The concept of relative survival was originally introduced as an outcome measure in population-based cancer survival analysis to approximate disease-specific survival in the absence of accurate and reliable information on causes of deaths (1). The method relies on dividing the observed absolute survival of a particular patient group by its expected survival, the latter being derived from life tables for the population from which the patients arise. Any death occurring among the patients beyond those that are expected are then supposed to be due to the disease at hand (or any comorbidity related to the disease). Relative survival is the standard measure in survival studies from epidemiological cancer registries (2–4), with recent applications in other medical field as well (5, 6).
In many human diseases, and also in solid organ transplantation, age is an important prognostic factor. Nominally, prognosis among older patients is often substantially worse than among younger peers (7). Although absolute survival estimates correctly reflect the actual survival chances of patients, they also inherently overestimate age-specific differences in prognosis, because they do not account for the differences in background mortality, which naturally contributes to lower survival levels among older patients. Relative survival estimates can be easily used to overcome this shortcoming of measuring age-related survival gaps.
In this study, we apply the relative survival methodology for the first time in the transplantation field to quantify transplantation-related surplus mortality among kidney transplant recipients in the United States.
Table 1 shows the donor type and age-specific numbers of patients who received a first kidney transplant overall between 1997 and 2009, and in the period of interest (2007–2009). In total, the number of first kidney transplants from deceased donors (100,391) was approximately 50% higher than the number of registered first kidney transplants from living donors (67,976). In the period of interest, patients with kidneys from living donors, the proportion of patients was fairly similar in the four adult age groups, with each of these contributing between 21% and 26% of patients. Recipients of kidneys from deceased donors were somewhat older, with a median age of 54 years compared with 48 years among recipients of living donor kidneys. In both donor groups, pediatric patients constituted the smallest group, with well below 10% of patients.
Table 2 provides age group and donor type specific estimates of 5-year observed (absolute), expected, and relative survival. All three survival measures decreased with age. Among recipients of kidneys from deceased donors, observed survival varied between 96.5% in the youngest and 72.8% in the oldest age group, with increasing age-specific declines for the two oldest age groups. Expected survival also decreased with age, and varied between 99.8% and 89.1% between the youngest and the oldest age group. After accounting for expected survival, the total age gradient of 23.7% units between the youngest and the oldest age group seen for absolute survival was reduced to 15% units for relative survival, which varied between 96.7% and 81.7%.
Observed survival estimates were higher among recipients of kidneys from living donors than among recipients of deceased donations, with the 5-year observed survival varying between 97.7% and 83.7% in the youngest and oldest age group, respectively. The age gradient between the youngest and the oldest age group was substantially smaller (14% units for observed survival) than seen among deceased donor recipients. Unsurprisingly, age-specific expected survival estimates were essentially equal to those seen for the deceased donor recipients group. Relative survival varied between 97.9% and 92.9% units, resulting in a total age gradient of 5% units among recipients of living donations, substantially smaller than the gradient seen among recipients of organs from deceased donors.
Table 3 provides age and donor type specific estimates of 10-year observed, expected, and relative survival. For both recipient groups, 10-year survival was lower, and age gradients were strongly increased in comparison with levels seen for 5-year survival. Among recipients of kidneys from deceased donors, observed survival varied between 93.0% and 43.9%, resulting in a total gradient of approximately 49% units, twice the gradient seen for 5-year survival. Over 10 years, expected survival was lower, particularly for older age groups, with estimates varying between 99.4% and 76.2%. Looking at relative survival, the age gradient was again reduced: relative survival varied between 93.5% and 57.6%, resulting in a total age gradient of approximately 36% units. Among recipients of organs from living donors, age-specific 10-year patient survival was uniformly higher than among recipients of organs from deceased donors, and observed survival estimates varied between 94.5% and 56.3%, resulting in an age gradient of approximately 38% units. Values of expected survival were again similar to those in the deceased donor group. Relative survival varied between 95.0% and 72.4%, resulting in a reduced age gradient of approximately 23% units, in comparison with the approximately 38% units seen for absolute survival.
This study provides the first application of the relative survival methodology in solid organ transplantation. The calculated relative survival estimates indicate that once differences in the general mortality of patients in different age groups is accounted for, age-specific differences in survival are substantially reduced between younger and older patients. In other words, this means that the effect of age is actually weaker as a prognostic factor than suggested by observed survival, as the latter is confounded by differences in general mortality. We also found a smaller age gradient in both absolute and relative survival among living donor recipients compared with deceased donor recipients. The survival of living donor grafts, potentially also due to factors inherent to the living organ itself (8, 9), is higher than the survival of deceased donor grafts, and this could possibly contribute to the differences seen in patient survival between the two donor groups.
In their essence, these results of this study are similar to those obtained in other medical areas in which the relative survival methodology has been applied before, notably cancer, the area where the methodology is generally applied for not only reporting population-based cancer survival estimates, but also HIV (5) and cardiovascular diseases (6). To our knowledge, a survival comparison between transplant patients and the underlying general population was only rarely done before (10, 11), and relative survival estimates were not calculated in those analyses.
Relative survival estimates may be interpreted in several closely related ways. The estimates quantify surplus mortality compared with the general underlying population from which the patients originate. Thereby, high relative survival estimates, as seen for younger transplant patients in this study, indicate that there is only a limited surplus mortality among kidney transplant recipients compared with the general population. In theory, a relative survival estimate of 100% would indicate that the patient group has the same mortality as the general population, in other words, that it experiences no condition-specific surplus mortality. Also, relative survival may be interpreted as a mortality measure in the hypothetical situation in which transplant-related causes of deaths were the only causes of death. In theory, such measures could be more directly estimated from cause-specific mortality. However, the correct attribution of the cause of death on death certificates is often problematic (12) and could cause major bias. Relative survival is not affected by these problems as it is calculated without using cause of death information.
For kidney transplant recipients, patients receiving long-term dialysis and transplant candidates on the waiting list have been used as clinical benchmark for survival comparison (13) and various other benchmarks may be used for other organs (14, 15). These comparisons enable the measuring of survival benefit from receiving a transplant in comparison with other forms of therapy or prognosis with organ failure, and can also help to improve organ allocation. Calculating relative survival/comparing transplant patient survival with that of the general population, while not clinical benchmark, seems justifiable in view of the good long-term prognosis already achieved for several types of solid organ transplants. Among other factors, adverse side effects of immunosuppression including increased infection risk (16) and malignancy (17, 18), and a higher prevalence of comorbidities as diabetes and cardiovascular disease may mean that transplant recipients have lower long-term survival chances than the general population. Relative survival estimates allow the quantification of this difference, and the monitoring of change thereof.
The relative survival estimates calculated here provide a summary measure for the excess mortality of transplant recipients compared with the general population, but do not quantify the relative contribution of the various reasons for excess mortality, such as renal disease, cardiovascular disease or diabetes, or transplantation-related complications. To quantify excess mortality due to the latter reasons, expected survival would have to be drawn from a matched patient sample with comparable comorbidity for whom pertinent life tables are currently not available.
Several methodological issues have to be considered when calculating relative survival. First, it is necessary that the patients for whom relative survival is calculated come from a well defined underlying population, such as a national or a regional population. Several different methods are available for the calculation of expected survival estimates, which differ only in the way they deal with changes in the age distribution of patients with the passing of time (causing, on the one hand, changes in the underlying age distribution of patients over time when prognosis is associated with age, and on the other hand, changes in the overall initial age distribution of patients in different time periods due to changes in patient mix over time). The Ederer II method (19) is most commonly used for calculating expected 5-year survival, whereas for long-term survival estimates (10 years and beyond), the Hakulinen method is mostly recommended (20). The standard error of relative survival is commonly estimated by dividing the standard error of observed survival (typically derived by the Greenwood formula ) by expected survival, even through this approach may overestimate to some extent the standard error of relative survival estimates (22).
As seen in this study, differences between absolute and relative survival estimates for younger patients were small. In general, in studies in which no elderly patients are involved, there is usually little need to quantify relative survival, as background mortality is usually negligible. When older patients are involved, or for comparative studies that involve patients coming from populations with differences in background mortality (these may exist between sexes, nations, ethnic groups, or even patients with different socioeconomic status), the calculation of relative survival estimates can be recommended, conditional on the existence of appropriate information on general mortality. The latter is ideally obtained from life tables relating to the specific underlying population, which are usually published by national and often also regional statistical offices. In the absence of such life table information, probabilities of deaths for single years of age intervals may be constructed from mortality data. Because of major sex differences and changes in general mortality and life expectancy over time, life tables should be sex specific and pertain to the time period for which survival is calculated.
In conclusion, this study suggests that comparisons of absolute survival estimates for younger and older patients are substantially influenced by differences in general mortality and may therefore be suboptimal in studies focusing on “disease-specific” age differences in survival. Relative survival estimates, which may be calculated not only for renal, but any other types of transplants, may be an important addition to the methods applied for epidemiological monitoring of transplant patient survival, and the use of this method may be encouraged for reporting population-specific survival estimates in solid organ transplantation in the future.
MATERIALS AND METHODS
Transplant and follow-up data were taken from the United Network for Organ Sharing (UNOS) data base as of October 31, 2010. The UNOS is the designated transplant agency of the United States and its database contains data on transplantations performed in the United States between 1987 and 2009. We selected first kidney transplants for this analysis, excluding multiorgan transplants and records with missing data on key survival analysis variables. Vital status was followed up without censoring in case of retransplantation. Patients were grouped into the age groups of 0 to 17, 18 to 39, 40 to 49, 50 to 59, and 60+.
We calculated period estimates of 5- and 10-year survival for the years 2007 to 2009, the most recent years for which data were available. Period estimates, which have been applied in the cancer field for calculating up-to-date survival estimates for over a decade (23–27), were recently shown (28, 29) to provide good predictions for the future survival of most recently transplanted organs and patients in solid organ transplantation. The method uses left truncation to include only the most recent survival experience into the survival calculation. Accordingly, for the 2007 to 2009 period, 5- and 10-year survival estimates are based on the survival experience of transplants performed during 2002 to 2009 and 1997 to 2009, respectively, with the survival experience being left truncated as of January 1, 2007. Figure 1 indicates the data utilization approaches for the calculation of 5- and 10-year survival estimates. Calculations were done using the SAS macro “period” (24, 30), which can be used to calculate observed and relative survival estimates. In practice, actuarial survival calculation involves the summing up of person time at risk and numbers of deaths for each follow-up year to determine the conditional survival probability for the particular follow-up year. During this procedure, using the demographic data of the patients, the expected numbers of deaths in the corresponding matched group of the general population is calculated using the age-, sex-, and ethnicity-specific survival probability of the general population as provided by the life tables for the latter. Relative survival is then calculated by dividing observed survival by expected survival of the matched group with similar age, sex, and ethnic distribution in the US general population. The expected survival estimates were calculated according to the Ederer II method (19), using age-, sex-, and ethnicity-specific life tables of the US general population for 2006, as published by the US National Center for Health Statistics (31). Life tables were available for whites, blacks (32), and Hispanics (33). UNOS ethnicity classification was used to determine the ethnicity of the patients, and the expected survival of other than the above ethnic categories was calculated using the life table for whites. The standard errors of survival estimates were calculated according to the Greenwood method (21).
In general, several practical approaches are available for the calculation of relative survival estimates. The SAS macros “period” and “periodh” (30) both derive absolute, expected, and relative survival estimates, and differ only in that the former uses the Ederer II method (19), whereas the latter the Hakulinen method (20) for calculating expected survival. On the basis of these macros, Poisson regression-based models have been developed (34, 35). Recently, a package in R has also been published (36). Other modeling applications (37), and detailed descriptions, code, and practical examples for estimating and modeling relative survival using both the SAS and the Stata statistical software systems are available online (38).
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