Statistical analysis

In all but study III, statistical analyses were conducted using SPPS software (IBM SPSS Statistics for Windows, Version 21.0. Armonk, NY: IBM Corp.). In study III, analyses were performed using R Software, version 3 (R Foundation, Vienna, Austria). In all studies, mean values with standard deviation (SD) were reported for normally distributed variables and medians with range and/or interquartile range (IQR) for variables with skewed distribution. Differences between non-normally distributed variables were compared using Mann-Whitney U-test. In all studies, p-values of <0.05 were considered statistically significant.

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In studies I and II, Spearman rank correlation was used to study the associations between different variables due to non-normal distribution of these variables. When analyzing the correlation between WB metal ion concentrations and other factors, we only included patients with unilateral hip arthroplasties to avoid the confounding effect of metal ions being released to the blood from the other implant.

In study III, two different cluster-based segmentation methods were used to detect the underlying latent groupings of cases. Latent class analysis (LCA) and cluster analysis with hierarchical approach (HCA) were used (Beckstead 2002, Schreiber 2017). Clusters of cases were then mapped against a recent consensus statement of joint-related histopathological classification (Krenn et al. 2014).

Between-group differences in clinical variables after HCA were compared using either Kruskal–Wallis test or chi-square test.

In HCA, our main interest was to find clusters of cases (hips) based on their dissimilarity. Since our data comprised binary and ordinal variables, we chose the Gower method to form the distance matrix (Gower 1971). After the selection of the appropriate dissimilarity measurement, clustering began by assigning each case to be an individual cluster forming a proximity matrix sized 284 columns × 284 rows. The matrix reflected the closeness of each cluster. Each case began as an individual cluster and was gradually merged with the most closely related cluster (of cases). We used the complete linkage method. This process was repeated until one single cluster remained. Our aim was to identify any meaningful and histologically relevant clusters. Hence, we did not use solely the agglomerative approach, which is the most commonly used method, to establish the optimal number of clusters.

The agglomerative process uses the agglomeration schedule in which the change in agglomeration coefficient is depicted as the distance between merged clusters. The higher the change in the agglomeration coefficient, the higher is the dissimilarity between clusters. We interpreted the last stages of the clustering process to define the meaningful clusters of observations as five or less clusters were expected to be seen. “Natural break” was defined as the largest change in agglomeration coefficient producing meaningfully distinguishable clusters.

In addition to HCA, LCA was also performed to further analyze the possible underlying structures in our data set. LCA also aims to identify meaningful groups or class memberships of cases according to their (dis)similarity. To identify the optimal set of groups, LCA was first performed with two groups, then three groups, and so on. Akaikes Information Criterion (AIC) indices were interpreted to assess the most suitable baseline model. By using cluster analysis with LCA, we

aimed to have both the optimal model suggested by the indices and a meaningful set of groups so that each group could be readily labeled.

We further aimed to validate our primary outcome after cluster analysis and LCA by first running a validation analysis using both techniques and then separately for both implant groups. The rationale for this was the different wear behaviors between stemmed THAs and hip resurfacings. Bearing wear is seen in both implants, but taper corrosion is only seen in THA. If our segmentation techniques are robust against one major etiological factor, similar clusters and class memberships should be produced regardless of the implant type included in the analysis. Each cluster formed by validation clustering was matched against primary clusters. The distribution of cases among clusters obtained from validation cluster analysis was cross-tabulated against primary clustering to see whether discordant cases, that is, negative matches among two different clustering processes, existed.

Validation LCA was performed in an equal way using the same principle as with the study cohort (all cases included).

In study IV, the statistical significance of the difference in wear volume between the higher and lower wearing side was tested using Wilcoxon signed ranks test (related samples). Mann-Whitney U-test was used to test the difference in wear volume distribution between the hips in patients with symmetric versus asymmetric histological and imaging findings (independent samples). The differences in histological findings between left and right hips were compared and the number of patients with identical findings, patients with a difference of one point and a difference of two points between the sides were calculated. The statistical significance of the difference in histological findings between the sides was tested with marginal homogeneity test except for the difference in presence of germinal centers, which did not fill the test requirements, and the McNemar test was used instead (Bonnini et al. 2014). Whether the presence of MRI-confirmed pseudotumor was similar between left and right sides was tested using McNemar test (related samples).

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