Abstract
This study investigated the relationship between apparent diffusion coefficient (ADC) measures and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) kinetics in breast lesions, and evaluated the relative diagnostic value of each quantitative parameter. Seventy-seven women with 100 breast lesions (27 malignant and 73 benign) underwent both DCE-MRI and diffusion weighted MRI (DWI). DCE-MRI kinetic parameters included peak initial enhancement, predominant delayed kinetic curve type (persistent, plateau or washout), and worst delayed kinetic curve type (washout>plateau>persistent). Associations between ADC and DCE-MRI kinetic parameters and predictions of malignancy were evaluated. Results showed that ADC was significantly associated with predominant curve type (ADC was higher for lesions exhibiting predominantly persistent enhancement compared to those exhibiting predominantly washout or plateau, p=0.006), but was not significantly associated with peak initial enhancement or worst curve type (p>0.05). Univariate analysis showed significant differences between benign and malignant lesions in both ADC (p<0.001) and worst curve (p =0.003). In multivariate analysis, worst curve type and ADC were significant independent predictors of benign versus malignant outcome and in combination produced the highest area under the ROC curve (AUC = 0.85, AUC=0.78 with 5-fold cross-validation).
Keywords: breast cancer, diffusion-weighted imaging (DWI), dynamic contrast-enhanced MRI (DCE-MRI), apparent diffusion coefficient (ADC)
Introduction
Breast MRI has proven an important adjunct to mammography for breast imaging. In particular, dynamic contrast-enhanced MRI (DCE-MRI) is highly sensitive for breast cancer detection with a reported range of 88% - 100% and is the most sensitive modality for breast cancer detection in high risk women (1,2). Further, it has been shown to be more accurate than either mammography or ultrasound in determining extent of malignancy (3-5). Despite these strengths, the relatively moderate specificity of DCE-MRI, with a reported range of 68% - 96%, can present challenges by detecting a significant number of benign lesions that overlap in their features with malignancies based on current interpretation criteria (6-10). As a result, additional MRI techniques which may improve the specificity and positive predictive value of breast MRI could reduce morbidity, economic costs, and psychosocial costs associated with unnecessary biopsies.
Quantitative MRI techniques have been shown to improve the accuracy of breast MRI. Specifically, evaluating lesion kinetics on DCE-MRI can increase the specificity of breast MRI (11). More recently, several studies have demonstrated that diffusion-weighted imaging (DWI) techniques are useful in differentiating benign from malignant lesions based on apparent diffusion coefficient (ADC) measures (12-19). As DCE-MRI kinetics are related to differences in vascular volume and permeability (20,21), it is reasonable to expect that the sensitivity of DWI to biophysical characteristics such as cell density, membrane integrity, and microstructure (22) would provide unique and complementary information to that of DCE-MRI kinetics data. This is supported by recent studies showing that a combination of DWI and DCE-MRI characteristics can achieve high diagnostic accuracy (23,24) and that DWI can improve the diagnostic performance of conventional breast MRI (25,26).
To our knowledge, the correlation between DCE-MRI kinetics and ADC values has not been examined. Given the inherently different physiological properties that these two techniques measure, we hypothesize that ADC values and DCE-MRI kinetic parameters will provide complementary information that could potentially improve breast MRI specificity. Therefore, the purpose of this study was to investigate the relationship between ADC values and DCE-MRI kinetics in breast lesions and to evaluate the relative diagnostic value of each quantitative parameter alone and in combination.
Materials and Methods
Subjects and Lesions
This study was approved by our internal review board and compliant with the Health Insurance Portability and Accountability Act. We retrospectively reviewed consecutive breast DCE-MRI examinations performed between October 2005 and November 2006. Inclusion criteria for the study consisted of all breast lesions identified on MRI that were assigned a final Breast Imaging Reporting and Data System (BI-RADS) (27) assessment of 3 (probably benign), 4 (suspicious) or 5 (highly suggestive of malignancy) and had a complete automated kinetic synopses generated by a computer-aided assessment (CAE) program (CADstream™, Merge Healthcare, Hartland, WI). BI-RADS 6 lesions (biopsy-proven, known malignancies) were excluded. Benign versus malignant outcomes were determined based on results of biopsy or minimum 2-year follow-up by either MRI or linkage with the regional Cancer Surveillance System (CSS) tumor registry.
In all, 168 breast lesions with a final MRI assessment of BI-RADS 3, 4 or 5 and definitive outcome were identified on 129 consecutive DCE-MRI examinations in 128 women over the course of the study period. DWI was not performed in the MR examinations for 29 lesions due to time constraints. Fourteen lesions were excluded from the study because of technical problems with the DWI sequences resulting from patient motion (n = 13) or inadequate fat suppression (n= 1). Further, 25 lesions were excluded because they were not CAE-evaluable due to issues including motion misregistration, very small or discontiguous lesion morphology and/or extensive background parenchymal enhancement. Therefore, the final cohort included 100 lesions in 78 examinations in 77 women. Although there were differences in study inclusion criteria, the lesions in this study constituted a subgroup of the lesions that were included in a prior study to evaluate the diagnostic value of enhancement kinetics (28) and another to characterize mammographically and clinically-occult lesions on DWI (29).
MRI Acquisition
MR imaging was performed on a GE LX 1.5T scanner using a dedicated 8-channel bilateral breast coil (General Electric Medical Systems, Milwaukee, WI). During the study period, two scanning protocols were used as clinical practice and technology evolved. Both protocols were in keeping with guidelines established by the International Breast MRI Consortium (IBMC) and by the ACR Imaging Network (ACRIN) MRI trials. Each MR examination included a T2-weighted fast spin echo sequence, T1-weighted non-fat suppressed sequence, T1-weighted DCE-MRI sequence with one pre-contrast and multiple post-contrast scans, and a DWI sequence. All scans were performed in the axial orientation.
DCE-MRI was acquired with a T1-weighted 3D fast spoiled gradient recalled echo sequence with parallel imaging (VIBRANT); TR/TE = 6.2/3 msec, flip angle = 10°, and field of view (FOV) = 32-38 cm. From October 2005 through June 2006 scans were performed with 2.2 mm slice thickness, 350 × 350 matrix, and five post-contrast acquisitions centered at 90, 180, 270, 360 and 450 seconds. From July 2006 through November 2006 three post-contrast acquisitions were performed with 1.6 mm slice thickness, 420 × 420 matrix, and three post-contrast acquisitions centered at 90, 270, and 450 seconds. The contrast agent administered was 0.1 mmol/kg-body weight Gd-DTPA (Omniscan, GE).
DWI was performed following the DCE-MRI acquisition using a diffusion-weighted echo planar imaging (EPI) sequence with parallel imaging (ASSET); reduction factor = 2, TR/TE = 7000/71.5 msec, 3 NEX, matrix = 192 × 192, FOV = 36 cm, slice thickness = 5 mm, and gap = 0. Diffusion gradients were applied in six directions with b = 0 and 600 s/mm2, and the scan time was 2:40 min.
Image Analysis
DCE-MRI scans were prospectively interpreted by one of four fellowship-trained radiologists specializing in breast imaging. Enhancement kinetics were assessed using a computer-aided evaluation software (CADstream™), as previously described (28). Briefly, the kinetic parameters calculated for each lesion included (1) peak initial enhancement, defined as the greatest percent increase in signal intensity by the first post-contrast sequence, (2) predominant kinetic curve type, defined as that comprising the largest percentage of the lesion delayed enhancement (washout, plateau, or persistent), and (3) worst curve type, defined as the single ‘most suspicious’ kinetic curve type exhibited in the lesion (any washout > any plateau > any persistent). This information, as well as ACR BI-RADS assessments and recommendations and pathology results, was entered into the clinical database for our institution and later extracted for the purposes of this study. Because the DCE-MRI scans were evaluated prospectively, the radiologists were blinded to lesion outcomes at the time of interpretation.
The diffusion-weighted images were retrospectively analyzed offline by researchers blinded to lesion outcomes at the time of image analysis. Diffusion maps were created using in-house Java-based software incorporating ImageJ (National Institutes of Health, public domain) and JDTI (Daniel P. Barboriak Laboratory, Duke University School of Medicine, Durham, NC) image processing tools. ADC maps were created from the spatially registered diffusion weighted images by
[1] |
where SDWI is the combined DWI (geometric average of individual b = 600 s/mm2 diffusion-weighted images), and S0 is the T2-weighted b = 0 s/mm2 reference image.
Lesions were identified from the DCE-MRI images based on description in the clinical radiology reports. A region of interest (ROI) was defined for each lesion at the corresponding location on the combined DWI (SDWI) series to include the area of hyperintensity. The ROI was drawn free-hand to encompass as much of the abnormality as possible while staying within the border of the hyperintense region. Care was taken to avoid non-enhancing regions of high T2 within a lesion, such as cyst, hematoma, or necrosis, by verifying the ROI against the T2-weighted (b = 0 s/mm2) image and ADC map. In the case that a lesion was not hyperintense on DWI, the ROI was drawn at the corresponding location and size as reflected on DCE-MRI. The lesion ADC value was calculated as the mean of the voxels in the ROI for each lesion.
Statistical Analysis
Associations between ADC and DCE-MRI kinetic variables and predictions of malignancy were evaluated by generalized estimating equations (GEE) so that standard errors would account for multiple lesions in the same patient (30). All tests were two-sided and model assumptions were checked using both influence statistics and visual inspection. The predictive abilities of the models were described using the area under the receiver operating characteristic curve (AUC), which is equivalent to the concordance measure c for logistic regression (or GEE with independence working correlation). Differences in AUC were assessed via pairwise ROC curve comparison (31). The AUC for the final multivariate model was also computed using predicted values from 5-fold cross-validation (32) to ensure that model assessment (AUC) was not conducted on precisely the same data as used for model development. Analyses were conducted using R version 2.8.1 (R Foundation for Statistical Computing, Vienna, Austria), SAS/STAT software, version 9.1 (SAS Institute, Inc., Cary, NC) and Medcalc version 10.4.5.0 (Medcalc Software, Mariakerke, Belgium).
Results
One hundred lesions in 77 women were evaluated for the study. Subjects ranged in age from 22 to 85 years (median, 49 years). The clinical indications for the examinations were high risk screening in 40/78 (52%), evaluation of extent of disease in patients with a new diagnosis of breast cancer in 33/78 (42%) and problem solving in 5/78 (6%). The study lesions detected in newly diagnosed cancer/evaluate extent of disease patients constituted additional lesions distinct from the known, biopsy proven cancers.
Of the 100 lesions in the study, and 27 (27%) were biopsy-proven malignancies and 73 (73%) were benign as determined by biopsy (n=44) or follow-up (n=29). Lesion characteristics are reported in Table 1. Nine of 27 malignancies were ductal carcinoma in situ (DCIS) and 18 were invasive carcinoma. Of the benign lesions that were biopsied, the most frequent histologies were fibroadenoma (n=9), atypical ductal hyperplasia (ADH, n=6), psuedoangiomatous stromal hyperplasia (PASH, n=5), focal fibrosis (n=4), and fibrocystic changes (n=4). Lesion sizes, as defined by the longest dimension on DCE-MRI, ranged from 0.3 to 8.3 cm (median, 1.0 cm). The average ADC (± one standard deviation) was 1.60 ±0.43× 10-3 mm2/s; the average peak initial enhancement on DCE-MRI was 145 ± 50 %. The large majority of lesions (88%) demonstrated persistent enhancement as the predominant curve type. By worst curve assessment, 51/100 (51%) lesions exhibited washout, 31/100 (31%) exhibited plateau, and 18 of 100 (18%) exhibited only persistent enhancement. Benign and malignant lesion characteristics are compared in Table 2.
Table 1.
n | (%) | |
---|---|---|
Size* | ||
≤ 5 mm | 13 | 13% |
6 mm - 1 cm | 38 | 38% |
1.1 cm - 2 cm | 22 | 22% |
> 2 cm | 27 | 27% |
| ||
BI-RADS Assessment | ||
3 | 23 | 23% |
4 | 66 | 66% |
5 | 11 | 11% |
| ||
Enhancement Type | ||
Focus | 8 | 8% |
Mass | 61 | 61% |
NMLE | 31 | 31% |
| ||
Source of Diagnosis | ||
Biopsy | 71 | 71% |
MRI follow-up | 19 | 19% |
Linkage with tumor registry | 10 | 10% |
| ||
Lesion Diagnosis | ||
Benign | 73 | 73% |
DCIS | 9 | 9% |
Invasive Malignancy | 18 | 18% |
IDC | 12/18 | |
ILC | 6/18 |
Abbreviations: BI-RADS = Breast Imaging Reporting and Data System, NMLE = non-mass-like-enhancement, DCIS = ductal carcinoma in situ, IDC = invasive ductal carcinoma, ILC = invasive lobular carcinoma
Size determined by longest diameter on DCE-MRI
Table 2.
Malignant (n=27) Mean ± SD or n (%) | Benign lesions (n=73) Mean ± SD or n (%) | p-value | |
---|---|---|---|
ADC (×10-3 mm2/s) | 1.29 ± 0.26 | 1.72 ± 0.43 | <0.001 |
| |||
Peak Initial Enhancement (%) | 140 ± 47 | 147 ± 51 | 0.586 |
| |||
Predominant Kinetic Curve Type | 0.047 | ||
Persistent | 21 (78%) | 67 (92%) | |
Plateau | 2 (7%) | 3 (4%) | |
Washout | 4 (15%) | 3 (4%) | |
| |||
Worst Curve Type | 0.003 | ||
Persistent | 2 (7%) | 16 (22%) | |
Plateau | 4 (15%) | 27 (37%) | |
Washout | 21 (78%) | 30 (41%) |
Note: P-values were from GEE with “independence” correlation structure
Abbreviations: ADC = apparent diffusion coefficient, SD = standard deviation
Small sample sizes precluded statistical comparisons of DWI and DCE-MRI characteristics between benign and malignant subtypes. By observational analysis, invasive lobular carcinoma (ILC) demonstrated less suspicious kinetics compared to invasive ductal carcinoma (IDC): all six ILC exhibited persistent enhancement as the predominant kinetic pattern (compared to 75% of IDC) and only 66% exhibited washout as the worst curve type (compared to 83% of IDC). On the other hand, there was little difference in ADC between ILC (mean, 1.28 × 10-3 mm2/s) and IDC (mean, 1.24 × 10-3 mm2/s). DCIS was not significantly different than invasive disease by either DCE-MRI kinetics or ADC. Of the most common benign histologies in the cohort, ADH and PASH exhibited lower mean ADC values (1.53 and 1.59 × 10-3 mm2/s, respectively) compared to fibroadenomas (mean, 1.85 × 10-3 mm2/s), while there was little difference in DCE-MRI kinetics between the three benign subtypes.
Univariate Differences Between Benign and Malignant Lesions
Table 2 summarizes univariate comparisons between benign and malignant lesions. Compared to benign lesions, malignancies exhibited lower mean ADC (p < 0.001), Figure 1a, and more often exhibited washout as the worst curve type (p=0.003), such as the example in Figure 2. Malignant lesions also tended to exhibit predominant curve types of washout or plateau more often than benign lesions (p = 0.047). However, there were exceptions, such as malignancies that did not exhibit any washout (n=6/27), and benign lesions displaying washout (n=30/73) and/or low ADC values (ADC<1.8 mm2/s, n=46/73); several examples are shown in Figure 3. No significant differences were observed between benign and malignant lesions for peak initial enhancement (p = 0.586, Figure 1b).
Association Between ADC and DCE-MRI Kinetics
ADC values and DCE-MRI kinetic parameters were compared for all lesions using GEE, Table 3. There was no significant correlation between ADC and peak initial enhancement (Figure 4, p=0.182). ADC was significantly higher for lesions exhibiting predominantly persistent enhancement (mean ADC, 1.64 ± 0.44 ×10-3 mm2/s) compared to those exhibiting predominantly washout or plateau enhancement (mean ADC, 1.39 ± 0.30 ×10-3 mm2/s, p=0.006). As seen in Figure 5, most lesions had predominately persistent enhancement, so pairwise comparisons with predominantly washout or plateau enhancement were not examined separately. For the worst curve, lesions with persistent delayed enhancement (mean ADC, 1.78 ± 0.47 ×10-3 mm2/s) showed a trend to have higher ADC than those exhibiting washout (mean ADC, 1.55 ± 0.43 ×10-3 mm2/s, p= 0.09), but did not differ from those exhibiting plateau delayed enhancement (mean ADC, 1.60 ± 0.41 ×10-3 mm2/s, p = 0.180).
Table 3.
n (%) | ADC (×10-3 mm2/s) (Mean ± SD) | Association with ADC (p-value) | |
---|---|---|---|
Peak Initial Enhancement (%) | 0.182* | ||
50-99 | 9 (9%) | 1.60 ± 0.58 | |
100-199 | 74 (74%) | 1.57 ± 0.43 | |
>200 | 17 (17%) | 1.77 ± 0.38 | |
| |||
Predominant Curve Type | 0.052** | ||
Persistent | 88 (88%) | 1.64 ± 0.44 | |
Plateau | 5 (5%) | 1.48 ± 0.12 | |
Washout | 7 (7%) | 1.32 ± 0.38 | |
| |||
Worst Curve Type | 0.310** | ||
Persistent | 18 (18%) | 1.78 ± 0.47 | |
Plateau | 31 (31%) | 1.60 ± 0.41 | |
Washout | 51 (51%) | 1.55 ± 0.43 |
P-value from generalized estimating equations (GEE) with “independence” correlation structure, analogous to Student’s t test with sandwich standard errors to adjust for multiple lesions in some patients.
P-value represents global factor effect, determined by score statistics for type 3 GEE analysis.
Multivariate Analysis to Discriminate Lesions
In a GEE model with binary outcome (malignancy) and independence working correlation, ADC and worst curve kinetics type were independent predictors of malignancy (p<0.001 and p=0.024, respectively). Table 4 summarizes predicted probabilities of malignancy based on the multivariable GEE model. At the 75th percentile observed for ADC (1.86 ×10-3 mm2/s), the predicted probability of malignancy was only 4% for persistent worst curve and 3% for plateau, but was 15% for washout. The respective probabilities of malignancy for persistent, plateau, and washout delayed worst curve kinetics at the 25th percentile for ADC (1.26 ×10-3 mm2/s) were 27%, 22%, and 62%. Of the 100 lesions, 24% had predicted probability of malignancy less than 5% (with one malignancy among the 24), and 36% had predicted probability of malignancy greater than 33% (with a 21/36 = 58% malignancy rate).
Table 4.
ADC Quartile | ADC Range (×10-3 mm2/s) | Worst Curve Type
|
|||||
---|---|---|---|---|---|---|---|
Persistent | Plateau | Washout | |||||
n | Probability of Malignancy | n | Probability of Malignancy | n | Probability of Malignancy | ||
25% | ≤1.26 | 3 | 0.266 | 7 | 0.219 | 15 | 0.618 |
50% | >1.26 – 1.85 | 7 | 0.121 | 19 | 0.097 | 24 | 0.381 |
75% | >1.85 – 3.0 | 8 | 0.038 | 5 | 0.029 | 12 | 0.149 |
Abbreviations: ADC=apparent diffusion coefficient, n=number of lesions
The model incorporating ADC and worst curve kinetics produced higher area under the ROC curve (AUC = 0.85, SE= 0.04, 95% CI = 0.77, 0.93) than either ADC (AUC = 0.79, SE= 0.05, 95% CI = 0.70, 0.87, p=0.05) or worst curve alone (AUC = 0.69, SE= 0.06, 95% CI = 0.59, 0.78, p=0.007), Figure 6. The AUC was attenuated but retained significance when 5-fold cross-validation was applied, fitting the model to 4/5 of the data at a time to create predicted probabilities of malignancy for the other 1/5 (AUC = 0.78, SE=0.06, 95% CI = 0.66, 0.90). The difference in AUC between ADC alone and worst-curve alone was not statistically significant (p=0.161).
Discussion
Our results suggest that the apparent diffusion coefficient (ADC) measured by diffusion weighted imaging (DWI) provides distinct and complementary information to dynamic contrast-enhanced MRI (DCE-MRI) kinetics for characterizing breast lesions and in combination may improve diagnostic accuracy. DWI provides information on the intrinsic tissue properties affecting the microscopic mobility of water (due to Brownian motion). ADC has been linked to tumor lesion aggressiveness and tumor response in oncologic imaging (33). The tissue properties affecting DWI are distinct from that of DCE-MRI, which relies on differences in tissue vascularity reflected by enhancement kinetics to identify breast malignancies. While DWI is not yet routinely used for clinical breast imaging, previous research studies have reported differences in ADC between benign and malignant breast lesions (12-19) and high diagnostic accuracy through a multivariate combination of ADC and DCE-MRI features (23,24).
Our study is the first to correlate quantitative DWI and CAE-generated DCE-MRI kinetic characteristics, and demonstrates that lower lesion ADC values (representing higher cellularity) are associated with more suspicious kinetics. Furthermore, multivariate analysis showed ADC and worst curve type to be significant independent predictors of benign versus malignant lesions and confirmed that DWI provided complementary information to DCE-MRI kinetics. The multivariate model provided significantly higher diagnostic performance (AUC=0.85) than worst curve kinetics (AUC=0.69) or ADC (AUC =0.79) alone. The large range of predicted probabilities of malignancy over worst curve kinetics and ADC values demonstrates that combined DCE-MRI and DWI-MRI information shows potential for increasing the specificity of breast MRI. These findings are in agreement with other recent studies demonstrating that incorporating DWI into the clinical breast MRI assessment can help to improve diagnostic performance (25,26). Future larger studies will enable evaluation of model performance for specific lesion subgroups, such as masses versus non-mass lesions and for different benign and malignant histologies.
Practical considerations of including DWI in routine breast MRI examinations are the additional scan time (on the order of 3 minutes) and radiologists’ time to review the DWI images. Although extensive cost-benefit analysis was not performed in this study, the improved specificity would almost certainly offset these drawbacks in the long term by potentially decreasing the number of unnecessary biopsies. Further, this would have the clinically desirable benefit of a reduction in patient morbidity associated with procedures.
In addition, the comparable diagnostic accuracies of ADC alone and worst-curve alone suggests that DWI could have potential benefit in patients for whom contrast (Gd-DTPA) is contraindicated such as those with renal insufficiency. This is particularly salient in view of recent evidence that reducing contrast doses in such patients could significantly decrease enhancement of some breast cancers (34). Further investigation comparing ADC to DCE-MRI is certainly needed, however, particularly in view of the fact that in this study all lesions were identified first with DCE-MRI and BI-RADs 2 lesions were excluded.
Our study has several limitations. The primary aim was to evaluate the association between quantitative tumor characteristics on DWI and DCE-MRI, and we therefore did not include the morphologic features of the lesions in the analysis, which can further improve the diagnostic accuracy of conventional breast MRI (35). Although they were not excluded, the study did not include any mucinous carcinomas, which tend to exhibit persistent enhancement and high ADC and could present a challenge for the model. ROIs were drawn manually on DWI images with reference to the DCE-MRI images. Automated segmentation of ADC maps based on DCE-MRI abnormalities was not possible due to the spatial distortions inherent to EPI-based DWI datasets (caused by B0 field inhomogeneities). However, reducing the spatial distortion of breast DWI is an active area of research involving new non-EPI pulse sequences (36,37) and post-processing correction techniques (38) and may enable direct voxel to voxel comparison of DWI and DCE-MRI and multi-parametric mapping in future work. DWI was performed with a diffusion sensitization of b=600 s/mm2. Higher b values and field strength (3 Tesla) may further improve the discrimination of breast lesions on DWI (39,40). Furthermore, ADC was calculated from only two b-values, with bmin = 0 s/mm2. Others have shown that the signal loss from diffusion in vivo is driven by both perfusion and diffusion, with the changes at low b values dominated by perfusion and the higher values characterizing intra- and extra-cellular diffusion (17,40,41). Although our simple approach has the advantage of being readily translatable to the clinic, calculation of ADC using a greater number of b-values and nonzero bmin would enable a more detailed comparison of DCE kinetic profiles in the fast and slow diffusion regimes and further extend knowledge in this area. In our study, DWI was performed after injection of a gadolinium-based contrast agent. While several prior studies have not shown a significant effect on ADC following administration of a contrast agent (16,42-44), it may be preferable to acquire DWI sequences prior to contrast injection to avoid any possible confounding effects.
In conclusion, we found that ADC provided unique and complementary information to DCE-MRI kinetic parameters for characterizing a variety of breast lesions and may improve the diagnostic accuracy of breast MRI. Future prospective studies are needed to determine the optimal way to incorporate ADC into the standard breast MRI assessment to reduce the number of unnecessary biopsies performed as a result of breast MRI
Acknowledgments
Grant Sponsors: Susan G. Komen for the Cure grant BCTR0600618, NCI Cancer Center Support Grant (Comprehensive) - Biostatistics Shared Resource P30 CA015704, and Institute of Translational Health Sciences grant 1 UL1 RR 025014-01.
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