Potential conflict of interest: Nothing to report.
We investigated the prognostic value of C-reactive protein (CRP) in patients with hepatocellular carcinoma (HCC) not amenable to surgery. A total of 615 patients diagnosed with HCC not amenable to surgery between April 1999 and December 2009 at the Department of Gastroenterology of the Medical Universities of Vienna and Innsbruck were included. We assessed the optimal CRP cutoff by regression spline analysis and tested its impact on median overall survival (OS) by the Kaplan-Meier method, univariate analysis (log-rank test), and multivariate analysis (Cox proportional hazard regression model) in a training cohort (n = 466, Vienna) and an independent validation cohort (n = 149, Innsbruck). We found a sigmoid-shaped association of CRP and the hazard ratio of death upon regression spline analysis and defined a CRP level <1/≥1 mg/dL as optimal cutoff for further survival assessments. Elevated CRP (≥1 mg/dL) at diagnosis was associated with poor OS (CRP-elevated versus CRP-normal; 4 versus 20 months; P < 0.001) and remained a significant negative predictor for OS upon multivariate analysis (hazard ratio, 1.7; P < 0.001), which was independent of age, Child-Pugh class, tumor characteristics, and treatment allocation. Analyses with respect to Barcelona Clinic Liver Cancer (BCLC) stage and Child-Pugh class supported the relevance of CRP (BCLC-stage C and Child-Pugh A: OS for CRP-elevated versus CRP-normal, 6 versus 14; P < 0.001; BCLC-stage C and Child-Pugh B: OS for CRP-elevated versus CRP-normal, 4 versus 15 months; P < 0.001). The prognostic significance of elevated CRP was reproducible at a second CRP determination timepoint and confirmed in the independent validation cohort. Conclusion: Elevated CRP is associated with a dismal prognosis in HCC patients and may become a useful marker for patient selection in HCC management. (HEPATOLOGY 2012)
Hepatocellular carcinoma (HCC) is the most common primary liver malignancy worldwide and accounts for more than 600,000 deaths annually.1 The implementation of the Barcelona Clinic Liver Cancer (BCLC) staging system2, 3 revolutionized the clinical management of HCC patients as it links tumor characteristics with liver function and general condition. The BCLC staging system identified five subgroups of patients (BCLC-0, A, B, C, D), of which three subgroups (BCLC-stage B, C, D) subdivide the large group of patients who are not amenable to potentially curative treatments. Even within a given BCLC-stage, HCC is biologically very heterogeneous and it has been shown that within these subgroups patients have different outcomes.4 This assumption has already been verified in patients at BCLC stage 0 or A, mostly by highly sophisticated genomic analysis in surgical tissue specimens.5 Similar studies in nonsurgical HCC patients are lacking, because tumor tissue is not so readily available in many cases. In the palliative setting, very expensive targeted therapies are standard of care but only benefit a fraction of the eligible patients. Identifying patients with very dismal prognostic features despite treatment would be helpful in the judicious use of these agents. Application of prognostic systems like CLIP can subgroup these patients into several strata4 but the discriminative power of CLIP in the palliative setting (BCLC B and C) is not strong enough to exclude patients from receiving these treatments. There is an urgent need for an easily determinable, simple, widely applicable, low-tech, and inexpensive marker from blood, which is able to identify patients with rapid progression to death despite treatment.
C-reactive protein (CRP) is an acute phase protein that is mainly produced in the liver. Following an acute phase stimulus, cytokines like interleukin (IL)-1 and IL-6 stimulate CRP production in hepatocytes, which is then released to the systemic circulation.6 CRP binds to several ligands, is involved in opsonization, interacts and activates the complement system, and has an fragment crystallizable (Fc)γ-receptor binding site.7 Thus, CRP plays a key role in a wide range of inflammatory processes and provides a link between the innate and adaptive immune systems.
Besides acute and chronic infections, CRP values may be elevated in cancer patients. In fact, several studies have reported a prognostic value of elevated CRP levels in different types of cancer8-10 including resectable HCC.11-13
In this study we investigated the prognostic value of CRP levels in nonsurgical HCC patients with respect to the BCLC classification.
The analyses were first performed in a training cohort of patients age ≥18 years who were diagnosed with HCC at the Department of Gastroenterology and Hepatology of the Medical University of Vienna after the publication of the BCLC classification in April 19992 and December 2009. HCC was diagnosed by computed tomography (CT) scan or magnetic resonance imaging (MRI) according to European Association for the Study of the Liver (EASL) diagnostic criteria14 and was mostly verified by biopsy. Patients who received any kind of liver surgery at any time after the diagnosis of HCC were excluded from this study.
The results of the training cohort were then confirmed in an independent validation cohort of patients age ≥18 years who derived from the transarterial chemoembolization (TACE) database of the Medical University of Innsbruck. This database includes all HCC patients (n = 252) who underwent TACE at the Medical University of Innsbruck between January 2001 and January 2008 and included BCLC B as well as BCLC C patients (Fig. 1). HCC was diagnosed by CT scan or MRI according to EASL diagnostic criteria.14 All patients who received TACE as first-line therapy after diagnosis were included. Patients who received any other first-line therapy (e.g., radiofrequency ablation), patients who received TACE despite Child-Pugh C cirrhosis at diagnosis and patients who received any kind of liver surgery at any time after the diagnosis of HCC were not eligible for the validation cohort (Fig. 1).
The local Ethics Committees of the Medical Universities of Vienna and Innsbruck approved the retrospective analysis of the patient data.
Collection of Data.
In the training cohort as well as the validation cohort, the date of HCC diagnosis was the baseline of this study.
In the training cohort the date of HCC diagnosis was recorded as the date of the diagnostic HCC biopsy when performed, or as the date of the diagnostic imaging procedure. A senior liver pathologist of the Department of Pathology of the Medical University of Vienna performed the histological diagnosis of HCC and tumor grading was staged according to Edmondson and Steiner.15 In the validation cohort, the date of the diagnostic imaging served as baseline for data collection.
Radiologic tumor characteristics (number of nodules, tumor size, macrovascular invasion, and extrahepatic spread) in either patient cohort derived from the diagnostic CT or MRI scan, which was analyzed by a senior radiologist of the Department of Radiology of the Medical University of Vienna or Innsbruck.
All blood values recorded in this study, including CRP levels, alpha-fetoprotein (AFP), prothrombin time, bilirubin, albumin, aspartate aminotransferase (AST), and alanine aminotransferase (ALT) were performed within 5-7 days prior to diagnostic HCC biopsy or diagnostic imaging in the ISO-certified laboratory of the Medical University of Vienna and Innsbruck. Additionally, we recorded the second CRP determination after the baseline CRP assessment, if available, to analyze CRP dynamics over time.
Child-Pugh score was recorded to describe liver function. Tumor stage was recorded according to the 6th Edition of the International Union Against Cancer (UICC) tumor node metastasis (TNM) classification16 and the BCLC-classification.2, 3 In the validation cohort, all patients received TACE as described.17
CRP Elevation Associated or Nonassociated with Clinically Evident Infection.
Several patients with HCC showed elevated CRP levels without any signs of clinically evident infection (CEI). To evaluate the prevalence of this frequently neglected clinical observation separately from CRP elevations with alternative explanations we created the variables “CRP, associated with CEI” and “CRP, nonassociated with CEI” and compared their frequencies in our HCC cohorts was well as in 104 well-defined cirrhosis patients of the TIPS-data base of the Medical University of Vienna (Supporting Methods, Supporting Fig. 2). Patients were summarized in the variable “CRP, associated with CEI” if at least one of the conditions outlined in the Supporting Methods section was documented during the hospital admission at the time of diagnosis. Additionally, we analyzed the association of “CRP, nonassociated with CEI” and “CRP, associated with CEI” with tumor characteristics, causes of death, and their impact on overall survival (OS).
In all cohorts, baseline patient characteristics were presented using descriptive statistics. To determine the optimal cutoff for CRP-related analysis, we used a spline-based approach in the training cohort to assess the functional form of CRP on OS.18 Based on this graphical representation a clinically sensible and applicable transformation of CRP was chosen.
Survival curves were calculated using the Kaplan-Meier method. OS was defined as the time between the date of diagnosis (date of HCC biopsy if available or diagnostic imaging) and the date of death. Additionally, we performed confirmatory analysis at a second timepoint based on a second independent CRP determination. In these confirmatory analyses, OS was defined as the time from the second CRP determination until death.
Patients who were still alive on December 1 2011 (end of follow-up) or who were lost to follow-up were censored at the date of the last contact. Univariate analyses were performed by means of the log-rank test. Variables that reached a P-value of ≤ 0.05 in the univariate analysis were entered into a multivariate analysis. The multivariate analysis was performed using a Cox proportional hazard regression model. P < 0.05 was considered significant.
The prognostic performance of CRP was evaluated in an independent external validation cohort with and without stratification according to the BCLC stage and within each BCLC stage according to the Child-Pugh stage. Statistical analyses were performed using SPSS v. 19.0 (Chicago, IL) and SAS v. 9.3 (Cary, NC).
A total of 466 patients met the inclusion criteria for the training cohort of this study (Fig. 1), of which 400 patients (86%) were diagnosed by radiologic imaging plus biopsy and 66 patients were diagnosed by radiologic imaging only. Patient characteristics of the training cohort are given in Table 1. Most patients (84%, N = 393) received antitumor therapy after the diagnosis of HCC, while 16% (N = 73) patients received best supportive care only. In summary, 114 patients (25%) underwent local therapy (percutaneous ethanol injection: n = 101 or radiofrequency ablation n = 13), 144 (31%) received TA(C)E (transarterial embolization: n = 32, or chemoembolization: n = 112), 133 (29%) received medical therapy (sorafenib: n = 32, somatostatin analogs: n = 53, doxorubicin: n = 7, other medical therapy: n = 41) and two patients (0.4%) received radiation therapy.
Between January 2001 and January 2008 252 patients were entered into the TACE database of the Medical University of Innsbruck, of which 149 patients were eligible for the validation cohort of this study (Fig. 1). All patients were diagnosed by radiologic imaging only. Patient characteristics of the validation cohort are given in Table 1. In total, 141 patients received conventional TACE with lipiodol and doxorubicin within 10 days of HCC diagnosis. Seven patients exceeded the maximum tolerated doxorubicin dose and were thereafter treated with TAE only. One patient received TACE with drug-eluting beads. The patients received a median number of three TACE cycles (range 1-20). Second-line therapies after TACE included best supportive care (n = 118), local-ablative intervention (radiofrequency ablation: n = 13, percutaneous ethanol injection: n = 1, radiation therapy: n = 1), and medical treatment (sorafenib: n = 7 and other therapies: n = 9).
In the training cohort 367 of 466 (79%) patients died during the observational period between April 1, 1999 and December 1, 2011, while 47 (10%) subjects were still alive and 52 (11%) patients were lost to follow-up.
CRP Distribution, Dynamics, and Association with OS.
The distributions and mean CRP levels of patients in the training and the validation cohort are given in Table 1 and Fig. 2A. Mean CRP levels slightly increased with increasing BCLC-stages (BCLC stage A/B/C/D: 0.9/ 1.8/2.7/3.6 mg/dL, P < 0.0001).
Table 1. Characteristics of Patients in the Training and Validation Cohort
HBV, Hepatitis B virus; HCV, Hepatitis C virus; ECOG PS, Eastern Cooperative Oncology Group Performance Status; TNM, tumor-node-metastasis; BCLC, Barcelona Clinic Liver Cancer.
The following explanations refer to the training cohort only. (No missing values in the validation cohort.)
We first evaluated the impact of CRP levels on patient outcomes by a regression spline analysis. We found a sigmoid-shaped association of CRP levels and the hazard ratio of death, and no increase of the hazard ratio of death was observed with CRP levels beyond 2 mg/dL (Fig. 2B). Thus, we next formed four different CRP cutoffs between 0 and 2 mg/dL (A: 0-0.5; B: >0.5 and <1, C: ≥1 and ≤2, D: >2 mg/dL). No statistical or clinically meaningful survival difference was observed between the cutoffs A and B or C and D (Fig. 2C). Hence, we used the CRP cutoff <1 versus ≥1 mg/dL (hereafter designated as “normal” and “elevated” CRP) and tested this cutoff in the validation cohort (Fig. 2D). Analysis of the validation cohort confirmed the prognostic power of elevated CRP levels regarding OS in patients with HCC (OS elevated CRP versus normal CRP: 6.2 versus 20.6 months [95% confidence interval, CI: 3.8-8.7 versus 14-27.2], P < 0.0001).
We tested the reproducibility of our findings by using another CRP determination at a second independent timepoint (Fig. 2E). In the validation cohort a second CRP determination was available in 92% of patients (137 of 149 patients) and was performed 41 days (median, 95% CI: 40.9-52.7) after the first CRP determination. Elevated CRP levels remained associated with poor OS (median OS for elevated-CRP versus normal CRP: 9.7 versus 21.8 months; 95% CI: 5.9-13.6 versus 14.2-29.2, P = 0.001, Fig. 2E).
Finally, we analyzed the impact of CRP changes (CRP normalization or new elevation) and CRP persistence (persistently normal or persistently elevated) between the first and second CRP determination on overall survival. Only 15% of patients experienced a CRP normalization or new CRP elevation. Persistence of CRP levels (elevated or normal) retained prognostic significance, while a new elevation of CRP was associated with a dismal prognosis (Supporting Table 1).
Uni- and Multivariate Analysis of Prognostic Factors.
The median overall survival of the whole patient population (N = 466) was 11 months (95% CI, 9.1-12.9). Besides CRP, age, the BCLC classification, and its constituent factors (Child-Pugh classification, ECOG performance status, macrovascular invasion and extrahepatic spread, tumor size, and tumor number), also elevated AFP (≥400 kU/L) and AST levels (≥100 U/L) as well as treatment allocation were significantly associated with OS (Table 2).
Table 2. Univariate Analysis of Prognostic Factors in Patients with Hepatocellular Carcinoma in the Training Cohort
Upon multivariate analysis, elevated CRP levels remained a highly significant predictor for overall survival (hazard ratio [95% CI], 1.7 [1.2-2.5], P < 0.001), which was independent from age, liver function, tumor characteristics, and treatment allocation (Table 3).
Table 3. Multivariate Analysis of Patients with Hepatocellular Carcinoma in the Training Cohort
ECOG PS, Eastern Cooperative Oncology Group Performance status; AST, aspartate aminotransferase, BSC, best supportive care, PEI, percutaneous ethanol instillation, RFA, radiofrequency ablation, TA(C)E, transarterial (chemo)embolization.
Number of nodules
C-reactive protein (mg/dl)
In the validation cohort, 130 patients (87%) died during the observational period between January 2001 and December 2011, while eight subjects were still alive and 11 were lost to follow-up. The OS of the whole population (n = 149) was 15.9 months (95% CI: 12.5-19.3). The same clinical factors as in the training cohort were significantly associated with OS, with the exception of age, AFP >400 mg/dL, AST >100 U/L, and extrahepatic spread, probably due to the smaller sample size (Supporting Table 2).
Strikingly, elevated CRP levels were significantly and independently associated with poor OS upon multivariate analysis (hazard ratio [95% CI], 2.0 [1.3-3.0], P < 0.001) (Supporting Table 3).
Prognostic Significance of CRP Within the BCLC Classification.
Given the independent prognostic significance of elevated CRP levels in the training and the validation cohort, we evaluated the discriminative power of elevated CRP levels within the BCLC staging system. The small number of patients with elevated CRP levels in BCLC-stage A (training cohort: CRP-elevated: n = 8, validation cohort: CRP-elevated: n = 5) precluded a reasonable survival analysis in this patient group. CRP levels also had no predictive role in endstage BCLC-D patients (data not shown).
In the training cohort, patients with BCLC stage B (n = 90), CRP levels-elevated (n = 29) were significantly associated with a shorter OS (median OS [95% CI] for CRP-elevated [n = 29] versus CRP-normal [n = 61]: 15 [5.1-24.9] versus 24 [17.9-30.1] months; P = 0.003; Fig. 3A). The same was true for patients with BCLC-stage B and Child-Pugh A cirrhosis (median OS [95% CI] for CRP-elevated [n = 14] versus CRP-normal [n = 48]: 21 [18.0-38.0] versus 28 [11.9-30.2] months; P = 0.042) (Fig. 3B) and a similar trend was observed in the 28 BCLC-stage B patients with Child-Pugh B cirrhosis (median OS [95% CI] for CRP-elevated [n = 15] versus CRP-normal [n = 13]: 9 [6.6-11.4] versus 16 [8.9-23.1] months; Fig. 3C), which did not reach statistical significance (P = 0.27) due to the small sample size.
In patients with BCLC-stage C disease (n = 190), elevated CRP levels were an even more powerful predictor for a poor OS (median OS [95% CI] for CRP-elevated [n = 112] versus CRP-normal [n = 78]: 5 [3.0-7.0] versus 15 [13.3-16.7] months, P < 0.001) (Fig. 4A) and remained strongly predictive after stratification according to Child-Pugh class (Fig. 4B,C). Patients with BCLC stage C and Child-Pugh A cirrhosis with elevated CRP levels (n = 37) had a median OS of 6 (95% CI, 3.7-8.3) months compared to 14 (95% CI, 12.5-15.5) months when CRP levels were normal (n = 46, P < 0.001, Fig. 4B).
Patients with BCLC stage C with Child B cirrhosis and normal CRP levels had not only a better median OS than those with elevated CRP (median OS [95% CI] for CRP-normal [n = 32] versus CRP-elevated [n = 75]: 15 [11.8-18.2] versus 4 [2.6-5.4] months; P < 0.001, Fig. 4C) but also a comparable median OS to patients at BCLC stage C, Child A cirrhosis, and elevated CRP. All results were confirmed in the independent validation cohort (Figs. 3A-C, 4A-C) at baseline and reproduced at a second independent timepoint with another CRP determination (Supporting Fig. 1a,b).
Prevalence and Impact of Different CRP Types (Associated or Nonassociated with Clinically Evident Infection) on Tumor Characteristics, Causes of Death, and OS.
We next investigated the prevalence of elevated CRP levels with clinically evident infection (“CRP, associated with CEI”) and elevated CRP levels without clear explanation (“CRP, nonassociated with CEI”) in the training cohort as well as in 104 well documented, in the majority advanced cirrhotic patients from the TIPS database of the Medical University of Vienna (Supporting Methods). Details about patient selection and characteristics of the TIPS-cohort are given in Supporting Fig. 2 and Supporting Table 5.
In the training cohort, 76 out of 246 patients with elevated CRP levels had some evidence of clinically evident infection (Supporting Table 4) at the time of the CRP determination as defined in the Supporting Methods and were designated as patients with “CRP, associated with CEI.” In contrast, 170 patients had a CRP elevation without a clear explanation and were designated as patients with “CRP, nonassociated with CEI.” The numeric distribution of CRP levels in each CRP group is given in Supporting Fig. 3.
Overall, “CRP, nonassociated with CEI” was significantly more prevalent in HCC patients with cirrhosis compared to patients with cirrhosis only (38% versus 17%, P < 0.001, Supporting Table 6). This difference was clearly obvious in all three Child-Pugh stages and therefore independent from liver function (Supporting Table 7).
Furthermore, “CRP, non-associated with CEI,” but not “CRP, associated with CEI” was associated with liver function independent tumor characteristics like tumor size, TNM stage, tumor extent, high AFP levels, number of tumor nodules, extrahepatic spread (Table 4). Finally, patients with “CRP, nonassociated with CEI” were significantly more likely to die from tumor progression, while patients with “CRP, associated with CEI” or “CRP, normal” died rather from cirrhosis-related complications (P < 0.001) (Supporting Table 8). Independent from the patients presentation with “CRP, nonassociated with CEI” or “CRP, associated with CEI,” both patient groups showed a similar dismal prognosis (Supporting Fig. 4).
Table 4. Association of CRP with Different Tumor Features in the Training Cohort
The aim of this study was to investigate the prognostic value of CRP levels in patients with HCC not amenable to surgery. Serum CRP levels showed a sigmoid-shaped association with the hazard ratio of death and CRP levels ≥1 mg/dL at the time of HCC diagnosis were strongly associated with poor OS, independently from liver function, tumor characteristics, and treatment allocation. All findings were reproducible in a second independent validation cohort and also at a second independent timepoint with another CRP determination.
Subgroup analyses with respect to BCLC stage and Child-Pugh class supported the prognostic relevance of serum CRP independent from tumor staging. Especially in patients with BCLC stage B and C disease the sample size was large enough to identify clinically meaningful survival differences within Child-Pugh class A and B patients. BCLC stage B and C patients with Child-Pugh B cirrhosis and normal CRP levels had a better OS than BCLC-stage C patients with Child-Pugh A or B cirrhosis and elevated CRP levels. And even more to our surprise, BCLC stage B and C patients with Child-Pugh B cirrhosis and normal CRP virtually had the same median OS as patients with Child-Pugh A cirrhosis and normal CRP (Figs. 3, 4). These findings are of key clinical relevance since serum CRP levels identified subgroups with different prognoses within a defined BCLC and Child-Pugh stage. So far this has only been shown for complex molecular signatures from resected human HCC tissue obtained by expensive, highly sophisticated gene expression analysis.5 In contrast, serum CRP determination is inexpensive, reproducible, objective, widely available, and routinely performed in clinical practice and it does not rely on invasive tissue collection. The reproducibility of our results with a second CRP determination at a second independent timepoint further supports the reliability of CRP as prognostic marker.
Our findings may also have impact for the design of future clinical trials. Most studies in advanced HCC only stratify according to variables like liver function, presence or absence of vascular invasion/extrahepatic spread, or AFP levels. The strong and independent prognostic significance of serum CRP levels in this study provides a clear rationale to collect serum CRP levels in future clinical trials.
In line with the strong prognostic significance of documented infections for cirrhotic patients,19 Cervoni et al.20 recently reported a significant prognostic impact of elevated CRP levels on short-term mortality in patients with advanced (Child-Pugh B ≥8 points) liver cirrhosis and without HCC. Given that all patients in our study were cirrhotic, one may presume that CRP elevations are just a risk factor for cirrhosis-related death independent from HCC. However, several lines of evidence in this study argue against this assumption. We could show that CRP elevations nonassociated with clinically evident infection were significantly more common in patients with HCC as compared to patients with cirrhosis only. In contrast to Cervoni et al.,20 who studied only advanced cirrhosis (Child-Pugh score ≥8), this difference was particularly impressive in HCC patients with well-preserved liver function (Child-Pugh stage A), where cirrhosis related infections and complications are usually rare. Furthermore, patients with CRP elevations nonassociated with clinically evident infection had more aggressive tumor characteristics and were more likely to die from tumor progression. Together with the mentioned prognostic power of CRP to substratify the BCLC-stages B and C, these data suggest that CRP elevations in patients with HCC may at least in part be tumor-related. Therefore, our data extend the prognostic significance of the inflammatory field effect, as indicated by elevated CRP, in cirrhosis observed by Cervoni et al.20 to cirrhosis patients with HCC, even in the presence of well-preserved liver function.
The mechanistic role of tumor-related CRP in HCC and in cancer in general is largely unclear. In particular, the question of whether aggressive tumor behavior prompts a prognostically detrimental inflammatory reaction or whether inflammation per se drives tumor progression remains to be elucidated. Notably, there is evidence that the inflammatory field effect, reflected by elevated CRP, may be directly involved in tumor progression, which could explain its prognostic significance in HCC. For example, IL-6, one of the main inducers of CRP production, has been shown to be associated with liver cancer progression21 and metastasis formation.22 A recent study in myeloma demonstrated that CRP directly promoted tumor cell proliferation under stressed conditions and protected myeloma cells from chemotherapy-induced apoptosis.23 Clearly, further preclinical studies in HCC are needed to elucidate the causal mechanisms of CRP in HCC progression.
The retrospective nature and the heterogeneous antitumor treatments of our patients in the training cohort are potential limitations of this study. But we confirmed the results in a completely independent, much less heterogeneous patient cohort that predominantly received TACE after diagnosis of HCC and hardly any second-line therapy with proven efficacy thereafter. In addition, the outcome of our patient population within the different BCLC stages matches exactly the published survival data for the BCLC classification.3 Furthermore, the independence of CRP from treatment allocation in the training and the validation cohort upon multivariate analysis and the reproducibility of our findings at a second independent timepoint confirmed the validity of our data. Prospective studies are needed to study the impact of CRP levels on response and outcome to specific antitumor treatments like TACE or sorafenib therapy.
In summary, our study identified serum CRP as a novel, noninvasive, inexpensive, objective, available, and widely applicable prognostic marker for patients with HCC, irrespective of tumor stage and Child-Pugh class and therapy. Thus, we recommend collecting serum CRP in future clinical trials, in particular in the setting of intermediate or advanced-stage HCC. The causal role of CRP in tumor progression merits further investigations in preclinical studies.
We thank Professor Harald Heinzl for excellent statistical consulting.