180 Chapter 7 Statistical analyses The cfDNA concentration was expressed in ng/mL urine and transformed using an inverse hyperbolic sine function to enhance normality of the data. The methylation levels of the target genes were normalized according to the Ct value of the reference gene ACTB 2-(Ct marker – Ct ACTB) x 100 to obtain Ct ratios, and square root transformed. Linear mixed-effects models were fitted separately for the repeated measurements of cfDNA concentration and methylation levels of each marker. Linear mixed-effects models contain both fixed (i.e. constant across the population) and random (i.e. varying per individual) effects, enabling estimation of both between- and within-subject variation (30). Models incorporated a random intercept for each patient to account for withinpatient correlation and included explanatory variables day (i.e. day 1 and day 2) and part of the day (i.e. morning, afternoon, and evening) as fixed effects. Models were estimated using restricted maximum likelihood (REML). Additional patient characteristics (i.e. sex, age, weight, therapy during study, survival, and histological subtype) were considered for inclusion as fixed effects by backward stepwise selection (p ≥ 0.05 for removal). Tobacco use could not be included as fixed effect due to missing data. Final models are available in the Supplementary material. The assumptions of linearity, normality of the residuals and random effects, and homoscedasticity (i.e. constant variance of the residuals) were checked visually using diagnostic plots (31). Differences in cfDNA concentration and methylation levels during the day and between the two days were evaluated by Type II Wald Chi-square tests. Model estimates and corresponding 95%-confidence intervals (CI), between-subject variances (σ2), withinsubject variances (τ00 subject), and intraclass correlation coefficients (ICC) were tabulated for both the cfDNA concentration and methylation levels of CDO1, SOX17, and TAC1. The ICC indicates the resemblance of repeated measurements and describes the proportion of between-subject variability with respect to the total variability (between plus within). The ICC can range from zero to one, with zero indicating a poor reproducibility and one indicating a perfect reproducibility (32). Differences in time were displayed in boxplots, demonstrating the cfDNA concentrations and methylation marker levels measured between the different days and time points at a group level. Between- and within-subject differences were visualized by conditional scatterplots, showing the cfDNA concentrations and methylation marker levels measured at each time point for each patient individually, stratified for sex. The added value of collecting multiple urine samples was determined by 1) comparing the methylation levels measured in the urine of patients (n=23) and controls (n=60),
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