Data driven model of midportion achilles tendinopathy health created with factor analysis

Achilles tendinopathy is a common overuse injury in sports [1] and represents 1.5 visits per 1000 in physicians general practice [2]. Exercise interventions have shown partially satisfactory results when assessed by patient reported outcomes as there are large variations in response to treatment [3, 4]. Despite this, few studies have examined variables that may explain the variability in treatment response. Reasons for the variability have been proposed to be due to sex or physical activity levels [5]. To further improve the outcome in all patients with Achilles tendinopathy there is a need to fully describe the patient presentation to identify individuals who might need special considerations or alternative treatments.

To meet this need, a conceptual model of Achilles tendinopathy has been proposed [6], composed of multiple discrete domains. The classical symptoms of Achilles tendinopathy [7] are included in the model, as well as structural alterations [8‐11], and lower extremity functional deficits [12, 13]. There are good reasons to believe that the model domains are at least somewhat independent, meaning that changes in one domain (like decreased symptoms) do not necessitate that other domains (like tendon structure) have changed. It’s been shown that tendon structural alterations consistent with Achilles tendinopathy also occur in asymptomatic tendons [14]. Similarly, lower extremity functional deficits may persist after resolution of Achilles tendinopathy symptoms [15]. Taken together, these studies support a model structure of at least three domains.

A fourth and fifth potential domain may also exist. The fourth domain, included in the conceptual model of Silbernagel et al. [6], was the psychological effects of Achilles tendinopathy [16], whose relationship to physical symptoms or tendon structure is less investigated. The fifth potential domain is related to metabolic factors. Two recent reviews have indicated that hypercholesterolemia [17] and hyperglycemia [18] are risk factors for Achilles tendinopathy and there is evidence of a mechanistic link as hypercholesterolemia and hyperglycemia may affect tendon structure [19, 20]. Patients may present with varying levels of these metabolic variables, and this may be a domain of an Achilles tendinopathy model.

Finding which variables across the various domains are related to treatment success is like finding a needle in a haystack. A way to systematically select variables to further investigate is needed. Using factor analysis [21], the first step would be to test if the proposed model of Achilles tendon health is consistent with the data. The resulting factor structure would be the basis of an Achilles tendinopathy model, and a patient can be described along each of the factors of the model. The factor analysis can also identify variables best suited to describe each of the domains of the model. Those variables would then be considered as the primary candidates to test if they are associated with treatment success.

The aim of this study was therefore to use an existing dataset with a range of variables representing the potential domains to fit a model of Achilles tendinopathy health, in order to profile the presentation of Achilles tendinopathy. The analysis will identify which factors are present in the data, what variables are important for each factor, and whether the factors are independent (uncorrelated) of each other. We hypothesize that a model will emerge that is consistent with the conceptual model previously proposed [6], with factors representing symptoms, psychological symptoms, lower extremity function, and tendon structure. We also hypothesize that an additional factor, metabolic variables, will emerge. The impact would be identifying variables that can define the clinical presentation and quantify the domains identified.

A total of 154 subjects were screened for inclusion in the ongoing trial, out of which 99 participants met the inclusion criteria. Inclusion criteria were age between 18 and 65 and a clinical diagnosis of midportion Achilles tendinopathy [23] made by study clinicians based on a history of pain with loading and tenderness to palpation [7]. Pain with loading refers to any pain or discomfort in the Achilles tendon during activities which involve any of the movements known to load the Achilles tendon [24], such as running, jumping, or other weight bearing plantarflexion activities. Subjects were excluded if they had a history of total Achilles tendon rupture, were currently receiving other treatments, were unable to perform the exercises due to other impairments, or if the source of pain was determined to be only insertional tendinopathy or bursitis. An ultrasound examination was available to clinicians to help make that determination. Subjects were not excluded if they had additional pathology such as bursitis if midportion Achilles tendinopathy was the main diagnosis. Subject characteristics are reported consistent with recommendations from a recent consensus statement [25] in Table 1.

Study data were collected and managed using REDCap electronic data capture tools hosted at the University of Delaware [38, 39]. REDCap (Research Electronic Data Capture) is a secure, web-based software platform designed to support data capture for research studies, providing 1) an intuitive interface for validated data capture; 2) audit trails for tracking data manipulation and export procedures; 3) automated export procedures for seamless data downloads to common statistical packages; and 4) procedures for data integration and interoperability with external sources.

A Kaiser-Mayer-Olkin index (KMO) [40] was used to assess whether the data set was suitable for a factor analysis and to select which variables were suitable for the exploratory factor analysis. Variables were stepwise excluded according to the lowest measure of sampling adequacy until a threshold of at least 0.6 was achieved for the remaining data set. Each excluded variable then entered a second KMO analysis step and included if the measure of sampling adequacy for the data set remained above 0.6. A “mediocre” [41] threshold for the measure of sampling adequacy was chosen due to the low number of observations available, and to include the maximum number of variables. All observations with a missing value for at least one variable were excluded from the analysis. This means that the final number of subjects is influenced by the results of the KMO analysis such that subjects with missing data are included in the analysis only if the variables for which data is missing is excluded from the analysis in the KMO analysis.

A mix of continuous, binary, and ordinal data entered the KMO analysis. A mixed correlation matrix was therefore calculated [42]. However, after the KMO analysis, all remaining variables were suitable for a regular correlation matrix which was calculated for the factor analysis.

To test if the data could be reduced to fewer variables with a factor analysis, we used the Bartlett´s test of sphericity [43]. The Bartlett´s test of sphericity tests if a correlation matrix is different from an identity matrix (all correlations equal to zero). A significance of 0.05 was used for the Bartlett´s test of sphericity.

A parallel analysis was used to determine the number of factors extracted using eigenvalues > 1 as the criteria. The exploratory factor analysis was performed using maximum likelihood method and the “oblimin” rotation. The model fit of the results were expressed as the standardized root mean square of the residuals (SRMS). The SRMS is a measure of model misfit (the difference between the suggested model, and the data) where lower numbers indicate a better fit. The SRMS performs well for models with few observations and many variables [44]. For similar conditions as the current study, a cut-off of 0.09 (where models with SRMS above 0.09 are rejected) for the SRMR minimized the combined risk of Type I and Type II errors in a simulation study [45]. An SRMR score below 0.09 will be described as acceptable for this study. All data processing was performed using the data.table package [46] for the R statistical language [47]. The factor analysis was performed with the psych package [42].

The ideal results from a factor analysis are interpretable results. There is currently no consensus for determining an appropriate loading cut-off to include a variable within a factor when interpreting the results. As we used variables that were not specifically designed to represent a latent factor, a loading cut-off of 0.3 was deemed appropriate to assign a variable to a factor. After the factor analysis, each factor was labeled according to our interpretation of the commonalities of the included variables.

Variables excluded based on the KMO score were presence of calcifications, bursitis, insertional symptoms, pressure pain threshold (both Achilles and medial Gastrocnemius muscle), having bilateral symptoms, neovascularization, skin autofluorescence, previous tendon injuries, sex, use of statin medications, previous diagnosis of hypertension, resting angle with knee extended, and thickness of a healthy tendon portion. After excluding variables, the overall measure of sampling adequacy was 0.64. The Bartlett´s test of sphericity indicated that a factor analysis could be carried out with p < 0.00001. The parallel analysis supported extracting 5 factors with Eigenvalues of 6.1, 5.2, 2.9, 2.6 and 1.5.

The five-factor model generated by the factor analysis with the researcher assigned labels is summarized in Fig. 1 and presented as an R readable file in Supplementary Information, Additional file 1 [2]. Factor loadings for each variable are reported in Tables 2, 3, 4,5 and 6 and summarized in Sect. 3.3. The variance explained by the factors were 0.14, 0.12, 0.10, 0.08, and 0.07 for factors 1:5 respectively. The cumulative variance explained was 0.51. The model fit was acceptable with an SRMS of 0.078. There were no correlations between any of the factors. Two variables that entered the analysis were not loaded into any factor (Table 7), thickness of the soleus muscle and tendon viscosity evaluated with cSWE.

The first factor was labelled as the biopsychosocial factor (Table 2, explained variance 0.14). The factor included the pain catastrophizing scale, the central sensitization index, all PROMIS subscales, the FAOS quality of life and sports subscales, TSK, the VISA-A, and the Achilles tendon resting angle with knee flexed.

The second factor was labelled as the lower extremity function factor (Table 3, explained variance 0.12). Included variables were height on all jumps and hopping measures, the heel-rise reps and heel rise work, subject age, height, length of Achilles tendon (gastrocnemius to calcaneus), resting heart rate and current physical activity level.

The third factor was labelled as body size (Table 4, explained variance 0.10). Included variables were weight, BMI, cross sectional area of both Gastrocnemius muscle heads, systolic blood pressure, pain during the heel-rises, and diastolic blood pressure. Secondary variables (variables that load above threshold, but load higher in another factor) were heel rise repetitions and height,

The fourth factor (Table 5, explained variance 0.08) was labelled as the load tolerance factor, and included pain reported during jump and hopping tests. The VISA-A was a secondary variable in load tolerance.

The fifth factor was labelled as the tendon structure factor (Table 6, explained variance 0.07). Included variables were thickness of the thickest portion of the tendon, tendon cross sectional area, length of Achilles tendon from soleus to calcaneus, and the tendon shear modulus. Secondary variables were age, length of the Achilles tendon from gastrocnemius to calcaneus and height.

This is the first study to create a statistical model of a suggested Achilles tendinopathy health model [6]. The primary hypothesis of a five-factor model structure was only partially supported. Out of the hypothesized factors, symptom severity, tendon structure and lower extremity function were distinguishable. The hypothesized psychological symptom factor did not emerge, and all psychological variables were included in symptom severity. The hypothesized metabolic variables factor did not emerge, however a factor representing body size which included diastolic and systolic blood pressure did. An unexpected factor, load tolerance, emerged. The secondary hypothesis was supported, as the factors were uncorrelated and therefore represent independent domains of tendon health.

The resulting model deviated in three important ways from the conceptual model. Firstly, there was no factor representing symptom severity, but this was replaced by the biopsychosocial factor. This factor was composed of the patient reported outcome measures and included all of the questionnaires administered in the study. The VISA-A loaded on the lower-end of this factor and was also included in the load tolerance factor. The VISA-A questionnaire has previously been reported to evaluate more than one factor which could explain why it was included in two factors. A sensitivity analysis was conducted with each VISA-A factor entering the analysis as separate variables, but the interpretability of the results was unchanged (see Supplementary Information, Additional file 3). A recent study has questioned the content and construct validity of the VISA-A that also exhibits differential item functioning (DIF) depending on the duration period of symptoms [48]. Our results show that the VISA-A may not be sufficient to evaluate the biopsychosocial domain. Unexpectedly, the pain catastrophizing scale was the highest loading variable on the biopsychosocial factor. Pain catastrophizing has not previously been described as important in this patient population, however a recent study has concluded that a sub-group of patients with Achilles tendinopathy can be described as ‘psychosocial-dominant’ – identified as having the worst symptoms and highest degree of psychological effects but minimal tendon structure changes [49]. Pain catastrophizing may be very important in this subgroup which would explain the high loading for pain catastrophizing on the factor.

Secondly, no factor emerged for metabolic variables, potentially since no direct measure was included for hyperglycemia or hypercholesterolemia. Body size emerged instead, with BMI, weight, blood pressure and calf muscle cross-sectional area. Considering that BMI is an important metabolic variable, and that blood pressure loaded on this factor as well it can certainly be argued that the factor of metabolic variables still emerged. However, since weight loaded higher than BMI and gastrocnemius muscle CSA higher than blood pressure, we considered the label body size to be a better fit. There are good reasons to think that hypercholesterolemia [17, 50] and hyperglycemia [18] are clinically relevant for Achilles tendinopathy. While the healthy Achilles tendon undergoes virtually no remodeling after skeletal maturity [51], symptomatic Achilles tendinopathy has likely undergone much more collagen turnover [52]. In the remodeling period the tendinopathic Achilles tendon may accumulate advanced glycation end-products which impact tissue remodeling [53]. Skin autofluorescence, as a proxy for tendon autofluorescence, could in theory have loaded on either tendon structure or with metabolic variables. Similarly, hypercholesterolemia can result in accumulation of xanthomas in the Achilles tendon [19] which could affect measures of tendon structure. However, neither skin autofluorescence nor statin medication use entered the factor analysis. Blood pressure was the only variable that entered the factor analysis out of those selected as potential metabolic variables. The relationship between BMI and blood pressure is well documented [54], and blood pressure therefore fits well in a body size factor. However, blood pressure can also be an indicator for other metabolic variables [55]. It may be that more direct measures are required. Serum cholesterol and glycated hemoglobin may be sufficient for the metabolic variables factor to emerge, but direct measures of tendon metabolic variables (such as tendon glycation) are difficult to measure.

Thirdly, the factor of load tolerance was not expected to emerge from the analysis, but pain with loading is a hallmark of Achilles tendinopathy and was expected to be part of a symptoms factor. A recent study suggested that pain with loading is independent from VISA-A scores [56], and our results expand on that result by establishing pain with loading as an independent factor of the clinical presentation. Pain on the 20 consecutive hops test was the highest loading variable on this factor. The 20 consecutive hops test challenges the ability of the Achilles tendon to withstand repeated high loads and has been reported as the loading test that best differentiates subjects with Achilles tendinopathy from controls [12].

Our results show that clinicians can evaluate some facet of the five factors in the model to form a holistic assessment of the presentation of Achilles tendinopathy. A recommendation is made below based on the factor loadings from our results, but the precision of estimates for factor loading is likely poor. The clinician should therefore use their best judgement for what specific variables to use to represent the factors.

To evaluate the biopsychosocial aspect, our results support the use of the PROMIS subscales which have been validated for various chronic conditions [57]. For specific subscales, the highest loadings were for the ability to participate in social roles and activities, pain, and anxiety subscales. For lower extremity function, we recommend the single-leg counter-movement jump as a general measure. The single-leg drop counter-movement jump had slightly higher loading but has a lower completion rate limiting its usefulness for patients with lower functional capacity. The heel-rise test may be more desirable for patients who are unable to jump. As the difference in factor loadings between the three tests are small, the appropriate test can be chosen for each individual subject.

For load tolerance, pain from the hopping test was the best variable. To evaluate the tendon structure, the best variable is tendon cross-sectional area measured with ultrasound. To evaluate body size, weight had the highest loading, but BMI is perhaps more useful and therefore the best variable. Higher BMI may require greater adjustment of daily activities, as heel rise pain was also loaded on body size and heel rises are close in intensity to that of daily activities.

This study has several limitations to consider. An important limitation is that of sample size. A popular rule of thumb for the number of observations per variable in the factor analysis is 10:1, which would require 420 subjects in the analysis. However, such rules of thumb are without empirical support. A simulation study has been performed to analyze the required sample sizes under various ratios of observations, factors, and variables [58]. It was found that under the conditions closest to our study (5 factors, 30 variables, 90 subjects and wide communalities [58]), the per element accuracy was 96%, indicating that the majority of the variables under these simulation conditions were factored correctly. The ratio of variables to factors was higher in our study, which increases accuracy, but the ratio of observations to variables was lower which decreases accuracy.

The model fit was adequate as determined by the SRMS of 0.078. While below the 0.09 cut-off suggested to minimize the error rate [45], it is challenging to determine if the results are precise enough to rule out a deviation which would significantly change the interpretation of the results. Variables which load on more than one factor increase the model misfit as evaluated by the SRMS. In a sensitivity analysis, we repeated the factor analysis except variables that load on more than one value were excluded (age, height, length of Achilles tendon to gastrocnemius, and the heel rise repetitions). The SRMS value for this model was 0.058—indicating closer fit to the data (see Supplementary Information, Additional file 2). However, the interpretation of the results, and the labelling of the factors, remained unchanged.

The final number of subjects included in the factor analysis was 74. It’s been shown that even with small sample sizes, the factor structure of data can still be extracted [59]. The imprecision due to a smaller sample size in this study is likely to be in the estimations of individual variable loadings on the factors rather than in the factor structure. As the main purpose of this study was to identify the factor structure rather than the precise variable loadings, the sample size used is likely adequate.

Factor analysis results are sensitive to the variables input into them, and the choice to include or omit a variable has implications for the results. This was addressed using the KMO score for variable selection with the intent of making the results less subjective and more repeatable.

There may be additional factors we could not identify such as the metabolic factor. As an inherently exploratory approach, this study may be considered the first step towards creating a robust model. As with all exploratory analyses in science, results should be taken with a grain of salt until they are replicated. The ideal replication is a primary study with sufficient statistical power, but this approach is unlikely to be performed due to the expensive and time consuming data collection required. As an alternative to a study with hundreds of participants, a more practical approach would be to replicate the analysis with existing data from other clinical trials.

The study population in the current study is mixed. This is both a strength and a weakness. Many studies in Achilles tendinopathy focus on athletes or other individuals with high physical activity levels. However, a significant portion of people with Achilles tendinopathy do not fit the classical athletic overuse model. Our results should rather be generalized to the older person with more comorbidities rather than the younger athlete with Achilles tendinopathy. Many of our subjects have only experienced symptoms for a relatively short time and can be considered as more of an acute presentation. However, it’s likely that the pathological processes of tendinopathy precede the onset of symptoms by as much as several years [52]. The duration of symptoms is therefore perhaps not be very useful but this is none the less a potential limitation.