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Discovery and Validation of a Molecular Signature for the Noninvasive Diagnosis of Human Renal Allograft Fibrosis

Anglicheau, Dany1,2; Muthukumar, Thangamani1,3,4; Hummel, Aurélie5; Ding, Ruchuang3; Sharma, Vijay K.3; Dadhania, Darshana3,4; Seshan, Surya V.6; Schwartz, Joseph E.1,3,7; Suthanthiran, Manikkam1,3,4,8

doi: 10.1097/TP.0b013e31824ef181
Clinical and Translational Research
Free
SDC

Background Tubulointerstitial fibrosis (fibrosis), a histologic feature associated with a failing kidney allograft, is diagnosed using the invasive allograft biopsy. A noninvasive diagnostic test for fibrosis may help improve allograft outcome.

Methods We obtained 114 urine specimens from 114 renal allograft recipients: 48 from 48 recipients with fibrosis in their biopsy results and 66 from 66 recipients with normal biopsy results. Levels of messenger RNAs (mRNAs) in urinary cells were measured using kinetic, quantitative polymerase chain reaction assays, and the levels were related to allograft diagnosis. A discovery set of 76 recipients (32 with allograft fibrosis and 44 with normal biopsy results) was used to develop a diagnostic signature, and an independent validation set of 38 recipients (16 with allograft fibrosis and 22 with normal biopsy results) was used to validate the signature.

Results In the discovery set, urinary cell levels of the following mRNAs were significantly associated with the presence of allograft fibrosis: vimentin (P<0.0001, logistic regression model), hepatocyte growth factor (P<0.0001), α–smooth muscle actin (P<0.0001), fibronectin 1 (P<0.0001), perforin (P=0.0002), plasminogen activator inhibitor 1 (P=0.0002), transforming growth factor β1 (P=0.0004), tissue inhibitor of metalloproteinase 1 (P=0.0009), granzyme B (P=0.0009), fibroblast-specific protein 1 (P=0.006), CD103 (P=0.02), and collagen 1A1 (P=0.04). A four-gene model composed of the levels of mRNA for vimentin, NKCC2, and E-cadherin and of 18S ribosomal RNA provided the most accurate, parsimonious diagnostic model of allograft fibrosis with a sensitivity of 93.8% and a specificity of 84.1% (P<0.0001). In the independent validation set, this same model predicted the presence of allograft fibrosis with a sensitivity of 77.3% and a specificity of 87.5% (P<0.0001).

Conclusions Measurement of mRNAs in urinary cells may offer a noninvasive means of diagnosing fibrosis in human renal allografts.

Supplemental digital content is available in the text.

1 DA and TM are co-first authors and JES and MS are co-senior authors of this article.

2 Currently, Department of Kidney Transplantation, Necker Hospital, Assistance Publique Hôpitaux de Paris (APHP), Université Paris Descartes Sorbonne Paris Cité; and Institut National de la Santé et de la Recherche Médicale (INSERM) Unité Mixte de Recherche (UMR-S775), Paris, France; formerly, Division of Nephrology and Hypertension, Department of Medicine, NewYork-Presbyterian/Weill Cornell Medical Center, New York, NY.

3 Division of Nephrology and Hypertension, Department of Medicine, NewYork-Presbyterian/Weill Cornell Medical Center, New York, NY.

4 Department of Transplantation Medicine, NewYork-Presbyterian/Weill Cornell Medical Center, New York, NY.

5 Currently, Department of Nephrology, Necker Hospital, APHP, Université Paris Descartes Sorbonne Paris Cité, Paris, France; formerly, Division of Nephrology and Hypertension, Department of Medicine, NewYork-Presbyterian/Weill Cornell Medical Center, New York, NY.

6 Department of Pathology, NewYork-Presbyterian/Weill Cornell Medical Center, New York, NY.

7 Department of Psychiatry, Stony Brook University, Stony Brook, NY.

This work was supported in part by a Method to Extend Research in Time award (2R37-AI051652) from the National Institute of Allergy and Infectious Diseases, National Institutes of Health, and an award (NPRP 08-503-3-11) from the Qatar National Research Foundation to M.S. This is also supported by a Clinical and Translational Science Center award (ULI RR 024996) to Weill Cornell Medical College and a Mentored Career Development award (K08-DK087824) from the National Institutes of Health to T.M.

The authors declare no conflicts of interest.

8 Address correspondence to: Manikkam Suthanthiran, M.D., Hamad bin Khalifa Biomedical Research Building, Division of Nephrology and Hypertension, Department of Medicine, NewYork-Presbyterian/Weill Cornell Medical Center, 525 East 68th Street, Box 3, New York, NY 10065.

E-mail: msuthan@med.cornell.edu

D.A., T.M., and S.V.S. participated in performing the research, analyzing the data, and writing the article. A.H., V.K.S., and D.D. participated in performing the research. R.D. participated in performing the research and contributing new reagents. J.E.S. and M.S. participated in designing the research, analyzing the data, and writing the article.

Supplemental digital content (SDC) is available for this article. Direct URL citations appear in the printed text, and links to the digital files are provided in the HTML text of this article on the journal’s Web site (www.transplantjournal.com).

Received 4 October 2011. Revision requested 28 October 2011.

Accepted 6 February 2012.

Renal allograft fibrosis is currently identified using the invasive allograft biopsy in patients with worsening renal allograft function. However, many challenges exist, including early diagnosis of allograft fibrosis (1), and neither serum creatinine nor estimated glomerular filtration rate seems to be an accurate indicator of fibrosis (2). Moreover, the biopsy is costly, complications still occur, sampling errors may bias the diagnosis, and interobserver variability in grading of biopsy specimens remains a challenge (3–9).

We have reported a method using a quantitative polymerase chain reaction (PCR) assay to measure messenger RNA (mRNA) levels of immune products within urinary cells of renal transplant recipients (10–12). In the current study, we investigated the feasibility of developing a noninvasive test for the diagnosis of human renal allograft fibrosis.

The pathogenesis of allograft fibrosis involves immune and nonimmune pathways and multiple cell types (1, 13–16). We reasoned that measurement in urinary cells of mRNA encoding proteins implicated in fibrogenesis and of mRNA for renal tubule epithelial cell–specific proteins would be informative of fibrosis. Because inflammation may coexist with fibrosis (1, 17–20), we measured mRNA levels for perforin and granzyme B, previously associated with acute rejection (10). In this report, we describe the discovery and validation of a four-gene urinary cell mRNA signature for the noninvasive diagnosis of human renal allograft fibrosis.

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RESULTS

Study Cohorts for the Discovery Set and the Validation Set

We profiled 114 urine samples from 114 renal transplant recipients who had undergone either a clinically indicated renal allograft biopsy or a scheduled (protocol) biopsy. The biopsy specimens were examined for the presence or absence of tubulointerstitial fibrosis as well as classified according to the Banff schema (21) by a pathologist (S.V.S.) blinded to the mRNA results.

Before data analysis, the 114 urine samples were assigned at a 2:1 ratio to a discovery set of 76 samples (32 from 32 recipients with renal allograft biopsy results showing fibrosis and 44 from 44 recipients with normal biopsy results) and an independent validation set of 38 samples (16 from 16 recipients with biopsy results showing fibrosis and 22 from 22 recipients with normal biopsy results) (Fig. 1). Neither the recipients’ characteristics nor the transplant or renal allograft–related variables differed between those assigned to the discovery set or the validation set (Table 1). The risk factors for fibrosis, such as acute rejection and deceased donor grafts, however, were more frequent in the fibrosis biopsy group compared with the normal biopsy group.

TABLE 1

TABLE 1

FIGURE 1

FIGURE 1

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Diagnostic Value of Individual mRNA Levels in the Discovery Set

We used our preamplification enhanced kinetic, quantitative PCR assay (11) for the absolute quantification of mRNAs in the urine of renal allograft recipients. This assay enables measurement of a large number of mRNAs using a very small quantity of complementary DNA, and the sequence and location of the gene-specific oligonucleotide primers and TaqMan probes (Applied Biosystems, Carlsbad, CA) that we designed for quantifying the mRNAs in the PCR assays are listed (see Table S1, SDC,http://links.lww.com/TP/A657). We used locally weighted scatterplot smoothing (LOESS) methods in the discovery phase of the analysis to initially examine the bivariate relationship of each mRNA measure to the diagnosis in the discovery set composed of 32 renal transplant recipients with biopsy-confirmed fibrosis and 44 recipients with normal allograft biopsy results, controlling for the quadratic relationship of 18S ribosomal RNA (rRNA). Logistic regression analysis was then used to parsimoniously model each relationship as a piecewise linear model.

Figure 2 illustrates that the levels of 12 of the 22 mRNAs measured are significantly associated with the diagnosis of fibrosis after using the Holm-modified (22) Bonferroni procedure to control the risk of a type I error. The lack of association between the remaining 10 mRNAs and allograft diagnosis is shown (see Figure S1, SDC, http://links.lww.com/TP/A657).

FIGURE 2

FIGURE 2

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Receiver Operating Characteristic Curve Analysis

Analysis involving the receiver operating characteristic (ROC) curve demonstrated that allograft fibrosis can be predicted accurately using urinary cell levels of mRNA (presented as area under the curve [AUC], 95% confidence interval) for vimentin (0.90, 0.82–0.97), hepatocyte growth factor (HGF; 0.91, 0.84–0.98), α–smooth muscle actin (0.88, 0.80–0.95), fibronectin 1 (0.83, 0.73–0.93), perforin (0.83, 0.74–0.93), transforming growth factor (TGF)–β1 (0.82, 0.72–0.92), tissue inhibitor of metalloproteinase 1 (0.81, 0.71–0.90), granzyme B (0.82, 0.71–0.92), fibroblast-specific protein 1 (0.81, 0.71–0.91), plasminogen activator inhibitor 1 (0.79, 0.68–0.90), collagen 1A1 (0.77, 0.66–0.88), or CD103 (0.76, 0.65–0.87).

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Multigene Prediction Model of Fibrosis Diagnosis in the Discovery Set

We chose to build a multigene prediction model of fibrosis around vimentin in view of the biologic properties of vimentin (23), data from preclinical models that vimentin is overexpressed preceding or during fibrosis, or both (24, 25), and the clinical observation that vimentin expression in the 3-month protocol biopsies of renal allografts is associated with fibrosis score at 12 months (26). Accordingly, we once again estimated a LOESS model and a corresponding piecewise linear model for the relationship of each mRNA measure to fibrosis, this time controlling for vimentin mRNA level and the quadratic relationship of 18S rRNA level. These analyses showed that, after controlling for vimentin mRNA levels, the levels of other mRNAs (HGF, TGF-β1, fibronectin 1, plasminogen activator inhibitor 1, fibroblast-specific protein 1, collagen 1A1, α–smooth muscle actin, CD103, granzyme B, or perforin) that were initially significantly associated with fibrosis were no longer significant (P>0.05), whereas the mRNA levels for NKCC2 and E-cadherin became significantly associated with the diagnosis (Fig. 3). Based on these findings, a four-gene diagnostic model that included vimentin, NKCC2, and E-cadherin mRNAs and 18S rRNA was developed. The parameter estimates for the model, provided in Figure 3, include terms accounting for the relationships, including nonlinear relationships, between the mRNAs and the diagnosis.

FIGURE 3

FIGURE 3

The composite score based on this model was highly associated with the diagnosis of fibrosis (Fig. 4A). The ROC curve (Fig. 4B) shows, for various levels of this composite score, the fraction of true-positive results (sensitivity) and false-positive results (1−specificity) for distinguishing recipients with allograft fibrosis from recipients with normal biopsy results. The AUC was 0.95 (95% CI, 0.90–0.99; P<0.0001) and was a significant improvement (P<0.05) over the AUC for vimentin and 18S only. By using the optimal cut point of 4.5 (the cut point yielding the highest combined sensitivity and specificity), the composite score predicted fibrosis with a specificity of 84.1% (95% CI, 73.3%–94.9%) and a sensitivity of 93.8% (95% CI, 85.4%–99.9%) (Fig. 4B).

FIGURE 4

FIGURE 4

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Independent Validation of the Diagnostic Signature

The final diagnostic equation predicting fibrosis in the discovery set was then validated in an independent validation set of 38 renal transplant recipients consisting of 16 patients with biopsy-proven fibrosis and 22 recipients with normal allograft biopsy results (Table 1). Figure 4(C) shows the ROC curve of this equation based on the urinary cell levels of vimentin, NKCC2, and E-cadherin mRNAs and 18S rRNA for the diagnosis of fibrosis. This four-gene classifier could diagnose fibrosis in the validation set with high accuracy, and the AUC for the diagnosis of fibrosis in the independent validation set was 0.89 (95% CI, 0.78–0.99; P<0.0001) (Fig. 4C). At the composite score cut point of 4.5 (the same cut point used in the discovery set), fibrosis was diagnosed in the validation set with a specificity of 77.3% (95% CI, 59.8%–94.8%) and a sensitivity of 87.5% (95% CI, 71.3%–99.9%).

We also examined the fit of the predictor model by dividing the discovery and validation sets into sextiles of the composite score and examined the predicted and observed number of transplant recipients with fibrosis, separately for each sets, for each sextile (Fig. 4D). Based on the Hosmer-Lemeshow test, the fit between the observed and the predicted number of subjects with fibrosis in each of the sextiles was excellent (P=0.69) in the discovery set (left half of Fig. 4D). For the validation set (right half of Fig. 4D), the P value was 0.04, suggesting a good fit, given that this set was not involved in the estimation of the model.

Serum creatinine levels were higher in the fibrosis biopsy group compared with the normal biopsy group (P<0.0001; Table 1). We assessed whether our composite score independently differentiates the fibrosis biopsy group and the normal biopsy group after controlling for serum creatinine. Our analysis showed that the composite score is statistically significant and is a slightly stronger predictor of group status (fibrosis vs. normal) than serum creatinine (each P<0.0001, controlling for the other).

We examined whether graft dysfunction independent of fibrosis was associated with the composite score. The log mean composite score of the four-gene signature was 4.58 (95% CI, 3.52–5.64) in the acute tubular necrosis group with graft dysfunction (n=9) and 6.49 (95% CI, 5.96–7.02) in the fibrosis biopsy group with graft dysfunction (n=48) (P=0.01). In addition, the composite score of the acute tubular necrosis group was not significantly different from that of the normal biopsy group (n=66) with normal graft function (P=0.12).

We investigated whether the time to biopsy was associated with the diagnostic signature (composite score). This analyses showed that there was no significant association between the diagnostic signature and the time to biopsy; Pearson correlation coefficients were 0.17 (P=0.24) in the fibrosis biopsy group (n=48) and 0.23 (P=0.07) in the normal biopsy group (n=66).

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Fibrosis Grades and the Four-Gene Composite Score

We investigated whether our four-gene composite score could strongly discriminate patients with differing degrees of fibrosis from patients with no evidence of fibrosis. Our analysis revealed that the log mean composite score derived from urinary cell levels of vimentin, NKCC2, and E-cadherin mRNAs and 18S rRNA was significantly different among the four groups (fibrosis grades I [<25% of cortical area], II [26%–50%], and III [>50%] and those with no evidence of fibrosis, P<0.0001, one-way analysis of variance) (see Figure S2, SDC,http://links.lww.com/TP/A657). Pairwise comparisons revealed that the mean composite score of those with normal biopsy results were significantly different from that of fibrosis grades I (P=0.0002), II (P<0.0001), and III (P<0.0001). The mean composite score, however, did not differ significantly among the three grades of fibrosis (P=0.58).

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Allograft Fibrosis with Concurrent Inflammation and the Four-Gene Composite Score

Among the 48 patients with allograft fibrosis, 32 biopsy specimens from 32 patients showed no inflammation, and 16 biopsy specimens from 16 patients displayed both fibrosis and inflammation. The log mean composite scores were 7.5±2.3 in the 16 urine samples from patients with both fibrosis and inflammation and 5.9±1.3 in the 32 urine samples from patients with fibrosis only and without concurrent inflammation (P=0.003).

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DISCUSSION

We have discovered and validated an mRNA signature for the noninvasive diagnosis of human renal allograft fibrosis. The AUC for the defined signature was 0.93 (95% CI, 0.88–0.97; P<0.0001) when all 114 samples (fibrosis biopsy group, n=48; normal biopsy group, n=66) were included, and at the composite score cut point of 4.5 (the same cut point used in the discovery and validation sets), fibrosis was diagnosed with a specificity of 81.8% (95% CI, 72.5%–91.1%) and a sensitivity of 91.7% (95% CI, 83.8%–99.5%). These estimates, however, are somewhat upwardly biased (because of the cut point being selected to optimize sensitivity and specificity within the discovery set). An important attribute of the defined signature is that early fibrosis can be distinguished from biopsy results without any fibrosis, and a weakness is that the diagnostic signature does not distinguish the different grades of fibrosis.

Several features of our study may have contributed to our development of a noninvasive test for allograft fibrosis. First, we measured the absolute levels of mRNA copy number using the standard curve method rather than the relative levels of gene expression calculated using the delta-delta Ct method; the absolute quantification approach avoids some of the ambiguities inherent to the ΔΔCt method of quantification of mRNA copy numbers because it is not always clear what should be used as the “control” for the “disease” studied. Second, we used a discovery set to develop a prediction equation and identify the composite score cut point and then used the same equation and cut point to validate the diagnostic accuracy of the urinary cell mRNA signature in an independent cohort of renal allograft recipients. Third, we gave consideration to the potential for nonlinear relationships of gene expression measures to renal allograft diagnosis, and our approach for the discovery phase of the analysis used LOESS methods to examine the relationship of the mRNA measures to the diagnosis (fibrosis vs. normal). The predicted probability plots, illustrated in Figures 2 and 3, capture well the threshold effects of mRNA copy number to the renal allograft diagnosis and the lack of a simple linear relationship between mRNA abundance and allograft status; these issues would have been missed if the transcript levels were summarized as group means. Another contributor to our successful testing of the hypothesis that urinary cell mRNA profiles distinguish allografts with fibrosis from allografts without fibrosis is our use of urine samples from patients with protocol biopsies with normal biopsy findings and without fibrosis as the control group. Had we used urine samples from renal allograft recipients with acute rejection, calcineurin toxicity, or BK virus nephropathy as the control group, the development of a robust biomarker that distinguishes biopsy specimens with fibrosis from biopsy specimens without fibrosis may have been compromised because each of these conditions may be associated with some degree of fibrosis.

Our use of protocol biopsies, performed primarily in the early posttransplantation period, as controls for the fibrosis biopsy group resulted in a significant difference (P<0.0001) in the time to biopsy between the fibrosis biopsy group and the normal biopsy group. This raised the interesting question whether the difference in the time to biopsy rather than the allograft biopsy findings (fibrosis present vs. fibrosis absent) was responsible for the diagnostic signature. Whereas this possibility cannot be conclusively excluded, the composite score being time dependent seems unlikely because there was no significant association (P>0.05) between the score and the time to biopsy within the fibrosis biopsy group or the normal biopsy group.

In the four-gene diagnostic signature defined in this study, vimentin showed the strongest association with the allograft fibrosis diagnosis. Vimentin is a major intermediate filament protein expressed by mesenchymal cells. Ivaska et al. (23) have reviewed the dynamic nature of vimentin expression and the role of this evolutionarily conserved protein in cell adhesion, migration, and signaling. Whereas healthy renal tubular cells are reported not to express vimentin protein, injured ones are decorated by vimentin. Vimentin-expressing, regenerating renal tubular cells have been reported by Nakatsuji et al. (24), and vimentin overexpression has also been reported in a folic acid–induced tubulointerstitial model (25). Hertig et al. (26) reported that renal allograft recipients with greater than 10% of renal tubular cells expressing vimentin in their 3-month protocol biopsy have a higher tubulointerstitial fibrosis score in their 12-month biopsy.

Urinary cell levels of several other mRNAs such as TGF-β1 and HGF were also significantly higher in the urine from the fibrosis biopsy group compared with the urine from the normal biopsy group. Their levels, however, were no longer significantly (P>0.05) associated with allograft fibrosis after controlling for vimentin mRNA levels and did not contribute to the diagnostic accuracy of the composite score. Nevertheless, we discussed in the next paragraphs their potential role(s) because of the biologic plausibility of their contribution to fibrosis/epithelial-mesenchymal transition (27, 28) or their association with allograft fibrosis (29–31), or both.

TGF-β1, a fibrogenic cytokine, may be responsible not only for the fibrosis but also for the tubular cell atrophy that is a consistent “companion” of interstitial fibrosis. Although there is an ongoing debate regarding whether the renal tubular epithelial cells indeed give rise to the interstitial fibroblasts/myofibroblasts (32, 33), the experimental findings of Koesters et al. (34) that in vivo overexpression of TGF-β1 in renal tubules results in peritubular fibrosis, tubular dedifferentiation, and decomposition by autophagy proffer an explanation for the invariable coexistence of tubular atrophy and interstitial fibrosis in native kidneys and renal allografts.

HGF can block TGF-β1–induced epithelial-mesenchymal transition, enhance matrix degradation in vitro, and reverse fibrosis in animal models of chronic renal injury (35–38). In accordance with our results, HGF is overexpressed in vivo in studies of acute kidney injury (38, 39), in most forms of chronic kidney diseases in animal models (40–42), and in the serum of patients with end-stage renal failure (43). HGF induction may serve as a protective, counterregulatory mechanism because HGF blockade promotes tissue fibrosis and renal dysfunction (40, 41, 44). The heightened expression of HGF in patients with allograft fibrosis is reminiscent of our earlier findings that mRNA for immunosuppressive cytokine interleukin 10 (45) and mRNA for regulatory T-cell specification factor FoxP3 (11) are present at high levels during an episode of acute rejection.

Emerging data suggest that the renal allografts with fibrosis and concurrent inflammation fare less well compared with grafts with fibrosis and without inflammation (20). Our findings that the urinary cell four-gene composite score is significantly higher in those with biopsy results showing both fibrosis and inflammation compared with those with biopsy results showing fibrosis without concurrent inflammation suggest that the score may also be useful in distinguishing those with fibrosis and concurrent inflammation from those with fibrosis alone.

A weakness inherent to our cross-sectional study design is that the temporal relationship between the urinary cell mRNA signature (the composite score of the four-gene signature) and histologic detection of allograft fibrosis cannot be resolved. Whether the urinary cell mRNA signature is of diagnostic value only (i.e., the composite score threshold is reached only when the allograft shows fibrosis) or whether it is also anticipatory of allograft fibrosis (i.e., the composite score threshold is reached days or weeks before biopsy results show allograft fibrosis) cannot be addressed with our study design. It is also possible that an elevated composite score is an intrinsic feature of patients who will eventually develop fibrosis; that is, the patients who overexpress mRNAs such as vimentin because of genomic or nongenomic reasons, or both, are at an increased risk for developing fibrosis. We speculate that the diagnostic signature defined in this study may serve also as an anticipatory biomarker, and this speculation is based on the recent findings from the Clinical Trials in Organ Transplantation 4 Trial that urinary cell mRNA profiles of longitudinally collected urine specimens predict acute rejection days to weeks before biopsy diagnosis (46). This hypothesis, however, needs to be tested using a longitudinal study design.

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MATERIALS AND METHODS

Study Cohorts

We examined 114 urine samples from 114 kidney transplant recipients who had undergone either a diagnostic (for cause) renal allograft biopsy or a scheduled (protocol) biopsy. The biopsy specimens were examined for the presence or absence of tubulointerstitial fibrosis and inflammation and classified according to the Banff schema (21) by a pathologist (S.V.S.) blinded to the mRNA results. The institutional review board at the Weill Cornell Medical College in New York approved the study, and each patient gave written informed consent (for additional information, see Methods, SDC,http://links.lww.com/TP/A657).

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Quantitation of mRNAs

Urine was centrifuged at 2000g for 30 min within 4 hr of collection. RNA was extracted from the pellet using the RNeasy mini kit (Qiagen, Valencia, CA) and reverse transcribed to complementary DNA using TaqMan Reverse Transcription Reagents (Applied Biosystems). We designed oligonucleotide primers and fluorogenic probes for the measurement of levels of mRNAs (see Table S1, SDC, http://links.lww.com/TP/A657). PCR analysis involved a preamplification step, followed by quantification of mRNA with an ABI Prism 7500 Fast detection system (Applied Biosystems). Transcript levels were calculated by a standard curve method (47) (for additional information, see Methods, SDC,http://links.lww.com/TP/A657).

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Statistical Analysis

One hundred fourteen patients (48 recipients with allograft fibrosis and 66 recipients with normal biopsy results) were rank ordered within the group by the copy number of 18S rRNA and partitioned into consecutive triplets. Within each triplet, the first and the third patients were assigned to the discovery set, and the second patient was assigned to the validation set, resulting in the two sets being exactly matched on fibrosis status and very closely matched on 18S. Twice as many patients were assigned to the discovery set to enhance statistical power for the exploratory analyses that included a procedure to protect against the risk of a type I error.

The distribution of each mRNA, as well as 18S rRNA, exhibited considerable positive skewness, which was substantially reduced by use of a log transformation. LOESS methods were used to examine the relationship of the mRNA measures to the diagnosis (fibrosis vs. normal). An initial LOESS model revealed a U-shaped relationship of 18S rRNA to the diagnosis that was well represented by a quadratic function. We then used a generalized additive model (48, 49) procedure to fit an additive LOESS model of the relationship of each individual mRNA measure with the diagnosis while statistically controlling for the quadratic effect of 18S. The smoothing parameter for the LOESS model was determined using the generalized cross-validation criterion (but restricted to df<5). After reviewing the smoothed relationship, we next fit a piecewise linear logistic regression spline model that closely approximated the LOESS-smoothed relationship. We present plots where the parametric model of the relationship of mRNA level to the probability of being in the fibrosis biopsy group is superimposed on the LOESS model. We also present the AUC and its 95% CI for each logistic model. Significance levels of the 22 parametric models were adjusted for the experiment-wise risk of a type I error using the Holm-modified (27) Bonferroni method. Based on the results, we chose one mRNA to be definitely included in the final model and then repeated the previously mentioned process for the remaining 21 mRNA measures to determine which, if any, could further improve the prediction of fibrosis diagnosis. This stepwise process was repeated until, after three steps, no further mRNA measures significantly improved the prediction model. The ROC curve for the final model and its AUC are presented.

In the validation phase, the final prediction equation from the discovery phase was used to calculate composite scores for those in the validation set. A logistic regression analysis predicting fibrosis diagnosis from this single composite score was estimated to test the significance of the prediction equation. The ROC curve for the prediction equation and its AUC for the validation set are presented. Finally, the discovery and validation sets were each divided into sextiles, and an exact test version of the Hosmer-Lemeshow test (50) was used to assess the fit of the equation in both the discovery set and the validation set.

All analyses were performed using SAS version 9.2 (SAS Institute Inc., Cary, NC).

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Keywords:

Kidney transplantation; Fibrosis; Gene expression

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