and estimate the factor loadings (pattern matrix). In all cases, promax rotation was used, since the factors were expected to be correlated (oblique) instead of orthogonal.

For each possible number of factors, the PAF and ML outcomes were compared. Based on the overlapping results, it was chosen which items to remove. The main criterion that was used was: remove an item if all (absolute) loadings are < 0.35. Cross-loading (loading > 0.35 on more than one factor) was also an indication for removal, but this was only proceeded when apparent in both the PAF and ML pattern matrices.

After removal of these items, PAF and ML extraction were performed again, in order to verify the results and check for new redundancies, using the same criteria as before. This was repeated until the final factor structure was found, containing a clear and meaningful distinction between the factors and the items all loading onto just one factor.

3.2.3 Comparison of short-forms

After a final model was found using the above mentioned criteria, the proposed short-form was compared with the HOOS, JR based on contents and underlying factor structure.

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Chapter 4

Results

4.1 Item eligibility process

As explained in 3.2.1, the four QoL domain questions were a priori removed. For the second criteria (i.e. checking for obvious redundancies), the correlation matrix of the HOOS with the remaining 36 items is presented in the Appendix. The content of the questions can be found in Appendix A.1. There were some questions for which the high inter-item correlation (> 0.75) can be attributed to the resemblance of the questions. To give an example, questions P4 and A6 both ask for the ability “Walking on a flat surface” and show a correlation of 0.821. In total, there are five of such concepts that are addressed both by the pain and the activities of daily living domain (Walking on flat surface; Going up or down the stairs; Sitting or lying; Standing upright; Walking on an uneven surface). This was also notified by Lyman et al. (2016) in their development of the HOOS, JR. When looking at the mean t0 scores of these items in table

A.1, it shows that for instance P5 “Going up or down the stairs” is preferred (mean = 2.35) to include in the analysis, compared to the similar questions A1 “Descending stairs” (1.88) and A2 “Ascending stairs” (2.24). Based on this criterion, A1, A2, P8 (“Standing upright”) and A6 (“Walking on flat surface”) were removed.

The items P10 and SP4 both questioning “Walking on an uneven surface” show, not surprisingly, the same mean score. Therefore, the difference in mean score between t0 and t1

(between the same n = 388 individuals 1 ) were compared. This showed that the score for P10 had reduced with 1.55, where this was 1.49 in the case of SP4. Therefore, also SP4 was removed.

1

The mean t0 scores of the same individuals as t1 (n=388) were used, to truly cover the difference. These mean t0scores (n=388) are not shown in table A.1, because they are not relevant for the rest. The used t0means for calculating the difference with t1 were: 2.73 (P10) and 2.75 (SP4).

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The last concept that is covered in two domains, is sitting/lying. Since the pain domain question (P7) showed a lower mean score (1.91) than the ADL question (A12) regarding lying in bed (1.96), but a higher mean than the other ADL domain question (A14) regarding sitting (1.64), it was decided to include all three questions for the factor analysis. This was also done considering that both A12 and A14 ended up in the HOOS, JR.

The third and last step was to check the remaining items for notable low intercorrelations. Two items showed more than half of their correlation coefficients lower than 0.30 (S1 with all questions and S2 with 19 of the remaining 30 questions). Item P6 showed some bad properties as well, by low intercorrelations with 14 of the 30 remaining questions, but was still included for the factor analysis.

4.2 Factor analysis results

The number of factors

After the exclusion criteria described in the previous section, a matrix containing 29 HOOS items remained for the factor analysis. It followed that the four techniques (Kaiser’s criterion, Scree Test, Parallel Analysis and Velicer’s Minimum Average Partial) used to determine the number of factors, resulted in different outcomes.

Figure 4.1: The Scree Plot for the Scree Test and Kaiser’s criterion of X29

Figure 4.2: The Scree Plot for the Parallel Analysis of X29

Figure 4.1 shows the scree plot for factors (instead of principal components considering the fact that principal axis factoring is employed instead of principal component factoring, which would result in higher eigenvalues). As described in chapter 3, the hinch in the plot tells the

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researcher how many factors to extract. Although interpretation of the plot remains subjective, I considered it safe to say that the Scree Test depicts 4 factors. This plot was also used to determine Kaiser’s criterion. It is clear that there are three factors with an eigenvalue lying above the horizontal line, thus this criterion suggests three factors.

Parallel Analysis also delivered a Scree Plot. In this Scree Plot (figure 4.2), one must look for those factors that have an eigenvalue that is greater than those from the resampled data. This results in a proposed number of 7 factors.

Velicer’s MAP is the only technique that doesn’t require the researcher to interpret the result, but gives one output: the Velicer minimum was achieved with 3 factors.

Based on these four techniques, the underlying factor structure consists either of 3, 4 or 7 factors. It is common to retain different outcomes from these techniques. To determine which number is the most suitable, factor analysis was conducted for all these values.

First extractions

Both PAF and ML were conducted, extracting 3 factors. The amount of variance explained by the factors were 56% (PAF) and 55%(ML). It turned out that these methods yielded practically the same results (the same questions loading on the same factors; no cross-loading and all factor loadings differed less than 0.15). Therefore, I chose to only report the results from the PAF. They are given in table A.3 in the Appendix. All factor loadings ¡0.35 have been removed and all questions have been ordered to factor loading size. This outcome is very ‘clean’, meaning that there are no cross-loadings, there are enough questions loading onto each factor and the proposed factor structure is understandable. When examining the items that load heavily on the respective factors, it is clear that this outcome would suggest a following factor interpretation: The first factor contains activities like walking, the second factor contains activities that require more bending of the hip, like putting on socks and the third factor contains the functioning in a resting position. Items S4 (“How severe is your hip stiffness after first wakening in the morning?”) and P1 (“How often is your hip painful?”) were suitable for removal. S4 showed factor loadings of 0.19, 0.34 and 0.20 respectively. The communality of S4 was 0.44, meaning that only 44% of the variance of this item can be explained by these three underlying factors. For P1 this result was even worse: a communality of 0.28 and loadings 0.27, 0.2 and 0.09 on the three factors.

As said, the pattern matrix proposed by ML is not shown, because of the resemblance with PAF. One notable difference between the pattern matrices that nonetheless needs to be

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pointed out, is that based on ML also items A3 “Rising from sitting”, S5 “How severe is your hip stiffness after sitting, lying or resting later in the day?” and A13 “Getting in/out of bath” would be deleted, with respective loadings onto their main factor of 0.28, 0.31 and 0.31. When comparing this result with the PAF findings, it is interesting that these three items are there the items that load onto the second factor the least (with loadings 0.43, 0.37 and 0.36 respectively). Where the situation with 3 factors delivered compatible results from the two extraction methods, this wasn’t the case for the extraction of 4 factors. To give a clear overview of the differences, the factor structures of PAF and ML are given in Appendix table A.4 (again, the questions are sorted from high to low loadings). The factor structure suggested by PAF is preferred for multiple reasons. First, the factor structure suggested by PAF made more sense for interpretation (mainly the first factor from ML is problematic and undefinable). Secondly, ML found one cross-loading (item A14 “Sitting” was assigned to factor 1 as well as factor 3). And thirdly, when comparing the results with the 3-factor result above, five of the six items suitable for removal by PAF were also suggested by the 3-factor structure (all but P2). ML would only exclude one item (P1), which makes it even less applicable for item reduction of the HOOS.

The pattern matrices resulting from 7-factor extraction did not give useful results (and are therefore not shown in tables). The PAF analysis resulted in three cross-loadings (for questions A14, A16 and A3) and the ML analysis in one (for question P7). On top of that, the proposed factor structures (both by PAF and ML) did not make much sense. For example, PAF suggested as third factor one with both the items “Getting in/out of bath” and “Sitting”. For these reasons it was chosen to not proceed factor analysis using the 7-factor structure. Another important motivation for this is the fact that factor analysis works best with enough items loading onto a factor. Factors that contain just three items (as was often the case with the 7-factor structure) are hard to reduce items from.

To summarize, the first factor extractions resulted in a few different pattern matrices. Although the outcomes of ML and PAF with 4 factors were divergent, this was not the case when comparing the combined 3-factor results with the 4-factor PAF pattern matrix. Apart from question P2, the 4-factor PAF matrix indicates the same redundant questions as the 3-factor case. It was therefore decided to remove the items S4, S5, P1, A3 and A13 and run the extraction again on the 24 items left to verify the 3 or 4-factor-structure.

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Second extractions

For the second factor analyses, again the number of factors were determined, using the same four methods. Scree test and Velicer’s MAP both suggested 4 factors, Kaiser’s criterion 3 and Parallel Analysis 6. The 6-factor case is left out of account, for the reasons mentioned above (with the 7-factor case).

The extractions of the factors (on X24) resulted in outcomes that are similar to the

ones described above (on X29). To explain the considerations made to remove two extra items

(resulting in a final model) and select a final factor structure, the results are briefly discussed here.

PAF The PAF 3-factor case resulted in all questions loading (> 0.35) on one single factor, so no cross-loadings, but also no redundant items. A total of 12 questions loaded onto the first factor (8 on second and 4 on third). The PAF 4-factor case would remove two other questions: P2 (“Straightening your hip fully”) and S3 (“Difficulties to stride out when walking”), both with a communality of 0.34. In the 3-factor case these communalities were also low (0.33 each). Therefore, these two extra items were considered suitable for removal.

ML The results for the ML 3-factor case are similar to the 3-factor PAF results (just as above with X29); the only difference being that ML would remove item SP1 “Squatting”, where by

PAF it would be retained (in factor 2). The results for the 4-factor case differ quite a lot. This was also noted for the 4-factor extraction with 29 items included (as mentioned above).

The choice of which model is the actual model, relies then on interpretation of the factors. Comparing the 3-factor and 4-factor case shows that the items of the fourth factor (heavy movements like squatting) are divided over the first and second factor in the 3-factor case. Also, the total variance explained by four factors is 61%, and for three factors 58%. Therefore it was chosen to keep the 4-factor PAF structure. Above that, because the original HOOS includes a seperate domain for questions regarding sport and recreational functioning it made sense to prefer the 4-factor-outcome. The pattern matrix of this final model, the PAF extraction of 4 factors, is shown in table 4.1.

Interpretation of the derived short-form

The final model suggests that there are four underlying factors that contribute to the quality of life of hip patients and that 22 items of the original HOOS are evidently covered by these

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Table 4.1: Pattern matrix of X24 using PAF extraction of 4 factors Question Loading on factor 1 Loading on factor 2 Loading on factor 3 Loading on factor 4 P9. Walking on a hard surface (asphalt, concrete, etc) 1,14

P4. Walking on flat surface 1,04 P10. Walking on an uneven surface 0,88 A8. Going shopping 0,70 P5. Going up or down stairs 0,47 A4. Standing 0,46 A17. Light domestic duties (cooking, dusting, etc) 0,42

A9. Putting on socks/stockings 1,17 A11. Taking off socks/stockings 1,13 A5. Bending to floor/pick up an object 0,73 A10. Rising from bed 0,47 P3. Bending your hip fully 0,47 A7. Getting in/out of car 0,44 A15. Getting on/off toilet 0,43

P7. Sitting or lying 1,00 A12. Lying in bed (turning over, maintaining hip position) 0,99 P6. At night while in bed 0,98

A14. Sitting 0,69

SP2. Running 0,86

SP1. Squatting 0,85

SP3. Twisting/pivoting on your injured hip 0,76 A16. Heavy domestic duties (moving heavy boxes, 0,52

scrubbing floors, etc) P2. Straightening your hip fully*

S3. Difficulties to stride out when walking*

* are the items that were removed after the second factor analysis

Table 4.2: Correlation matrix of the four factors

Factor 1 Factor 2 Factor 3 Factor 4

Factor 1 1.00

Factor 2 0.65 1.00

Factor 3 0.59 0.65 1.00

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common factors (see table 4.1). Although one can never be certain of how to name the factors, the items loading onto each factor give an idea. The factors can be attributed to four types of movements or motion requirements.

The first factor covers activities that require some light, continuous movements or func-tionality of the hip, like walking. The second factor contains movements of the hip that require the full, or at least a broader range of motion, such as putting on socks and bending your hip. This means that heavier flexion and extension are required in order to fulfill the activity. The third factor can be attributed to being in rest, where minimal movements of the hip are needed, but still the hip might find itself in flexion or extension (e.g. when not being able to fully sit straight). The last factor clearly accounts for the heaviest movements (sports). This insight makes it also clear why such high correlations are present among the factor (table 4.2): for instance, a correlation of 0.77 between the first and the fourth factor. These correlations also justify having obtained promax (oblique) rotation.

It is of course relevant to compare the proposed HOOS short-form with the previously derived HOOS-PS (Davis et al., 2008) and HOOS, JR (Lyman et al., 2016). This is summarized in table A.2 of the Appendix. Since this thesis focuses on evaluation of THR, comparison with the HOOS, JR is more relevant. As can be seen in table A.2, five of the six questions from the HOOS, JR are also suggested by the principal axis factor analysis performed in this study. Only question A3 “Rising from sitting” did not meet the chosen criteria for factor analysis. To recap, item A3 was removed after the first factor extraction based on low loadings (0.26, 0.28 and 0.27 based on a 3-factor ML). This makes investigation to why this item is included in HOOS, JR wanted. The question arises whether item A3 shouldn’t be replaced with some other item more evidently loading onto the second factor (full range of motion) found in the current short-form, like the similar item A10 “Rising from bed”.

When placing the six HOOS, JR items into the factor structure of the final model from this study, we find that P5 and P10 follow factor 1, A5 follows factor 2 and A12 and A14 follow factor 3. This means that the implied factor structure of this study is in line with the items found by Lyman et al. (2016), with the exception of the fourth factor of heavier movements.

With respect to the research performed by Lyman et al. (2016), the following can be stated: more research to why item A3 was included is needed and the fact that no heavy movements (the fourth factor in this study) should be questioned.

There are various limitations to the current study. About factor analysis can be said that the method requires a lot of arbitrary steps, which can be interpreted the wrong way

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by the researcher. The plethora of methods to find the number of factors and the fact that interpretation is needed to determine the actual factor interpretations, give examples of this subjectivity. Another example of possible misleading conclusions is the fact that hoos.s1 and hoos.s2 were deleted before the factor analysis, which makes sense when wanting to identify a factor structure, but it does not particularly mean that these two symptoms of osteoarthritis are irrelevant for the evaluation of the surgery. Above this, factor analysis is a method that removes items that are very unique (meaning that their variance is not particularly explained by the common factors). This however does not have to mean that these items alone are not relevant for the short-form. Factor analysis has furthermore not proven to be able to reduce the HOOS further than 22 items. This is due to the fact that the extracted factors need a minimum amount of items loading onto these factors, to identify the factors. This resulted in not being able to properly compare the found short-form with the HOOS, JR.

This also points out some recommendations for further studies. Proper statistical meth-ods are needed to compare the HOOS, JR and the presented short-form. Above that, the post-operative observations of patients being treated were not taken into account in this thesis. However, these observations could be used to find a short-form HOOS that really covers the changes in quality of life improvements after THR surgery.

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Chapter 5

Conclusion

The aim of this thesis was to examine to what extent factor analysis can be used to reduce the HOOS to a shorter version that is relevant for measuring the effect of THR surgery. Two previous studies resulted in two short-forms, containing respectively 5 (HOOS-PS) (Davis et al., 2008) and 6 items (HOOS, JR) (Lyman et al., 2016), but those were developed using Item Response Theory (Rasch modelling) instead of factor analysis, another common method for item-reduction.

This thesis has made some subjective choices for item-reduction. These consisted of reducing all questions from one irrelevant HOOS domain, selecting (based on mean sample scores) the most important question from multiple items covering the same subject and removing items based on low inter-correlations. After having removed eleven items based on these criteria, principal axis factoring and maximum likelihood were used in combination with promax rotation. This thesis supports the notion that different methods for determining the possible number of underlying factors present in the dataset, results in different outcomes. This makes it hard to directly identify the underlying factor structure and the degree to which the items are determined by these factors. Therefore, multiple pattern matrices have been estimated for three, four and seven factors using both techniques, until no redundancies were left. The final model consisted of twenty-two questions loading onto four factors.

This study has demonstrated that factor analysis can be used for item-reduction of the HOOS. The recommended application of this method is to determine the possible number of factors by multiple statistical tools and combine these results by estimating multiple pattern matrices using promax rotated principal axis factoring (or the somewhat less preferred maxi-mum likelihood method). Although a short-form has been found using this methodology, factor analysis generally brings along two downsides that have played a part in this study. The first is

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the prominent role the interpretation and decision-making of the researcher fulfills in the analy-sis. The second is that this research has not found a proper method to reduce the HOOS further than 22 items, making it impossible to properly compare the short-form with the HOOS, JR.

Nevertheless, the content of the proposed short-form HOOS was somehow compared with that of the HOOS, JR. This study adds to the ongoing process of validating the HOOS, JR, because the six items of the HOOS, JR are (to a certain extent) compatible with the found underlying factor structure of the original HOOS. The results from this thesis however also question the inclusion of one item (A3 “Rising from sitting”) and the fact that neither of the six HOOS, JR questions cover heavier movements, like sports.

Proposed follow-up studies consist of including post-operative scores of treated patients into the analysis and validating the proposed factor-structure and new derived short-form by comparison with other hip-specific scores, like the Oxford Hip Score.

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Appendix A

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Table A.1: The HOOS items, including mean scores (standard deviations)

Questions Mean score of t 0

(SD)

Mean score of t 1 (SD)

S1. Do you feel grinding, hear clicking or any other type of noise from you hip? 1.08 (1.26) 0.47 (0.86)

S2. Difficulties spreading legs wide apart 2.61 (1.31) 1.16 (1.23)

S3. Difficulties to stride out when walking 2.57 (1.30) 1.35 (1.28)

S4. How severe is your hip joint stiffness after first wakening in the morning? 2.55 (0.98) 1.54 (1.10)

S5. How severe is your hip stiffness after sitting, lying or resting later in the day? 2.39 (1.06) 1.55 (1.09)

P1. How often is your hip painful? 3.17 (0.77) 1.42 (1.47)

P2. Straightening your hip fully 1.86 (1.10) 0.82 (0.95)

P3. Bending your hip fully 2.21 (1.16) 1.03 (1.02)

P4. Walking on flat surface 2.01 (1.03) 0.73 (0.99)

P5. Going up or down stairs 2.35 (1.09) 1.02 (1.10)

P6. At night while in bed 2.14 (1.14) 0.88 (1.10)

P7. Sitting or lying 1.91 (1.06) 0.70 (0.94)

P8. Standing upright 1.78 (1.06) 0.59 (0.87)

P9. Walking on a hard surface (asphalt, concrete, etc) 2.10 (1.02) 0.77 (0.98)

P10. Walking on an uneven surface 2.60 (1.03) 1.18 (1.09)

Al. Descending stairs 1.88 (1.08) 0.73 (0.97)

A2. Ascending stairs 2.24 (1.13) 0.95 (1.05)

A3. Rising from sitting 2.40 (1.03) 1.19 (1.10)

A4. Standing 1.94 (1.06) 0.69 (0.96)

A5. Bending to floor/pick up an object 2.39 (1.14) 0.98 (1.03)

A6. Walking on flat surface 1.95 (1.02) 0.68 (0.96)

A7. Getting in/out of car 2.67 (0.98) 1.19 (1.03)

A8. Going shopping 2.48 (1.10) 1.11 (1.12)

A9. Putting on socks/stockings 2.51 (1.16) 1.14 (1.04)

A10. Rising from bed 2.10 (1.06) 0.88 (0.97)

A11. Taking off socks/stockings 2.33 (1.17) 0.99 (0.99)

A12. Lying in bed (turning over, maintaining hip position) 1.96 (1.14) 0.68 (1.00)

A13. Getting in/out of bath 1.59 (1.07) 0.47 (0.81)

A14. Sitting 1.64 (1.04) 0.50 (0.83)

A15. Getting on/off toilet 1.94 (1.10) 0.78 (0.91)

A16. Heavy domestic duties (moving heavy boxes, scrubbing floors, etc) 2.66 (1.14) 1.54 (1.19)

A17. Light domestic duties (cooking, dusting, etc) 1.57 (0.99) 0.59 (0.84)

SP1. Squatting 2.72 (1.20) 1.77 (1.26)

SP2. Running 3.12 (1.11) 2.18 (1.38)

SP3. Twisting/pivoting on your injured knee 2.86 (1.10) 1.42 (1.26)

SP4. Walking on uneven surface 2.60 (1.08) 1.26 (1.15)

Q1. How often are you aware of your hip problem? 3.41 (0.58) 2.43 (1.29)

Q2. Have you modified your life style to avoid potentially damaging activities to your hip? 2.80 (1.14) 1.77 (1.41)

Q3. How much are you troubled with lack of confidence in your hip? 1.53 (1.51) 2.24 (1.54)

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Table A.2: The questions included in the HOOS and two short-forms

Questions in HOOS Included in HOOS-PS

Included in HOOS, JR S1. Do you feel grinding, hear clicking or any other type of noise from you hip?

S2. Difficulties spreading legs wide apart S3. Difficulties to stride out when walking

S4. How severe is your hip joint stiffness after first wakening in the morning? S5. How severe is your hip stiffness after sitting, lying or resting later in the day? P1. How often is your hip painful?

P2. Straightening your hip fully P3. Bending your hip fully P4. Walking on flat surface

P5. Going up or down stairs x P6. At night while in bed

P7. Sitting or lying P8. Standing upright

P9. Walking on a hard surface (asphalt, concrete, etc)

P10. Walking on an uneven surface x Al. Descending stairs x

A2. Ascending stairs

A3. Rising from sitting x A4. Standing

A5. Bending to floor/pick up an object x A6. Walking on flat surface

A7. Getting in/out of car A8. Going shopping

A9. Putting on socks/stockings A10. Rising from bed

A11. Taking off socks/stockings

A12. Lying in bed (turning over, maintaining hip position) x A13. Getting in/out of bath x

A14. Sitting x x

A15. Getting on/off toilet

A16. Heavy domestic duties (moving heavy boxes, scrubbing floors, etc) A17. Light domestic duties (cooking, dusting, etc)

SP1. Squatting x

SP2. Running

SP3. Twisting/pivoting on your loaded leg x SP4. Walking on uneven surface

Q1. How often are you aware of your hip problem?

Q2. Have you modified your life style to avoid potentially damaging activities to your hip? Q3. How much are you troubled with lack of confidence in your hip?

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Table A.3: Pattern matrix of X29using PAF extraction of 3 factors Question Loadings on factor 1 Loadings on factor 2 Loadings on factor 3

P9. Walking on a hard surface (asphalt, concrete, etc) 1.03

P4. Walking on flat surface 1.00

P10. Walking on an uneven surface 0.95

A8. Going shopping 0.89

SP2. Running 0.65

P5. Going up or down stairs 0.59

A16. Heavy domestic duties (moving heavy boxes, scrubbing floors, etc) 0.59

A17. Light domestic duties (cooking, dusting, etc) 0.59

A4. Standing 0.55

SP3. Twisting/pivoting on your injured knee 0.52

S3. Difficulties to stride out when walking 0.47

P2. Straightening your hip fully 0.35

A9. Putting on socks/stockings 1.10

A11. Taking off socks/stockings 1.05

A5. Bending to floor/pick up an object 0.87

P3. Bending your hip fully 0.59

A15. Getting on/off toilet 0.55

A10. Rising from bed 0.54

A7. Getting in/out of car 0.53

SP1. Squatting 0.52

A3. Rising from sitting 0.43

S5. How severe is your hip stiffness after sitting, lying or resting later in the day? 0.37

A13. Getting in/out of bath 0.36

A12. Lying in bed (turning over, maintaining hip position) 0.99

P7. Sitting or lying 0.98

P6. At night while in bed 0.98

A14. Sitting 0.67

S4. How severe is your hip joint stiffness after first wakening in the morning?

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Table A.4: Differences in the factors proposed by PAF en ML 4-factor extraction

Principal Axis Factoring Maximum Likelihood Factor 1 Factor 1

A9. Putting on socks/stockings A3. Rising from sitting A11. Taking off socks/stockings A15. Getting on/off toilet A5. Bending to floor/pick up an object SP1. Squatting

A10. Rising from bed A16. Heavy domestic duties (moving heavy boxes, scrubbing floors, etc) P3. Bending your hip fully A10. Rising from bed

A7. Getting in/out of car S5. How severe is your hip stiffness after sitting, lying or resting later in the day? A15. Getting on/off toilet A17. Light domestic duties (cooking, dusting, etc)

Factor 2 S4. How severe is your hip joint stiffness after first wakening in the morning? P6. At night while in bed SP3. Twisting/pivoting on your injured knee

P7. Sitting or lying A7. Getting in/out of car A12. Lying in bed (turning over, maintaining hip position) SP2. Running

A14. Sitting A13. Getting in/out of bath Factor 3 A14. Sitting†

P9. Walking on a hard surface (asphalt, concrete, etc) P2. Straightening your hip fully P4. Walking on flat surface S3. Difficulties to stride out when walking P10. Walking on an uneven surface A4. Standing

A8. Going shopping Factor 2

A4. Standing P9. Walking on a hard surface (asphalt, concrete, etc) P5. Going up or down stairs P4. Walking on flat surface

A17. Light domestic duties (cooking, dusting, etc) P10. Walking on an uneven surface Factor 4 A8. Going shopping

SP2. Running P5. Going up or down stairs SP1. Squatting Factor 3

SP3. Twisting/pivoting on your injured knee P6. At night while in bed

A16. Heavy domestic duties (moving heavy boxes, scrubbing floors, etc) A12. Lying in bed (turning over, maintaining hip position) S3. Difficulties to stride out when walking P7. Sitting or lying

Remove A14. Sitting†

S4. How severe is your hip joint stiffness after first wakening in the morning? Factor 4

S5. How severe is your hip stiffness after sitting, lying or resting later in the day? A9. Putting on socks/stockings P1. How often is your hip painful? A11. Taking off socks/stockings P2. Straightening your hip fully A5. Bending to floor/pick up an object A3. Rising from sitting P3. Bending your hip fully A13. Getting in/out of bath Remove

P1. How often is your hip painful?

(37)

Table A.5: Item-reduction-process

1st set of reduction-criteria

Reduction criteria (all loadings <0.35; no cross-loadings)

for factor analysis

Question Items deleted

a priori

Duplicate items deleted based on mean scores

Items deleted as inter-item correlation low

1st factor analysis (29 items)

2nd factor analysis (24 items) S1. Do you feel grinding, hear clicking or any other type of noise from you hip? x

S2. Difficulties spreading legs wide apart x

S3. Difficulties to stride out when walking x

S4. How severe is your hip joint stiffness after first wakening in the morning? x S5. How severe is your hip stiffness after sitting, lying or resting later in the day? x

P1. How often is your hip painful? x

P2. Straightening your hip fully x

P3. Bending your hip fully P4. Walking on flat surface P5. Going up or down stairs P6. At night while in bed P7. Sitting or lying

P8. Standing upright x

P9. Walking on a hard surface (asphalt, concrete, etc) P10. Walking on an uneven surface

Al. Descending stairs x

A2. Ascending stairs x

A3. Rising from sitting x

A4. Standing

A5. Bending to floor/pick up an object

A6. Walking on flat surface x

A7. Getting in/out of car A8. Going shopping A9. Putting on socks/stockings A10. Rising from bed A11. Taking off socks/stockings

A12. Lying in bed (turning over, maintaining hip position)

A13. Getting in/out of bath x

A14. Sitting A15. Getting on/off toilet

A16. Heavy domestic duties (moving heavy boxes, scrubbing floors, etc) A17. Light domestic duties (cooking, dusting, etc)

SP1. Squatting SP2. Running

SP3. Twisting/pivoting on your injured knee

SP4. Walking on uneven surface x

Q1. How often are you aware of your hip problem? x Q2. Have you modified your life style to avoid potentially damaging activities to your hip? x Q3. How much are you troubled with lack of confidence in your hip? x Q4. In general, how much difficulty do you have with your hip? x

Assessing quality of life : reducing the items of a survey used for hip patients by item-reduction techniques

Bachelor Thesis