Non-parametric distributions were calculated using the Kruskal–Wallis rank sum test (multiple groups) and the Wilcoxon rank sum test (two groups). A p value < 0.05 was considered significant. Pearson's product-moment correlation and Spearman's rank correlation were used to measure relationships between different variables. A receiver operating characteristic curve (ROC) analysis was performed and the associated area under the curve (AUC) values were calculated to evaluate how well dd-cfDNA (cp/mL) and dd-cfDNA fraction (%) discriminated between rejection group and other groups. All statistical analyses were performed using R and IBM SPSS Statistics (v.19).

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