• Outcome analysis;
  • risk adjustment;
  • statistical process control


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix

Access to timely, risk-adjusted measures of transplant center outcomes is crucial for program quality improvement. The cumulative summation technique (CUSUM) has been proposed as a sensitive tool to detect persistent, clinically relevant changes in transplant center performance over time. Scientific Registry of Transplant Recipients data for adult kidney and liver transplants (1/97 to 12/01) were examined using logistic regression models to predict risk of graft failure (kidney) and death (liver) at 1 year. Risk-adjusted CUSUM charts were constructed for each center and compared with results from the semi-annual method of the Organ Procurement and Transplantation Network (OPTN). Transplant centers (N = 258) performed 59 650 kidney transplants, with a 9.2% 1-year graft failure rate. The CUSUM method identified centers with a period of significantly improving (N = 92) or declining (N = 52) performance. Transplant centers (N = 114) performed 18 277 liver transplants, with a 13.9% 1-year mortality rate. The CUSUM method demonstrated improving performance at 48 centers and declining performance at 24 centers. The CUSUM technique also identified the majority of centers flagged by the current OPTN method (20/22 kidney and 8/11 liver). CUSUM monitoring may be a useful technique for quality improvement, allowing center directors to identify clinically important, risk-adjusted changes in transplant center outcome.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix

The provision of timely, risk-adjusted outcome information is crucial to improving clinical care processes. Frequent, real time monitoring of surgical outcomes allows physician leaders to validate clinical process improvements or to identify potentially correctable practice patterns. While standard statistical techniques, including average mortality, risk-adjusted average mortality and multivariate modeling, can be used to identify changing levels of performance at a national level, they have been found to be relatively insensitive to small changes in outcomes that occur at the hospital level (1–4). Furthermore, over time, these methods are likely to produce false positive results due to the need for multiple comparisons of the same data.

The cumulative summation method (CUSUM) is a technique of continuous monitoring derived from industrial statistical process control techniques. CUSUM monitoring has been shown to be a sensitive method to identify persistent deviations from expected results. Recently, Steiner et al. developed a risk-adjustment method permitting clinical implementation of CUSUM in a diverse patient population (5). CUSUM has the potential to be used by transplant centers as a quality improvement and monitoring tool to determine the impact of changing clinical practice (e.g. the use of induction therapy) on transplant center outcomes adjusted for patient and donor risk factors. The CUSUM methodology uses currently collected data and will ‘signal’ when risk-adjusted, charted clinical outcomes reach a pre-determined threshold value. This signal may initiate a comprehensive review by the program to determine if CUSUM has generated a false positive signal or if the signal represents a true improvement or decline from previous performance.

This study was designed to demonstrate the utility of the CUSUM method for tracking and analyzing center outcomes using a cohort of transplanted patients at multiple centers. Data were collected for all patients who underwent kidney and liver transplantation during a recent 5-year period. CUSUM charts were constructed for all transplant centers, blinded to center identity; transplant centers with significant improvement or deterioration in performance were identified. As a validity test, transplant centers flagged for declining performance were compared with transplant centers identified using the existing evaluation methods of the Scientific Registry of Transplant Recipients (SRTR) and the Organ Procurement and Transplantation Network (OPTN).


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix

Data sources

Data from the SRTR were analyzed for all kidney and liver transplants performed between January 1997 and December 2001. The SRTR database includes information on all wait-listed candidates and transplant recipients in the United States, supplemented by mortality information from the Social Security Death Master File (6). Primary outcomes of interest were death at 1 year for liver recipients and graft failure, including death with a functioning graft, at 1 year for kidney recipients.

Multivariable logistic regression risk-adjustment model construction

Descriptive statistics were compiled and analyzed to assess the relationship between the available covariates and the outcomes of interest, using the Student's t-test and chi-square analyses, as appropriate. We used a stepwise procedure to select covariates that were significantly associated with mortality or graft failure (p < 0.05). Endpoints for the regression models were death at 1 year post-transplant (liver) and graft failure including death at 1 year post-transplant (kidney).

Multivariable models were adjusted for the following covariates: donor characteristics [living or deceased donor source, age, race, expanded criteria donor status (kidney), donor-to-recipient weight ratio [kidney], ethnicity [liver], deceased donor cause of death, weight [liver], anti-cytomegalovirus status [liver], history of cancer [liver], donation after cardiac death [liver], liver biopsy, deceased donor history of hypertension [kidney], deceased donor serum creatinine > 1.5 mg/dL [kidney]); recipient characteristics (age, ethnicity, race, cause of end-stage organ failure, HLA mismatches [kidney], panel reactive antibody (PRA) level [kidney], previous transplants [kidney], dialysis modality [kidney], body mass index [BMI; kidney], history of symptomatic peripheral vascular disease [kidney], angina pectoris [kidney], previous transfusions, medical condition at transplant, time on dialysis [kidney], drug-treated hypertension [kidney], insulin-dependent diabetes mellitus [liver], symptomatic cerebrovascular disease [liver], height [liver], serum creatinine [liver], uncontrollable variceal bleeding [liver], ascites [liver], incidental tumor found at transplant [liver], previous upper abdominal surgery [liver], inotropes for blood pressure support [liver], portal vein thrombosis [liver], split liver transplant, geography—local, regional, or national [liver]); and cold ischemia time [kidney] (7). All data were blinded with regard to patient and transplant center identity. During the development of the renal transplant model, separate models were constructed for deceased donor and living donor kidney transplants. In this analysis, the receiver operating characteristic (ROC) curves for these models were nearly identical for the individual models and the combined (0.66 and 0.64, respectively, vs. 0.68). Thus, in this initial investigation the combined model was used for further analyses. In addition, because this was a retrospective analysis, values were missing for at least one significant variable in a sizable minority of the patients. The variables with the highest rate of missing values were donor to recipient weight ratio (missing in 33%) and recipient BMI (missing in 30%). Instead of dropping these cases from the analysis, binary indicators for missingness for given variables were included in the model as additional covariates to preserve these observations for CUSUM chart construction.

CUSUM chart construction

A separate CUSUM chart was constructed for each liver and kidney transplant center that was active during the 5-year period. Next, the CUSUM chart was analyzed to determine if center performance exceeded the a priori control limit of 3.0 when tuned to detect a doubling of the expected rate of graft failure (kidney) or mortality (liver) at 1 year. Similarly, CUSUM charts were constructed with the goal of identifying centers with a 50% reduction in graft failure or mortality, when the CUSUM exceeded a threshold value of 5.0, to increase the specificity for center improvement. Centers in which the CUSUM chart signaled a significant deterioration in performance were identified and compared with centers identified using existing statistical methodology (8). A detailed description of the CUSUM methodology is provided in the Appendix.

Current SRTR/OPTN center-specific report methodology

The SRTR provides quarterly reports to the OPTN Membership and Professional Standards Committee (7). In these analyses, individual centers are flagged for review if 2-year, center-specific outcome meets the following criteria: observed-to-expected failure ratio exceeds 1.5, the difference between the observed and expected outcomes is statistically significant (p < 0.05), and the absolute number of excess deaths or graft failures exceeds three (1). Centers identified by the SRTR methodology were compared in a blinded fashion with those identified using the CUSUM technique.

Data analysis

Data analyses were conducted using SAS 9.1 (SAS Institute, Cary, NC, USA). The project was approved by the University of Michigan Medical School Institutional Review Board.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix

Kidney transplants

A total of 59 650 kidney transplants were performed at 258 transplant centers during the period of study. Overall, 9.2% of renal allografts failed within 1 year (including death with a functioning graft). Donor and recipient characteristics are summarized in Tables 1 and 2. Among the 258 centers, there was a very large range in the rate of graft failures in the first year post-transplant (mean 9.0%; range 0–66.7%).

Table 1.  Renal transplant donor characteristics
Living Donor36.5
Deceased Donor Cause of Death
 Head trauma29.2
 CNS tumor0.7
Donor age (years)
Donor race
 Other (not White, African-American or Asian)1.3
Deceased donor serum creatinine > 1.5 mg/dL6.9
Deceased donor history of hypertension12.4
Expanded criteria donor9.9
Donor-to-recipient weight ratio
 Quartile 1 (0–0.75)15.1
 Quartile 2 (0.75–0.90)12.5
 Quartile 3 (0.90–1.15)19.3
 Quartile 4 (1.15+)20.2
 Weight ratio missing33.0
Table 2.  Renal transplant recipient characteristics
Variable% (or Mean)
Recipient age (years)
Recipient ethnicity
Recipient race
 Other (not White, African-American or Asian)2.2
Cause of end-stage renal disease
 Tubular and interstitial diseases5.6
 Polycystic kidneys8.8
 Congenital, rare familial and metabolic disorders1.5
 Renovascular and other vascular diseases4.6
 Hypertensive nephrosclerosis15.0
 Retransplant/graft failure9.2
 Glomerular diseases25.6
Number of A mismatches
Number of B mismatches
Number of DR mismatches
Peak PRA
 PRA missing0.9
Previous transplant13.5
Dialysis status
 No dialysis13.5
 Peritoneal dialysis17.0
 Dialysis—unknown type was performed1.7
Recipient BMI
 BMI Missing30.3
Symptomatic peripheral vascular disease3.8
Symptomatic peripheral vascular disease missing9.1
Angina/coronary artery disease9.6
Any previous transfusions30.4
Previous transfusions unknown or missing18.7
No previous transfusions50.9
Medical condition hospitalized, in ICU or on life support2.4
Time on dialysis (years)3.56
Preemptive or date of first dialysis missing13.2
Drug-treated systemic hypertension82.2
Drug-treated systemic hypertension missing7.1
Cold ischemia time (hours)

Multivariable logistic regression analysis included 25 donor and recipient characteristics (Table 3). For the overall cohort, the area under the ROC curve attributable to the model was 0.68. After risk adjustment using this model, the predicted probability of graft failure at 1 year for the average recipient ranged from 1.9% to 22.2% among the transplant centers studied.

Table 3.  Renal transplant risk-adjustment model
VariableAdjusted odds ratiop-value
Donor Cause of Death
 None—living donor0.73<0.0001
 Head trauma1.00Ref
 CNS tumor0.690.0658
Donor age (years)
Donor race
 Other (not White, African-American or Asian)1.030.8440
Deceased donor serum creatinine > 1.5 mg/dL1.200.0003
Deceased donor history of hypertension1.21<0.0001
Expanded criteria donor1.180.0096
Donor-to-recipient weight ratio
 Quartile 1 (0–0.75)1.190.0015
 Quartile 2 (0.75–0.90)1.190.0014
 Quartile 3 (0.90–1.15)0.990.7679
 Quartile 4 (1.15+)1.00Ref
 Weight ratio missing1.230.0002
Recipient age (years)
Recipient ethnicity
Recipient race
 Other (not White, African American or Asian)0.900.3210
Cause of end-stage renal disease
 Tubular and interstitial diseases1.210.0053
 Polycystic kidneys0.800.0008
 Congenital, rare familial and metabolic disorders1.030.8333
 Renovascular and other vascular diseases1.160.0418
 Hypertensive nephrosclerosis1.190.0005
 Retransplant/graft failure1.200.0265
 Glomerular diseases1.00Ref
Number of A mismatches
Number of B mismatches
Number of DR mismatches
Peak PRA
 PRA Missing0.850.4187
Previous transplant1.190.0148
Dialysis status
 No dialysis0.820.0019
 Peritoneal dialysis1.010.8031
 Dialysis—unknown type was performed1.030.7922
Recipient BMI
 BMI missing1.180.0012
Symptomatic peripheral vascular disease1.260.0018
Symptomatic peripheral vascular disease missing1.010.9028
Angina/coronary artery disease1.120.0146
Any previous transfusions1.120.0010
Previous transfusions unknown or missing1.060.1180
No previous transfusions1.00Ref
Medical condition hospitalized, in ICU or on life support1.46<0.0001
Time on dialysis (years)1.010.0023
Preemptive or date of first dialysis missing0.860.0250
Drug treated systemic hypertension0.880.0011
Drug treated systemic hypertension missing0.960.6484
Cold ischemia time (hours)

Using a signaling control limit of 3.0 and a CUSUM tuned to detect a doubling of the risk-adjusted incidence of graft failure, 52 centers (20%) were flagged by CUSUM over the 5-year period. The CUSUM chart of a representative center with declining performance demonstrates a dramatic increase in the incidence of graft failure beginning at transplant number 230 (Figure 1). The CUSUM methodology also demonstrated significant improvement in 92 centers whose 1-year graft failure rate was reduced by at least 50%. This improvement may reflect a natural learning curve effects (Figure 2) or may be due to an abrupt change in clinical practice (Figure 3).


Figure 1. CUSUM chart of renal transplant center with declining performance.

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Figure 2. CUSUM chart of renal transplant center with evidence of improvement consistent with a learning curve effect.

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Figure 3. CUSUM chart of kidney transplant center with a statistically significant improvement in outcome.

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Among the 52 centers identified as having a period in which graft failure rates were unexpectedly high, 20 (38%) were also flagged using the existing statistical methodology reported in national center-specific reports (2). Two centers (0.8% of all comparisons) were flagged by existing methods and not by CUSUM. Centers flagged by both the CUSUM method and current techniques had an average graft failure rate of 16.1% versus 7.6% at the centers not flagged by either method (p < 0.0001).

Liver transplants

Over the 5-year period of this analysis, 18 277 patients underwent liver transplantation at 114 transplant centers. Overall 1-year mortality was 13.9% and ranged from 0% to 50% among the centers studied. The 5-year transplant volume averaged 160 transplants per center (range 1–724). Demographic characteristics of the liver donors and recipients are summarized in Tables 4 and 5.

Table 4.  Liver transplant donor characteristics
Variable% (or Mean)
Donor Age (Years)
 Age missing0.2
Donor ethnicity
Donor race
 Other (not Black or White) or missing2.8
Donor cause of death
 Head trauma43.4
Log of donor weight4.25
Donor weight missing0.6
Donor anti-CMV Positive59.0
Donor history of cancer2.3
Donation after cardiac death0.8
Donor liver biopsy13.7
Table 5.  Liver transplant recipient characteristics
Variable% (or Mean)
Recipient Race
 Other or missing6.0
Recipient ethnicity
Recipient age (years)
Recipient insulin-dependent diabetes7.4
Recipient symptomatic cerebrovascular disease0.5
Recipient previous transfusions32.9
Cause of end-stage liver disease
 Acute hepatic necrosis7.9
 Cholestatic liver disease/cirrhosis12.7
 Metabolic diseases3.0
 Malignant neoplasms3.3
 Non-cholestatic cirrhosis69.8
Recipient medical condition
 Recipient on life support at transplant7.5
 Recipient in ICU, not on life support at transplant12.6
 Recipient hospitalized, not in ICU at transplant15.5
 Recipient not hospitalized at transplant64.4
Log of recipient height5.14
Recipient height missing3.4
Log of recipient creatinine (set to 4 mg/dL for patients on dialysis)0.06
Complications of ESLD
 Variceal bleeding5.9
 Ascites missing4.9
Incidental tumor found at time of transplant3.7
Recipient previous upper abdominal surgery43.4
Recipient inotropes for blood pressure support4.2
Recipient portal vein thrombosis2.1
Partial or split liver transplant6.3
 Regional transplant19.2
 National transplant9.7
 Local transplant71.1
Living donor4.6

A multivariable logistic regression model was developed for risk adjustment. The model included 27 donor and recipient characteristics (Table 6). The overall area under the ROC curve was 0.66. Donor characteristics associated with significantly higher 1-year mortality rates included increased donor age and African-American race. Significant recipient factors included a history of diabetes mellitus, cerebrovascular disease, older age, a diagnosis of a malignant neoplasm and requiring intensive care unit admission pre-operatively. After risk adjustment, the overall predicted probability of death at 1 year for the average recipient was 12.1% and varied from 6.4% to 37.6%.

Table 6.  Liver transplant risk-adjustment model
VariableAdjusted odds ratiop-value
Donor age (years)
Donor ethnicity
Donor race
 Other (not African-American or White) or missing1.130.3314
Donor cause of death
 Head trauma1.00Ref
Log of donor weight0.790.0055
Donor weight missing0.430.0889
Donor anti-CMV positive1.050.3473
Donor history of cancer0.970.8232
Donation after cardiac death1.330.1977
Donor liver biopsy1.090.1576
Recipient ethnicity
Recipient race
 Other race (not African-American or White) or missing0.840.0694
Recipient insulin-dependent diabetes1.260.0026
Recipient symptomatic cerebrovascular disease1.990.0043
Recipient previous transfusions1.140.0058
Recipient age (years)
Cause of end-stage liver disease
 Acute hepatic necrosis1.160.0621
 Cholestatic liver disease/cirrhosis0.740.0001
 Metabolic diseases0.920.5322
 Malignant neoplasms1.410.0026
 Non-cholestatic cirrhosis1.00Ref
Recipient medical condition
 Recipient on life support at transplant2.12<0.0001
 Recipient in ICU, not on life support at transplant1.38<0.0001
 Recipient hospitalized, not in ICU at transplant1.44<0.0001
 Recipient not hospitalized at transplant1.00Ref
Log of recipient height0.490.0032
Recipient height missing1.150.2235
Log of recipient creatinine (set to 4 mg/dl for patients on dialysis)1.54<0.0001
Complications of ESLD
 Variceal bleeding0.980.8258
 Ascites missing1.500.0001
Incidental tumor found at time of transplant1.340.0063
Recipient previous upper abdominal surgery1.22<0.0001
Recipient inotropes for blood pressure support1.170.1163
Recipient portal vein thrombosis1.300.0632
Partial or split liver transplant1.190.2621
 Regional transplant1.100.0868
 National transplant1.280.0069
 Local transplant1.00Ref
Living donor0.950.8258

CUSUM charts were constructed for each liver transplant center and flagged for review at a control limit of 3.0. The CUSUM was initially tuned to detect a doubling in expected mortality. Over the 5-year period, 24 centers were flagged using the CUSUM method. A representative CUSUM chart for a center with declining performance is shown in Figure 4. The 1-year mortality rate for this center was 22.9% (1.65 times the overall national rate). This chart indicates higher than expected mortality throughout the period of examination. Subsequent analysis was conducted to identify centers with rapidly improving performance. During the period of study, improvement in performance was documented at 48 centers.


Figure 4. CUSUM chart of a liver transplant center with a significant decline in risk-adjusted outcome.

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Among the 24 centers flagged by CUSUM for declining performance, eight were also identified using current methodology. The average 1-year mortality rates among patients transplanted at the eight centers flagged by both methods were significantly higher than at centers not flagged by either method (22.1% vs. 12.2%; p < 0.0001). Three centers identified by the SRTR methods were not flagged by CUSUM. The average yearly volume of transplants at these centers was 13.7 (range 12–14.8). Although these centers had higher than expected 1-year mortality rates (21.7–27.8% vs. 13.9% for all other centers), there was insufficient volume for the CUSUM to signal at the chosen threshold level. Review of the CUSUM charts suggested that performance was declining but failed to reach the control limit.

Among the 16 centers not flagged using current methodology, there were periods of declining performance that appear to have been corrected internally (Figure 5). Review of the CUSUM chart suggests that there was a decline in clinical outcomes between transplants 50 and 90 followed by an abrupt clinical improvement. Given the blinded nature of this data, correlation with changes in clinical practice was not possible in this examination.


Figure 5. CUSUM chart of liver transplant center flagged by CUSUM for declining performance, which was followed by improvement.

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  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix

Our analysis has demonstrated the successful application of a continuously updated, risk-adjusted outcome monitoring technique for the evaluation of transplant center performance. Over the 5-year study period, 52 renal transplant centers and 24 liver transplant centers with a period of higher-than-expected graft failure and 1-year mortality, respectively, were identified using the CUSUM method. The CUSUM method also identified 92 kidney and 48 liver transplant centers with markedly improving clinical outcomes. The CUSUM method appears to have face validity when compared with existing techniques for assessing transplant center performance. Within the limits of current risk-adjustment techniques, CUSUM charting appears to offer a useful tool for transplant center management and quality improvement.

Center-specific transplant outcomes have been associated with a variety of factors, including center volume, case mix, immunosuppression management, donor quality and technical expertise (9–11). High volume has been correlated with improved outcomes for liver, kidney and heart transplant. In addition, there are important differences between centers related to case mix. Centers with higher numbers of African-Americans, older patients, repeat transplants and patients with lower socio-economic status are often noted to have worse outcomes. In addition, variation in donor supply and recipient demand may affect outcome. As waiting lists increase in size, liver transplants are performed for patients with more advanced disease, contributing to generally worse post-transplant outcome (11).

Therefore, effective performance assessment and improvement tools should include a risk-adjustment methodology. The CUSUM technique reported here includes the results of two logistic regression analyses designed to predict post-transplant outcome using donor and recipient data. Unfortunately, post-transplant survival remains very difficult to predict, as it reflects the intersection of donor, recipient, operative and post-operative factors (12). The ROC curves for the models in the current study (0.68 kidney and 0.66 liver) compare favorably with the index of concordance for the Cox regression models currently used to prepare the SRTR center-specific reports (0.67 for kidney and 0.70 for liver) (7). As is true with any risk-adjustment technique, these models remain imperfect tools for making comparisons between centers. However, within any single transplant center, the risk adjustments using various patient and donor characteristics that are available do improve the results provided by CUSUM charting.

Regular reporting of center-specific outcomes has been performed primarily by the SRTR, under provisions of the National Organ Transplant Act (13). The current method used to generate center-specific outcome reports uses Cox regression models and the indirect adjustment method; this provides expected outcomes by adjusting the national sample to mirror the center's case mix for relevant patient and donor factors. Observed results are compared with expected outcomes for each center twice per year, which can result in flagging due to chance (false positive), as a result of repeated comparisons (1,14). For center review purposes by the OPTN, this risk is minimized though the use of three assessment measures, including the absolute number of excess failures and the ratio of observed-to-expected failures, in addition to the test of statistical significance. However, for internal center management, this approach may miss early trends that could be identified through statistical process control techniques like CUSUM before externally applied measures of performance are triggered.

The modified CUSUM approach proposed by Steiner and colleagues provides a method of assessing surgical outcome using a risk-adjusted, continuously updated, easily interpretable chart (5). As applied in this analysis, clinical outcomes were weighted using a risk-adjustment model to assess the probability of 1-year mortality (liver) or 1-year graft failure (kidney). A pre-set signal level was then determined based on clinical judgment and the severity of the outcome of interest. Once the CUSUM chart reached this threshold, a signal was reported. CUSUM signaling does not necessarily prove that a clinically important decline or improvement in clinical quality has occurred. Rather, the signal suggests that closer examination by a program's quality improvement team may be indicated.

The CUSUM method has several distinct advantages over other techniques. First, the CUSUM technique explicitly accounts for the impact of time as a variable. Thus, multiple graft failures within a short time are more likely to generate a signal than if the same number of graft failures were randomly spread across a longer period of analysis (15). Second, empirical assessment of risk-adjusted CUSUM charts, also known as CRAM charts, demonstrated the greatest sensitivity in detecting clinically important deterioration in performance when compared with other statistical techniques (1). Third, unlike standard modeling techniques, the CUSUM charting method does not suffer from the problem of multiple statistical examinations of highly overlapping data, which is likely to produce false positive alarms. Finally, and perhaps most importantly, given the graphical nature of the CUSUM, the slope of the chart can provide valuable insight into transplant center performance even before a signal occurs. Thus, the CUSUM can be used as a real time tool to assist transplant centers in improving clinical practice and patient management protocols.

Like other statistical techniques, CUSUM entails a tradeoff between the desire to rapidly recognize changes in clinical practice (sensitivity) and the necessity of limiting the number of false alarms (specificity). In CUSUM analysis, this tradeoff is reflected in the average run length (ARL), which reflects the average number of transplants that would occur prior to the CUSUM signaling by chance if there was no true change in outcome. Ideally, an effective CUSUM analysis will have a long ARL when the process is in control and a short ARL when the process deviates from the expected results. In the case of transplant center outcomes, it is perhaps better to err on the side of over-signaling rather than to miss a clinically important deterioration in outcome. In our study, an a priori control limit of 3.0 was set. However, with experience, the CUSUM can be adjusted to improve the ratio of true positives to false positives to allow efficient application of quality improvement procedures (Appendix). Furthermore, the CUSUM chart requires that a specific point be chosen as the endpoint of interest (e.g. 1-year graft survival). Consideration of additional endpoints (e.g. 3-year graft survival) requires construction of alternative CUSUM charts and, potentially, a revised risk-adjustment model. Utilization of a short-term outcome is important if the CUSUM is to be successfully used as an active transplant center management tool.

This study represents the first report of CUSUM analysis for multiple centers using an endogenously derived risk-adjustment model. Previous examples of CUSUM monitoring in surgical analysis have been limited principally to single center studies to illustrate the learning curve inherent in new techniques. Novick and colleagues have applied CUSUM in a variety of analyses for outcomes following telerobotic cardiac surgery (3) and off-pump coronary bypass procedures (2). The authors reported that standard statistical methods failed to identify the reduction in the rate of complications over the course of the center's learning experience with telerobotic cardiac surgery that was clearly evident in CUSUM analysis. Similarly, Forbes and colleagues examined the outcome of endovascular aneurysm repair (4). Using CUSUM analysis, they demonstrated that the learning curve for endovascular repair was nearly 60 patients, which was much longer than expected. Finally, the United Kingdom Transplant Service has begun supplying its members with CUSUM charts designed to assess 30-day renal graft failure (D. Collett, Director of Statistics and Audit, UK Transplant, personal communication April 1, 2005). These reports have assisted transplant center directors in determining whether or not a series of graft failures is likely to be due to chance or is a reflection of transplant center modifiable issues of medical and/or surgical management.

There are several important limitations in our analysis. First, to protect center confidentiality, we did not validate CUSUM findings with changes in clinical management or process at the blinded centers. Therefore, it was not possible to determine whether centers flagged by CUSUM analysis had experienced a genuine change in outcome that resulted from a change in clinical practice or, by chance, had experienced several adverse outcomes in rapid succession. Prospective application of the CUSUM technique is necessary to accurately assess the ratio of true positive to false positive signals. Because CUSUM can be set up as a very sensitive method of detecting changes in clinical outcomes, its best application would appear to be as a quality improvement and management tool at the transplant center level, rather than as a replacement or addition to existing OPTN methodology. Second, the risk-adjustment methodology remains imperfect. This analysis made use of all available clinical data elements; further refinement in the risk-adjustment model may require the collection of more detailed data. Furthermore, the presence of missing data may have affected the model, and future implementation should require that data from all relevant fields are included. As with any measure of outcome, a careful review of all relevant data must be conducted to eliminate the possibility that there has been a false positive signal prior to changing clinical practice. Finally, because this analysis is retrospective and other OPTN-based center outcome measurements were already being performed, it was not possible to determine the incremental benefit of concurrent CUSUM reporting on center outcomes. A prospective trial of this method in which CUSUM results are returned regularly to program directors would be useful to assess the potential utility of the technique for transplant center quality improvement.

In summary, CUSUM techniques can be used to assist transplant centers in assessing their outcomes using a real time, risk-adjusted process. Further analysis and prospective studies are needed to assess the impact of CUSUM monitoring on center outcomes and to fine tune the analysis to balance the need for early identification of genuine changes in care with the desire to reduce unnecessary scrutiny.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix

This work was supported by contract number 231-00-0116 from the Health Resources and Services Administration, U.S. Department of Health and Human Services. Presented in part at the American Transplant Congress, May 2004, Boston, MA.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix
  • 1
    Poloniecki J, Sismanidis C, Bland M, Jones P. Retrospective cohort study of false alarm rates associated with a series of heart operations: the case for hospital mortality monitoring groups. BMJ 2004; 328: 375.
  • 2
    Novick RJ, Fox SA, Stitt LW et al. Cumulative sum failure analysis of a policy change from on-pump to off-pump coronary artery bypass grafting. Ann Thor Surg 2001; 72: S1016S1021.
  • 3
    Novick RJ, Fox SA, Kiaii BB et al. Analysis of the learning curve in telerobotic, beating heart coronary artery bypass grafting: a 90 patient experience. Ann Thorac Surg 2003; 76: 749753.
  • 4
    Forbes TL, DeRose G, Kribs SW, Harris KA. Cumulative sum failure analysis of the learning curve with endovascular abdominal aortic aneurysm repair. J Vasc Surg 2004; 39: 102108.
  • 5
    Steiner SH, Cook RJ, Farewell VT. Risk-adjusted monitoring of binary surgical outcomes. Med Decis Making 2001; 21: 163169.
  • 6
    Social Security Administration Death Master File. Springfield , VA : Federal Computer Products Center, National Technical Information Service, U.S. Department of Commerce ; 2003.
  • 7
    Scientific Registry of Transplant Recipients: Center-Specific Reports. Available at Accessed September 23, 2005.
  • 8
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  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Appendix

APPENDIX: Statistical Methods for Quality Monitoring Using a CUSUM Chart


The CUSUM method accumulates evidence about an ongoing process (e.g. a series of surgeries) to identify a clinically important change in performance. Mathematically, the technique involves plotting a continuous sum of the scores (outcomes) versus time. If the process remains ‘in control’, resulting in expected surgical outcome, the CUSUM will remain near zero. If the surgical results deteriorate, the CUSUM will increase. When the score exceeds a pre-set value, the chart is said to signal.

Calculation of the CUSUM:

As proposed by Steiner and colleagues, the CUSUM (Xt) is calculated as a continuous sum of wt, a weighted score that depends upon the patient's predicted pre-operative risk (5). As shown in Equation 1, three factors are included in the calculation of wt:

  • pt: the patient's predicted risk of death as derived from a logistic regression model.

  • ORA: a pre-determined ratio of expected versus actual outcomes. To detect a doubling of expected mortality, ORA would be set to 2.

  • y: an indicator variable equals 1 if there is a transplant failure and zero if the transplant is successful.

The CUSUM (Xt) is calculated using Equation 2. Based upon Equation 1, a transplant failure results in a positive value that increases the CUSUM by a risk-adjusted amount, while a success reduces the score. The CUSUM score is restricted to non-negative values to increase the sensitivity to detect clinical failures.

Equation 1:

  • image

Equation 2:

  • image
Signaling and Average Run Length

Because a transplant success results in a negative value, the CUSUM score will remain close to 0 for an in-control process. However, if a cluster of failures occurs, the CUSUM will rise. The CUSUM chart signals a change in performance when the sum of wt reaches or exceeds a pre-set control limit (h). Choosing an appropriate control limit is empirical and reflects the trade off between sensitivity and specificity. A high control limit will reduce the number of false positive signals, but will require more failures prior to signaling. Conversely, a lower control limit will increase the sensitivity of CUSUM to clusters of surgical failures at the expense of false alarms. The average length of time prior to signaling, referred to as the average run length (ARL), is a reflection of the choice control limit. Ideally, the ARL should be long for processes that are in control and short for processes out of control. Determination of the appropriate value of (h) is an empiric process. As shown below, the number of centers flagged for review varies considerably according to the chosen control limit (Table).

Table 7. 
Control Limit (h)Number of centers flagged (Kidney)Ratio CUSUM flagged to SRTR flagged (Kidney)Number of centers flagged (Liver)Ratio CUSUM flagged to SRTR flagged (Liver)
Analysis of CUSUM data:

Following a CUSUM signal, an examination of the process under review should be undertaken. A signal is not proof of a failure in care. Rather, it represents the canary in the mineshaft, which may alert the transplant team to the potential need for a revision in care plans or technique. Furthermore, the CUSUM can also be adjusted to reflect improving care, and therefore demonstrate the positive impact of a change in care (e.g. the impact of induction therapy on graft outcome).