Supplemental Materials Table of Contents
Supplemental Table 1. Performance indices for a range of k values used to define the optimal number of clusters in the semi-supervised clustering algorithm (N=3549 biopsies of the training cohort).
Supplemental Table 2. Details of the individual Banff lesions scores of the training cohort according to the chronic clusters (N=3549).
Supplemental Table 3. Demographic, clinical, and histological characteristics of the patients and biopsies included in the validation cohort.
Supplemental Figure 1. Density distribution of time post transplantation of the biopsies in the training cohort (N=3549), per cluster.
Supplemental Figure 2. Association between graft failure and biopsy clustering based solely on the time post-transplant variable, irrespective of the lesion scores, for various k (N=3549 biopsies of the training cohort).
Supplemental Figure 3. Results for the semi-supervised consensus clustering for k=3 on the training cohort (N= 3549 biopsies).
Supplemental Figure 4. Distribution of the individual acute lesion scores in the different chronic clusters, and post-biopsy Kaplan-Meier graft survival curves relative to cluster 1 of the training cohort (N=3549 biopsies).
Supplemental Figure 5. Distribution of total chronicity scores per cluster (N=3549 biopsies of the training cohort).
Supplemental Figure 6. Various combinations of lesion scores and year post-transplant displayed on the polar plots (N=3549 biopsies of the training cohort).
Supplemental Figure 7. Unsupervised dimensionality reduction with Principal Component Analysis (N=3549 biopsies of the training cohort).
Supplemental Figure 8. The acute rejection clusters and IFTA grades on the chronic polar plot (N=3549 biopsies of the training cohort).
Supplemental Figure 9. Distribution of the chronic lesions scores among the IFTA categories (N=3549 biopsies of the training cohort).
Supplemental Figure 10 The association of the IFTA phenotypes and graft failure.
Supplemental Figure 11 Comparison of the proportion of clusters in the biopsies of the training (N=3549) and the validation (N=4031) sets.
Supplemental Figure 12. Association of the polar plot radius with graft survival in the validation cohort (N=4031 biopsies).
Python code for semi-supervised consensus clustering.
Supplemental Table 1. Performance indices for a range of k values used to define the optimal number of clusters in the semi-supervised clustering algorithm (N=3549 biopsies of the training cohort).
Performance index K=3 k=4 k=5 k=6 k=7
Unsupervised clustering (unweighted lesion scores)
Proportion of Ambiguous Clustering (PAC) 0.060 0.191 0.239 0.196 0.40
7 Log-rank p-value between best and 2nd best survival cluster 0.0003 0.004
9
0.004 0.593 0.34 2
Highest log-rank p-value 0.0003 0.931 0.861 0.593 0.76
5
Minimal distance between centroids* 0.861 0.489 0.487 0.442 0.53
1 Semi-supervised clustering (weighted lesion scores)
Proportion of Ambiguous Clustering (PAC) 0.016 0.014 0.198 0.233 0.22
4 Log-rank p-value between best and 2nd best survival cluster 0.0063 0.094 0.630 0.726 0.70
3
Highest log-rank p-value 0.0063 0.094 0.630 0.726 0.70
3
Minimal distance between centroids* 0.889 0.509 0.449 0.501 0.48
3
*Minimal distance in scaled lesions space
Supplemental Table 2. Details of the individual Banff lesions scores of the training cohort according to the chronic clusters (N=3549).
Banff lesion Lesion
score
CLUST ER 1 (N=28
76)
Cluste r 2 (n=42
0)
Cluste r 3 (n=19
5)
Cluste r 4 (n=58
) GLOMERULAR BASEMENT
MEMBRANE DOUBLE CONTOURS, CG
0 98.5% 97.9% 97.4% 0.0%
1 1.3% 2.1% 2.1% 20.7%
2 0.1% 0.0% 0.5% 31.0%
3 0.1% 0.0% 0.0% 48.3%
Average
score 0.02 0.02 0.03 2.28
INTERSTITIAL FIBROSIS, CI
0 63.4% 0.0% 0.0% 6.9%
1 34.9% 0.5% 0.0% 50.0%
2 1.7% 69.3% 20.0% 24.1%
3 0.0% 30.2% 80.0% 19.0%
Average
score 0.38 2.30 2.80 1.55
TUBULAR ATROPHY, CT
0 29.2% 1.9% 0.0% 3.4%
1 70.3% 35.7% 1.0% 72.4%
2 0.5% 59.0% 34.4% 17.2%
3 0.0% 3.3% 64.6% 6.9%
Average
score 0.71 1.64 2.64 1.28 VASCULAR FIBROUS
INTIMAL THICKENING, CV
0 51.8% 36.4% 21.0% 34.5%
1 32.2% 35.7% 30.3% 41.4%
2 15.0% 25.5% 40.0% 22.4%
3 1.0% 2.4% 8.7% 1.7%
Average
score 0.65 0.94 1.36 0.91 MESANGIAL MATRIX
EXPANSION, MM
0 92.8% 89.8% 89.2% 43.1%
1 5.7% 6.9% 8.2% 24.1%
2 1.3% 2.9% 2.1% 13.8%
3 0.2% 0.5% 0.5% 19.0%
Average
score 0.09 0.14 0.14 1.09 ARTERIOLAR HYALINOSIS,
AH
0 66.7% 61.7% 27.2% 39.7%
1 24.4% 29.0% 24.6% 22.4%
2 8.4% 8.8% 40.0% 27.6%
3 0.5% 0.5% 8.2% 10.3%
Average
score 0.43 0.48 1.29 1.09
Glomerulosclerosis, gs
0 84.0% 66.2% 45.1% 62.1%
1 12.5% 22.6% 25.1% 32.8%
2 3.1% 8.8% 17.4% 3.4%
3 0.3% 2.4% 12.3% 1.7%
Average
score 0.20 0.47 0.97 0.45
Supplemental Table 3. Demographic, clinical and histological characteristics of the patients and biopsies included in the validation cohort. eGFR: estimated glomerular filtration rate, SD: standard deviation.
Cohort characteristics
Total N=2054
Donor type (%)
Donation after Brain Death 1531 (74.5)
Donation after Cardiac Death 100 (4.9)
Living Donation 423 (20.6)
Age in years– mean (SD) 54.5 (17.1)
Sex - Male (%) 1088 (53.0)
Recipient demographics
Age in years – mean (SD) 50.9 (14.8)
Sex – male (%) 1280 (62.3)
Body-mass index (kg/m2) – mean (SD) 24.2 (4.4)
Repeat transplantation (%) 285 (13.9)
Cold ischemic time (h) –mean (SD) 14.9 (10.5) Mismatch total (A+B+DR) mean (SD) 3.4 (1.4) Biopsy characteristics
Total N=4031
Interstitial fibrosis – tubular atrophy (IFTA)
IFTA 0, N (%) 1518 (37.7)
IFTA 1, N (%) 1376 (34.1)
IFTA 2, N (%) 785 (19.5)
IFTA 3, N (%) 352 (8.7)
Indication biopsies, N (%) N=1467
(36.4) Days since transplantation, median (interquartile
range) 189 (48-599)
eGFR at day of biopsy, mean (SD) 36.9 (17.8)
Protocol biopsies, N (%) N=2564
(63.6) Days since transplant –median (interquartile
range)
159 (94-374) eGFR at day of biopsy –mean (SD) 54.9 (22.0)
Supplemental Figure 1. Density distribution of time post transplantation of the biopsies in the training cohort (N=3549), per cluster.
Supplemental Figure 2. Association between graft failure and biopsy clustering based solely on the time post-transplant variable, irrespective of the lesion scores, for various k (N=3549 biopsies of the training cohort).
Supplemental Figure 3. Results for the semi-supervised consensus clustering for k=3 on the training cohort (N= 3549 biopsies). These plots display the distribution of the individual chronic lesion scores in the three clusters, and the corresponding post-biopsy Kaplan-Meier graft survival curves relative to cluster 1. cg = glomerular basement membrane double contours, ci= interstitial fibrosis, ct= tubular atrophy, cv= vascular fibrous Intimal thickening, mm= mesangial matrix expansion, ah= arteriolar hyalinosis, gs= glomerulosclerosis.
Supplemental Figure 4. Distribution of the individual acute lesion scores in the different chronic clusters, and post-biopsy Kaplan-Meier graft survival curves relative to cluster 1 of the training cohort (N=3549 biopsies). t=tubulitis, i=interstitial inflammation, g= glomerulitis, v=intimal arteritis, C4d_ptc=C4d deposition in peritubular capillaries, ptc=peritubular capillaritis, thrombi=thrombotic microangiopathy, DSA= donor specific anti-HLA antibodies.
Supplemental Figure 5. Distribution of total chronicity scores per cluster (N=3549 biopsies of the training cohort). This plot represents the density distribution of the radius from the polar plot, stratified per cluster.
Supplemental Figure 6. Various combinations of lesions scores and year post-transplant displayed on the polar plots (N=3549 biopsies of the training cohort). A. Sum of the glomerular basement membrane double contours (cg) and mesangial matrix expansion (mm) scores. B. Sum of the tubular atrophy (ct) and interstitial fibrosis (ci) scores. C. Year post-transplant. The chronic clusters are displayed on plot D. for comparison purposes
Supplemental Figure 7. Unsupervised dimensionality reduction with Principal Component Analysis (N=3549 biopsies of the training cohort).
2-dimensional PCA stratifies the set of Banff lesions into two sets of lesions almost orthogonal to each other. ah= arteriolar hyalinosis, C4d_ptc=C4d deposition in peritubular capillaries, cg = glomerular basement membrane double contours, ci= interstitial fibrosis, ct= tubular atrophy, cv= vascular fibrous Intimal thickening, DSA= donor specific anti-HLA antibodies, g= glomerulitis, gs= glomerulosclerosis, i=interstitial inflammation, mm= mesangial matrix expansion, ptc=peritubular capillaritis, t=tubulitis, thrombi=thrombotic microangiopathy, v=intimal arteritis.
Supplemental Figure 8 The acute rejection clusters and IFTA grades on the chronic polar plot (N=3549 biopsies of the training cohort). The acute rejection clusters are obtained from Vaulet et al.12
IFTA: Interstitial fibrosis – tubular atrophy
Supplemental Figure 9. Distribution of the chronic lesions scores among the IFTA categories (N=3549 biopsies of the training cohort).
IFTA: Interstitial fibrosis – tubular atrophy
cg = glomerular basement membrane double contours, ci= interstitial fibrosis, ct= tubular atrophy, cv=
vascular fibrous Intimal thickening, mm= mesangial matrix expansion, ah= arteriolar hyalinosis, gs=
glomerulosclerosis. P-values refer to HR from the Cox models.
Supplemental Figure 10 The association of the IFTA phenotypes and graft failure in the training cohort.
IFTA: Interstitial fibrosis – tubular atrophy
Supplemental Figure 11 Comparison of the proportion of clusters in the biopsies of the training (N=3549) and the validation (N=4031) sets.
Supplemental Figure 12. Association of the polar plot radius with graft survival in the validation cohort (N=4031 biopsies). The biopsies were stratified along the radius axis in the same four strata as in the training cohort (Fig 2B). The corresponding Kaplan-Meier survival curves are plotted on the right. Similarly to the training cohort, the total chronicity (as the sum of the reweighted chronic lesions scores, scaled to the unit interval from 0 to 1), represented by the radius of the polar plot, is also positively associated with the risk of graft failure in the validation cohort. The total chronicity score was discretized into 4 different levels of chronicity, corresponding to the following radiuses : “Minimal” : radius <= 0.3; “Moderate”: radius 0.31 – 0.5 ; “Severe” : radius 0.51 – 0.60; and “Very severe”: radius > 0.6.
