Transplant Statistics: Annual Report

Technical Notes and Analytic Methods
Center-Specific Graft and Patient Survival

Transplant center-specific graft and patient survival are presented as follows in Appendix A of the print copy of the Annual Report.

These tables are taken from the center-specific reports that were published on the SRTR Web site (www.ustransplant.org) in July 2001.  [These static tables are not reproduced in this electronic copy of the Annual Report. Instead the most recent center-specific survival data may be obtained at the SRTR Web site.]

Graft survival is the percentage of a cohort of transplants for which the graft was still functioning at the end of the follow-up time period after the transplant. Patient survival is the percentage of a cohort of transplants for which the patient was still alive at the end of the follow-up period. Patient survival is reported only for the first transplant of a given type for this patient. Graft and patient survival are reported for adult (age 18 and over) and pediatric (age under 18) patients. Survival is reported at three follow-up intervals after the transplant: one month, one year, and 34 months. The one month and one year follow-up periods are based on transplants performed between July 1, 1997, and June 30, 1999. The 34-month follow-up periods are based on transplants performed from July 1, 1995, and June 30, 1997.

Not all transplant recipients had complete graft or patient survival follow-up data through the end of the time interval since transplant. However, all available follow-up data for each graft was used in the calculation of the statistics reported here using standard censored data methods of survival analysis (Cox 1972, Kaplan-Meier 1958). An exception is that transplants with a graft failure date recorded as having occurred prior to the transplant (N=5 total for all organs) and transplants with no follow-up forms, missing last follow-up date or last follow-up date before the transplant (N=1,033 total for all organs) were analyzed as censored (lost to follow-up) one dayafter transplant. This means they do not affect the reported results, and they are included only to retain consistency with the reported number of transplants.

In addition to the actual survival, expected survival is estimated using a Cox model, as described below. Table 2.2 shows for each organ the groups that are included and whether expected survival is estimated using a Cox model. Six statistics are presented, as described in the next sections.

Number of Transplants

The total number of transplants reported during the accrual periods for the one-month, one-year and three-year graft survival analyses are shown for each patient age cohort. The one-month and one-year counts are the same since the accrued periods are the same. Note that for patient survival this line reports counts of patients receiving a first transplant only rather than all transplants and therefore will not be the same as the count of transplants in the graft survival portion of the tables.

Actual Graft Survival

A graft is counted as failed when follow-up information indicates that one of the following has occurred: graft failure, re-transplant, death, or dialysis treatment has been resumed (for kidney only).

The follow-up time for each graft (i.e., the days at risk) is the number of days from transplantation until graft failure (as defined above), last known follow-up date, or the reporting time point (e.g., one month, one year, or 34 months) occurs, whichever is earliest. Grafts that were known to be functioning at their last reported follow-up time were analyzed as censored if that time was before the reporting time point. The actual graft survival status at the reporting time point is not known for censored patients.

The Actual Graft Survival at one month, one year and 34 months was calculated from the follow-up data using the Kaplan-Meier method and is an estimate for the percentage of all grafts that would still be functioning at the reporting time point had they been followed to that time. In these calculations, the Kaplan-Meier method uses the incomplete data for patients who were lost before the end of the period.

After a patient was recorded as lost to follow-up on one follow-up record, any subsequent follow-up records were disregarded. These calculations do not include any deaths that occurred after loss to follow-up, since they are not consistently available in the current OPTN/SRTR data.

Actual Patient Survival

A patient is counted as having died when follow-up information indicates that a death has occurred prior to the reporting time point.

The follow-up time for each patient (i.e., the days at risk) is the number of days from transplantation until death, last known follow-up date for the transplant, or the reporting time point (e.g., one month, one year, or 34 months) occurs, whichever is earliest. Patients who were known to be alive at their last reported follow-up time were analyzed as censored if that time was before the reporting time point. The actual survival status at the reporting time point is not known for censored patients.

The Actual Patient Survival at one month, one year and 34 months was calculated from the follow-up data using the Kaplan-Meier method and is an estimate for the percentage of all accrued patients who would still be alive at the reporting time point had they been followed to that time. The Kaplan-Meier method uses the incomplete data for patients who were lost before the end of the period in these calculations.

After a patient was recorded as lost to follow-up on one follow-up record, any subsequent follow-up records were disregarded. These calculations do not include any deaths that occurred after loss to follow-up, since they are not consistently available in the current OPTN/SRTR data.

Expected Graft Survival

The Expected Graft Survival is the percentage of grafts that would be expected to be functioning at each reported time point, based on the national experience for patients similar to those at this center. The Actual Graft Survival can be compared with the Expected Graft Survival as the percentage of grafts functioning at the reporting time points. If the Actual Graft Survival is greater than the Expected Graft Survival, then the graft survival is better at this center than would be expected, based on the national transplant experience for similar grafts and patients.

The national experience was estimated using data for all grafts at all facilities in the United States. A Cox proportional hazards regression model for time to graft failure (Cox 1972) was fitted to the national data, which yielded the probability of graft failure for each patient, based upon the characteristics of each patient and the reporting time point. The characteristics accounted for in these calculations are reported below and are similar to those that have been used by the OPTN in previous reports. The Expected Graft Survival for each organ was adjusted for the patient characteristics. A complete description of the model is available on the SRTR Web site www.ustransplant.org. Details of the calculation of the Expected Graft Survival are presented in a later section.

Expected Patient Survival

The Expected Patient Survival is the percentage of patients who would be expected to be alive at each reported time point, based on the national experience for patients similar to those at this center. The Actual Patient Survival can be compared with the Expected Patient Survival as the percentage alive at the reporting time points. If the Actual Patient Survival is greater than the Expected Patient Survival, then the patient survival is better at this center than would be expected, based on the national transplant experience for similar patients.

The national experience was estimated using data for all accrued transplants at all facilities in the United States. A Cox proportional hazards regression model for time to death (Cox 1972) was fitted to the national data, which yielded the probability of survival to the reporting time point for each patient, based upon the characteristics of each patient and the reporting time point. The expected survival is the average of these computed probabilities. The characteristics accounted for in these calculations are reported below and are similar to those that have been used by the OPTN in previous reports. The Expected Patient Survival for each organ was adjusted for the patient characteristics as listed in the Model Description Tables. Details of the calculation of the Expected Patient Survival are presented in a later section.

For statistical comparisons, it is appropriate to compare the number of deaths observed during follow-up (which is shorter than the reporting time point for censored patients) to the number that would be expected during follow-up, rather than by comparison of observed and expected survival rates at the reporting time points.

P-value

The p-value measures the statistical significance (or evidence) for testing the (two-sided) hypothesis that the difference between the observed and expected graft survival is 0. A p-value less than or equal to 0.05 indicates that at least 95% of the time, the difference between the actual and expected patient survival is probably real and is not due to random chance alone, while a p-value greater than 0.05 indicates that the difference could plausibly be due to random chance alone. The p-value was calculated by testing whether the observed number of graft failures was statistically greater or less than the expected number of graft failures at a center, based on the Poisson distribution for the observed number of graft failures. These values are not shown if there is no expected graft survival calculated.

Statistically Different than Expected

This line indicates whether the actual graft survival is statistically different than the expected graft survival based on the p-value on the previous line. If the p-value is less than or equal 0.05 then this line reads "Higher" or "Lower," depending on whether the actual graft survival is higher or lower than the expected graft survival. If the p-value is greater than 0.05 then this line reads "Not Different." These values are not shown if there is no expected graft survival calculated.

Follow-up Days Reported

This line reports the percentage of days that are targeted for inclusion during the follow-up period relative to the number of days that were actually reported with follow-up forms. For grafts that did not fail before the end of the period, the targeted number of days of follow-up is the entire period (30, 365, or 1,035 days; see next section for details on maximum follow-up). For grafts that failed before the end of the period, the number of targeted days of follow-up is the number of days until graft failure. The number of days of reported follow-up is less than the targeted number of days for censored patients. Examples are shown in Table 2.3. The total number of days of follow-up reported for all patients are summed and divided by the total number of days of follow-up targeted to obtain the percentage reported in this line.

Patients with incomplete follow-up are included in the analyses until the date of the last reported follow-up. The presence of incomplete, or censored, data reduces the precision and interpretability of the statistics reported here. A low percentage may indicate a non-random sample from this center for follow-up. Examples of incomplete follow-up and the calculation of the percentage of follow-up reported are shown in Table 2.3.

See also the discussion of "Limitations of the Patient Survival Analyses."