Association between number of months below K/DOQI haemoglobin target and risk of hospitalization and death

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1 Nephrol Dial Transplant (2008) 23: doi: /ndt/gfm845 Advanced Access publication 8 December 2007 Original Article Association between number of months below K/DOQI haemoglobin target and risk of hospitalization and death Areef Ishani 1,2, Craig A. Solid 1, Eric D. Weinhandl 1, David T. Gilbertson 1, Robert N. Foley 1,2 and Allan J. Collins 1,2 1 Chronic Disease Research Group, Minneapolis Medical Research Foundation, USA and 2 Department of Medicine, University of Minnesota, Minneapolis, MN, USA Abstract Background. A proportion of haemodialysis patients experience periods below target haemoglobin levels due to longer time required to reach the target or to haemoglobin level variability. We aimed to determine the consequences associated with cumulative number of months below target haemoglobin concentrations. Methods. We constructed an incident cohort including patients whose day 91 after dialysis initiation fell between 1 January and 31 December Haemoglobin concentration, erythropoiesis-stimulating agent dose, comorbid condition and hospitalization data were obtained from Medicare claims. Patients were classified by 0, 1, 2 or 3 months with haemoglobin concentration below the K/DOQI target (11 g/dl). Using an inverse probability weighted marginal structural model to adjust for time-varying factors associated with haemoglobin concentration, we determined the association between number of months below target and subsequent risk for hospitalization and mortality. Results. The final cohort included patients who met criteria. Those with more months below haemoglobin target were less likely to have received intravenous iron. More months below target were associated with increased risk of hospitalization (RR 1.70, 95% CI ) and mortality (RR 2.48, 95% CI ). Conclusions. Future interventions should focus on modifiable factors associated with greater time below target haemoglobin concentrations to determine whether altering the time below target can alter the risk of hospitalizations or mortality. Keywords: Erythropoiesis-stimulating agent; haemoglobin level; hospitalization; mortality Correspondence and offprint requests to: Areef Ishani, Chronic Disease Research Group, Minneapolis Medical Research Foundation, 914 South 8th Street, Suite S-253, Minneapolis, MN 55404, USA. Tel: ; Fax: ; AIshani@cdrg.org Introduction Several studies have defined the association between anaemia and adverse health outcomes among haemodialysis patients. Randomized controlled trials have demonstrated an association between anaemia and reduced quality of life and data conflict regarding progression of left ventricular hypertrophy [1 6]. Observational studies have suggested an inverse relationship between haemoglobin concentration, risk of hospitalization and mortality and cost among haemodialysis patients [7 14]. Given the available evidence, the National Kidney Foundation-Kidney Disease Outcomes Quality Initiative (K/DOQI) guidelines recommend a target haemoglobin of at least 11 g/dl among haemodialysis patients [15]. Since publication of these guidelines in 1997, the percentage of patients achieving target haemoglobin concentrations has increased due to earlier initiation, higher doses of erythropoietin and increased use of parenteral iron [16,17]. While overall haemoglobin values have increased, a proportion of incident haemodialysis patients experience periods below target due to longer time required to reach the target level or to haemoglobin level variability [18]. The consequences associated with the cumulative number of months below target haemoglobin concentrations have not been studied extensively. Previous studies have attempted to define the association between time to target haemoglobin concentration and outcomes [13,19]. Using a variety of methodologies, including time-dependent Cox models and propensity scores, these studies have demonstrated that persistently low haemoglobin concentrations are associated with increased risks of hospitalization and mortality. However, in addition to baseline population differences, significant timevarying features influence both the predictor (haemoglobin) and outcomes, leading to potential bias when using conventional analytic techniques such as time-dependent Cox models [20]. Specifically, haemoglobin concentrations over time are influenced by ongoing comorbid conditions, hospitalizations, previous erythropoietin dose and previous haemoglobin concentrations. Current haemoglobin values determine future therapy with erythropoietin and iron. C The Author [2007]. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved. For Permissions, please journals.permissions@oxfordjournals.org

2 Haemoglobin targets and hospitalization and mortality risk 1683 Haemoglobin has been demonstrated to be an independent predictor of both hospitalization and survival. The problem of time-dependent confounders, affected by prior treatment, with standard analytic techniques can be addressed using marginal structural modelling (MSM). MSM is a methodology for estimating the causal effect of a timedependent exposure in the presence of time-dependent covariates that may be simultaneous confounders and intermediate variables [21 23]. MSM attempts to create a pseudorandomized population that is balanced on all measured confounders [24]. Unlike randomized controlled trials, which balance on unmeasured confounders, MSM is unable to account for unmeasured confounders. Using MSM, we aimed to estimate if longer time to a threshold haemoglobin value of 11 g/dl in an incident haemodialysis cohort is associated with greater risk of hospitalization and death. Methods We performed a retrospective analysis of incident US haemodialysis patients using data from the United States Renal Data System (USRDS), a national system that collects information on all new dialysis patients in the United States. The information includes comorbid conditions, selected laboratory values and functional status at dialysis initiation. For individuals with Medicare as primary insurance payer, the USRDS obtains Medicare claims data, forming the basis of longitudinal comorbidity adjustment. For individuals receiving erythropoietin, providers are required to report monthly haemoglobin concentrations and erythropoietin dose. The study included patients whose day 91 after haemodialysis initiation fell between 1 January and 31 December 2002 and who did not change renal replacement therapy modality or die before day 91 (n = ). Additionally, we required participants to have Medicare as primary payer on day 91 and to survive for at least 9 months after dialysis initiation, resulting in a final cohort size of (66.8%). Excluded patients tended to be younger (almost 70% aged <65 years) and were more often male, but distributions of race and primary cause of renal failure were similar (data not shown). We defined a patient clock for each individual, a series of exposure periods each with its own follow-up period. The first patient clock began with the first full calendar month after day 91. In MSM, patients are included in multiple, rolling, exposure periods, each with its own follow-up period [21]. Consequently, each individual may be included in multiple, overlapping exposure periods, each with his or her own unique outcome period. In this way, multiple, mutually exclusive outcome periods are analyzed for each patient and are adjusted for demographic characteristics, health encounters (from claims data, including diagnoses and procedures performed) and disease severity in the exposure period before the outcome and at baseline. Exposure months Because erythropoietin claims are required to ascertain haemoglobin levels, only individuals on erythropoietin therapy are included in the cohort. Because haemoglobin levels over multiple months are required to identify a persistent haemoglobin level, participants were required to have erythropoietin claims during a particular exposure period to be included in the analysis for that period. Participants were required to have three sequential months of erythropoietin claims to allow haemoglobin levels to stabilize [25]. Patients with mean haemoglobin values <11 g/dl in a month were identified as having low haemoglobin for that month. The total number of months (three) with low haemoglobin was calculated, giving each participant a score between 0 and 3. Total erythropoietin dose was obtained during the same month as the haemoglobin value, so erythropoietin claims for an additional month were not required of patients in the sample. Haemoglobin values reported in claims data are typically the second-to-last of the billing period; thus, almost all erythropoietin doses on the claims were administered before that haemoglobin measurement. Identifying covariates To establish each patient s expected haemoglobin level for each month, used to determine weights in MSM, hospital admissions and lengths of stay, blood transfusions, intravenous (IV) vitamin D, IV iron and comorbid conditions were identified from Medicare claims data in the period before each exposure month. In an attempt to ensure that patients had adequate exposure for those adjusters without extending the exposure period for too long, we identified hospitalizations, anaemia treatment and comorbid conditions in the 3-month period before the three sequential months of erythropoietin claims. These data together with data obtained from the three sequential months of erythropoietin claims allowed a total exposure duration of 6 months. Due to the relatively short exposure time, comorbid conditions were defined based on a single Part A or Part B claim. Demographic characteristics were obtained from the Identification and Medical Evidence portions of the Centers for Medicare & Medicaid Services (CMS) Renal Beneficiary Utilization System. Dialysis provider characteristics were obtained from the annual CMS end-stage renal disease facility survey. Each patient was linked to a specific dialysis provider through the CMS-assigned provider number. Outcomes Immediately following each exposure period was a 1-month outcome period, during which Medicare Part A claims were searched to identify inpatient hospital admissions, and the CMS Death Notification form (CMS-2746) was used to determine mortality. Hospitalization rates were calculated as the number of inpatient admissions divided by the time at risk during the month, where days already in the hospital were excluded from the time at risk. The time at risk for mortality rates included the entire follow-up month up to the date of death, regardless of whether or not the patient was in the hospital. Individuals were followed for up to 2 years after initiation, giving a total of 15 possible exposure/outcome periods. Thus, once individuals were defined as eligible for cohort entry, months 1 through 3 were used to define time-varying comorbid conditions (in addition to baseline information).

3 1684 A. Ishani et al. Months 4 through 6 were defined as the exposure period during which haemoglobin concentrations and erythropoietin doses were defined, and month 7 was used to define outcomes. For the next rolling period, months 2 through 4 were used to define time-varying comorbid conditions, months 5 through 7 were used to define haemoglobin concentrations and erythropoietin doses and month 8 was used to define outcomes. This rolling patient-clock methodology pattern continued until the end of study follow-up (15 periods). Estimation in MSM involves multiple steps. The first is obtaining the weights for each month of haemoglobin values, which was done by using logistic regression to obtain a propensity for each patient to have a low haemoglobin in that month given the adjusters obtained during the exposure period and the observed haemoglobin for the month. That was repeated for each month with a haemoglobin value in every exposure period for which that patient was included. Next, we constructed a marginal structural logistic model (to obtain odds ratios) and a marginal structural Poisson model (to obtain rate ratios) on the pooled set of rolling exposure/outcome periods, using the weights for each patient in each exposure period included in the total follow-up time, and information from the baseline time period. As estimates from the Poisson model are similar to those from the logistic model, only the logistic model is presented. Results The final study cohort included incident haemodialysis patients. Table 1 presents the total number of patients included in each of 15 identified exposure/outcome periods after applying the inclusion criteria (alive, on haemodialysis with Medicare as primary payer, and 3 months of erythropoietin claims) for each period. The final cohort is representative of individuals undergoing haemodialysis in the USA in demographic characteristics, primary cause of end-stage renal disease and dialysis unit characteristics (Table 2). In Table 1. Numbers of eligible patients per 6-month exposure period (study cohort n = ) Inclusion criteria Remained On haemodialysis with Valid erythropoietin Period alive Medicare as primary payer claims Table 2. Demographic variables (n = ) Variable N Percent Age (years) < to to Race White Black Other/unknown Gender Male Female Primary cause of ESRD Diabetes Hypertension Other/unknown Dialysis unit characteristics Profit status For-profit Non-profit Unknown Location Urban Rural Unknown Affiliation Chain Hospital Independent Unknown ESRD: end-stage renal disease. general, patients with persistently low haemoglobin levels had higher disease prevalence than those with at least 1 month with a haemoglobin level of at least 11 g/dl (Table 3). Patients with persistently low haemoglobin levels were the minority (Figure 1) as most patients respond to erythropoietin therapy within 2 to 3 months. Interestingly, those with persistently low haemoglobin levels seemed less likely to have received IV iron compared with those with haemoglobin levels >11 g/dl (Table 4). IV vitamin D use was similar in frequency and pattern across haemoglobin groups. Blood transfusions were rare, but slightly more common for patients with persistently low haemoglobin levels (data not shown). Unadjusted outcomes As expected, hospitalization and mortality were more common among patients with persistently low haemoglobin and increased steadily with increasing number of months with haemoglobin <11 g/dl. Regardless of the measure (raw mortality, relative mortality, raw hospitalization, hospitalization rate per time at risk) each additional month with low haemoglobin was associated with worse outcomes (Table 5). Even before adjusting for other covariates and employing MSM, these results demonstrate that, compared with patients with no months <11 g/dl, those with 3 months <11 g/dl were hospitalized more than twice as frequently and were between three and four times more likely to die during the follow-up month (Figures 2 and 3).

4 Haemoglobin targets and hospitalization and mortality risk 1685 Table 3. Comorbid conditions, exposure periods 1 through 15 Months Average across Months Average across Condition <11 g/dl periods a Condition <11 g/dl periods a Atherosclerotic heart disease COPD Congestive heart failure Gastrointestinal bleeding Cerebrovascular accident Liver disease Peripheral vascular disease Dysrhythmia Cardiac (other) Cancer COPD: chronic obstructive pulmonary disease. a Values are percents. Fig. 1. Percent of patients in each haemoglobin (Hb) group by a 6-month exposure period. Table 4. Percent of patients receiving no IV iron during exposure periods, by period and number of months with low haemoglobin Exposure period Months <11g/dL

5 1686 A. Ishani et al. Fig. 2. Percent of patients who died during the follow-up month by the number of months with haemoglobin <11.0 g/dl (0 month or 3 months). Adjusted outcomes The adjusted MSMs also demonstrate that persistently low haemoglobin is associated with increased risk of hospitalization and mortality (Table 6). Compared with patients with no months <11 g/dl, those with 3 months <11 g/dl were 1.8 times more likely to be hospitalized and almost 2.5 times more likely to die during the follow-up month. Additionally, the confidence intervals for each additional month s effect do not overlap, indicating that each additional month with a haemoglobin level below target adds to the cumulative risk of adverse outcome. Finally, when we substituted total erythropoietin dose in place of haemoglobin concentration, our results did not change. There was a significant, positive association between erythropoietin dose and the risk of hospitalization and mortality. This is not unexpected, as higher erythropoietin doses are highly correlated with low haemoglobin levels. Discussion We demonstrate, using an incident haemodialysis cohort, that 40% of patients require at least 1 month after day 91 on dialysis to achieve the lower limit of the K/DOQI haemoglobin targets. Additionally, in unadjusted analysis, those with more months below the target haemoglobin concentration were less likely to have received IV iron in the preceding months. We also demonstrate a progressive relationship between the number of months below the target haemoglobin concentration of 11 g/dl and the risk of hospitalization and mortality in the subsequent month. These results persisted in a marginal structural model that allows adjustment for differences in characteristics at baseline and for time-varying factors (ongoing illness and erythropoietin dose) related to both haemoglobin values and outcomes. Table 5. Percent, relative percent and relative rate of mortality and hospitalization by period and number of months with low haemoglobin Months Average <11 g/dl across periods Death (percent) Any hospitalization (percent) Hospitalization relative rate, unadjusted Specifically, each additional month with a haemoglobin concentration <11 g/dl was associated with progressive non-overlapping risk of hospitalization and mortality using both logistic regression and Poisson MSM models. Several factors have been associated with intractable anaemia and, to a lesser extent, require more time to reach target haemoglobin levels [18,26]. Institutional variability in anaemia care is a large, potentially modifiable factor associated with the inability to achieve target haemoglobin concentrations. For example, a recent study using a Medicare sample demonstrated that between 67 and 81% of individuals achieve the lower boundary of the K/DOQI haemoglobin target [27]. This variability is likely due in large part to institutional policies that are likely modifiable [28]. Use of catheters for vascular access has been associated with higher EPO doses, lower haemoglobin concentrations and increased risk of intractable anaemia [18,29]. Several mechanisms have been postulated to explain this association, including a higher risk of infection [30 39], an

6 Haemoglobin targets and hospitalization and mortality risk 1687 Fig. 3. Unadjusted hospitalization rate (per 100 patient-months) during the follow-up month by the number of months with haemoglobin <11.0 g/dl (0 month or 3 months). Table 6. Adjusted odds ratios from history-adjusted, time-dependent marginal structural models Outcome Months <11 g/dl Odds ratio 95% lower confidence limit 95% upper confidence limit P Death 0 Reference < < < Hospitalization 0 Reference < < < inflammatory state resulting from placement of the access [40] and possibly poor dialysis [41 44], though this mechanism is controversial. While iron administration in haemodialysis patients has increased steadily over time, a percentage remain who do not receive it; lack of IV iron has been associated with intractable anaemia (defined as at least 5 of 6 months with haemoglobin <11 g/dl) [18]. We confirm this finding by demonstrating that individuals with more time with haemoglobin concentrations below target were less likely to have received IV iron in the preceding months. These three factors, institutional variability, catheter use and lack of IV iron, represent opportunities for improvement in anaemia management. Future randomized controlled trials should determine if modification of these factors can decrease the time below target haemoglobin concentrations, and specifically if this reduction decreases the incidence of adverse outcomes. Numerous observational studies have suggested an inverse association between achieved haemoglobin concentration and risk of hospitalization, morbidity and mortality among dialysis patients [7 14]. These studies, along with modifications in CMS erythropoietin reimbursement, have led to widespread erythropoietin use among dialysis patients [45]. Recently, proposed haemoglobin concentration targets have come under question, especially the upper end of the K/DOQI target range ( 13 g/dl). The CREATE [46] and CHOIR [47] studies attempted to determine if higher haemoglobin concentrations were associated with improved outcomes in CKD patients not requiring dialysis. Neither study was able to demonstrate a benefit to higher haemoglobin concentrations and both suggested harm associated with higher haemoglobin concentrations. However, both studies have flaws [48]. While we have demonstrated that more months below the haemoglobin target of 11 g/dl are associated with greater risk of hospitalization and mortality, caution should be taken in applying our results, as any attempt to decrease the number of months below haemoglobin target may have the unintended consequence of exceeding the upper haemoglobin target, thereby potentially increasing adverse health outcomes. Our results are based on retrospective observational data and have all the limitations associated with retrospective registry studies. We attempted to mitigate these limitations by using extensive observational data and by using a new methodology for controlling baseline and time-varying confounding (MSM). Additionally, we used different models (logistic regression and Poisson) and multiple rolling exposure/outcome time periods. The main benefit of using

7 1688 A. Ishani et al. MSM is that results derived from this methodology more closely estimate the results of an intent-to-treat trial. However, this holds only under the assumption of no unmeasured confounders, which is likely not the case. For example, while we are able to adjust for the presence of comorbid conditions, we were unable to adjust for their severity. Similarly we were unable to adjust for factors for which we had no information, such as type of vascular access or inflammatory state, an important limitation of all multivariable models. Further, MSMs can lead to bias if the model used to obtain the propensity-score-based weights is incorrectly specified, or if the structural model of the MSM itself is incorrectly parameterized. An additional limitation of our study is the number of individuals who were ineligible to be included in our final cohort. Reasons for exclusion included primary insurance payer other than Medicare, haematocrit concentrations not reported to Medicare, not being on erythropoietin therapy, or infrequent haematocrit determination. Whether inclusion of these individuals would have altered our results, or whether our observations are generalizable to those excluded, is unknown. We demonstrate that greater time below the lower K/DOQI haemoglobin target is associated with increased risk of hospitalization and mortality in an incident haemodialysis cohort. Future interventions should target modifiable factors associated with a greater number months below target haemoglobin concentrations to determine if altering the time below target haemoglobin can alter the risk of hospitalizations or mortality. Acknowledgements. The authors thank Chronic Disease Research Group colleagues Shane Nygaard, BA, for manuscript preparation and Nan Booth, MSW, MPH, for manuscript editing. This study was supported by a research contract from Roche Laboratories, Nutley, NJ, USA. The contract provides for the authors to have final determination of the manuscript content. Conflict of interest statement. Areef Ishani, Craig A. Solid and Eric D. Weinhandl have no conflicts of interest with the subject matter of this study. David T. Gilbertson, Robert N. Foley and Allan J. Collins have received consulting fees from Roche. References 1. Cannella G, La Canna G, Sandrini M et al. Reversal of left ventricular hypertrophy following recombinant human erythropoietin treatment of anaemic dialysed uraemic patients. Nephrol Dial Transplant 1991; 6: Fellner SK, Lang RM, Neumann A et al. Cardiovascular consequences of correction of the anemia of renal failure with erythropoietin. Kidney Int 1993; 44: Foley RN, Parfrey PS, Morgan J et al. Effect of hemoglobin levels in hemodialysis patients with asymptomatic cardiomyopathy. Kidney Int 2000; 58: London GM, Zins B, Pannier B et al. Vascular changes in hemodialysis patients in response to recombinant human erythropoietin. Kidney Int 1989; 36: Pascual J, Teruel JL, Moya JL et al. Regression of left ventricular hypertrophy after partial correction of anemia with erythropoietin in patients on hemodialysis: a prospective study. Clin Nephrol 1991; 35: Silberberg J, Racine N, Barre P et al. Regression of left ventricular hypertrophy in dialysis patients following correction of anemia with recombinant human erythropoietin. Can J Cardiol 1990; 6: Churchill DN, Muirhead N, Goldstein M et al. Effect of recombinant human erythropoietin on hospitalization of hemodialysis patients. Clin Nephrol 1995; 43: Collins AJ, Li S, Ebben J et al. Hematocrit levels and associated Medicare expenditures. Am J Kidney Dis 2000; 36: Ma J, Ebben J, Xia H et al. Hematocrit level and associated mortality in hemodialysis patients. J Am Soc Nephrol 1999; 10: Madore F, Lowrie E, Brugnara C et al. Anemia in hemodialysis patients: variables affecting this outcome predictor. J Am Soc Nephrol 1997; 8: Ofsthun N, Labrecque J, Lacson E et al. The effects of higher hemoglobin levels on mortality and hospitalization in hemodialysis patients. Kidney Int 2003; 63: Regidor DL, Kopple JD, Kovesdy CP et al. Associations between changes in hemoglobin and administered erythropoiesis-stimulating agent and survival in hemodialysis patients. J Am Soc Nephrol 2006; 17: Robinson BM, Joffe MM, Berns JS et al. Anemia and mortality in hemodialysis patients: accounting for morbidity and treatment variables updated over time. Kidney Int 2005; 68: Xia H, Ebben J, Ma J et al. Hematocrit levels and hospitalization risks in hemodialysis patients. J Am Soc Nephrol 1999; 10: National Kidney Foundation-Dialysis Outcomes Quality Initiative. NKF-DOQI clinical practice guidelines for the treatment of anemia of chronic renal failure. Am J Kidney Dis 1997; 30: S192 S St Peter WL, Obrador GT, Roberts TL et al. 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8 Haemoglobin targets and hospitalization and mortality risk Powe NR, Jaar B, Furth SL et al. Septicemia in dialysis patients: incidence, risk factors, and prognosis. Kidney Int 1999; 55: Marr KA, Kong L, Fowler VG et al. Incidence and outcome of Staphylococcus aureus bacteremia in hemodialysis patients. Kidney Int 1998; 54: Dobkin JF, Miller MH, Steigbigel NH. Septicemia in patients on chronic hemodialysis. Ann Intern Med 1978; 88: Hoen B, Paul-Dauphin A, Hestin D et al. EPIBACDIAL:Amulticenter prospective study of risk factors for bacteremia in chronic hemodialysis patients. J Am Soc Nephrol 1998; 9: Kairaitis LK, Gottlieb T. Outcome and complications of temporary haemodialysis catheters. Nephrol Dial Transplant 1999; 14: Bonomo RA, Rice D, Whalen C et al. Risk factors associated with permanent access-site infections in chronic hemodialysis patients. Infect Control Hosp Epidemiol 1997; 18: Muirhead N, Hodsman AB. Occult infection and resistance of anaemia to rhuepo therapy in renal failure. Nephrol Dial Transplant 1990; 5: Macdougall I, Coles G, Williams J. Inhibition of a response to erythropoietin in the presence of infection or malignancy. Erythropoiesis 1992; 3: Ishani A, Collins AJ, Herzog CA et al. Septicemia, access and cardiovascular disease in dialysis patients: the USRDS Wave 2 study. Kidney Int 2005; 68: NKF-K/DOQI Clinical practice guidelines for vascular access: update Am J Kidney Dis 2001; 37: S137 S Athirakul K, Schwab SJ, Twardowski ZJ et al. What is the role of permanent central vein access in hemodialysis patients? Semin Dial 1996; 9: Ifudu O, Feldman J, Friedman EA. The intensity of hemodialysis and the response to erythropoietin in patients with end-stage renal disease. NEnglJMed1996; 334: Sehgal AR, Snow RJ, Singer ME et al. Barriers to adequate delivery of hemodialysis. Am J Kidney Dis 1998; 31: Dhingra RK, Young EW, Hulbert-Shearon TE et al. Type of vascular access and mortality in U.S. hemodialysis patients. Kidney Int 2001; 60: Powe NR, Griffiths RI, Anderson GF et al. Medicare payment policy and recombinant erythropoietin prescribing for dialysis patients. Am J Kidney Dis 1993; 22: Drueke TB, Locatelli F, Clyne N et al. Normalization of hemoglobin level in patients with chronic kidney disease and anemia. N Engl J Med 2006; 355: Singh AK, Szczech L, Tang KL et al. Correction of anemia with epoetin alfa in chronic kidney disease. N Engl J Med 2006; 355: Levin A. Understanding recent haemoglobin trials in CKD: methods and lesson learned from CREATE and CHOIR. Nephrol Dial Transplant 2007; 22: Received for publication: Accepted in revised form:

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