CERIM, EA 2694, Faculty of Medicine, Research Department, 1 Place Verdun, F-59045, Lille, CEDEX, France

University of Lille, Lille, France

Department of Biostatistics, EA2694, UDSL, Lille, France

Nephrology Department, CHU, Lille, France

Nephrology Department, EA 4003, INSERM CIC-EC CIE6, Nancy University, Nancy, France

Abstract

Background

In survival analysis, patients on peritoneal dialysis are confronted with three different outcomes: transfer to hemodialysis, renal transplantation, or death. The Kaplan-Meier method takes into account one event only, so whether it adequately considers these different risks is questionable. The more recent competing risks method has been shown to be more appropriate in analyzing such situations.

Methods

We compared the estimations obtained by the Kaplan-Meier method and the competing risks method (namely the Kalbfleisch and Prentice approach), in 383 consecutive incident peritoneal dialysis patients. By means of simulations, we then compared the Kaplan-Meier estimations obtained in two virtual centers where patients had exactly the same probability of death. The only difference between these two virtual centers was whether renal transplantation was available or not.

Results

At five years, 107 (27.9%) patients had died, 109 (28.4%) had been transferred to hemodialysis, 91 (23.8%) had been transplanted, and 37 (9.7%) were still alive on peritoneal dialysis; before five years, 39 (10.2%) patients were censored alive on peritoneal dialysis. The five-year probabilities estimated by the Kaplan-Meier and the competing risks methods were respectively: death: 50%

Conclusion

The competing risks method appears more appropriate than the Kaplan-Meier method for estimating the probability of events in peritoneal dialysis in the context of univariable survival analysis.

Background

Patients with stage 5 chronic kidney disease (CKD) can be treated by peritoneal dialysis (PD), hemodialysis (HD) or renal transplantation. The efficacy of PD is frequently assessed from the patient survival, estimated by the Kaplan-Meier method and compared to patient survival on HD using the Cox proportional-hazards model

A competing risk is an event which either hinders the observation of the event of interest, or modifies its probability of occurrence

Analysis of time-to-event data when competing risks are present requires specific methods because standard approaches can lead to estimation and interpretation errors

The purpose of the present study was to assess the validity of the survival estimations in PD obtained by the Kaplan-Meier method compared to the competing risks method developed by Kalbfleisch and Prentice in a cohort of 383 PD patients. The Kaplan-Meier method is often considered to estimate the survival that would be observed in the absence of transfer to HD or transplantation. We used simulations to investigate this assumption, and also tested the competing risks approach under the same conditions.

Methods

Patients

This study was performed at the Lille University Medical Center Nephrology Department (France). All consecutive incident patients starting PD treatment between January 1, 1992, and July 1, 2007 were included in the study. The cut-off date was January 1, 2008. Data on age, gender, diabetic status and primary renal diagnoses were collected at baseline. The primary renal diagnosis was classified according to the French renal epidemiology and information network

Statistical methods

The current paper only focuses on univariate methods for survival analysis. Two approaches can be used in the survival analysis of PD patients. In the intention-to-treat approach, death is taken into account if it occurs during PD or after transfer to HD

Estimation of event-free survival and cumulative incidences

Event-free survival is the probability of being free from any event, which corresponds here to the probability of staying alive on PD. All events are taken into account in this survival estimation, so that there is no competition between events. It can be assessed by the Kaplan-Meier method

The cumulative incidence function of cause

A: Event-free survival, which corresponds to the probability of staying alive on peritoneal dialysis (PD)

**A: Event-free survival, which corresponds to the probability of staying alive on peritoneal dialysis (PD). ****B-D:** Cumulative incidence estimations obtained by the Kaplan-Meier (KM) and the competing risks (CR) methods for: death during PD; renal transplantation; transfer to hemodialysis (HD).

Sum of probabilities estimated by the Kaplan-Meier and competing risks methods

**Sum of probabilities estimated by the Kaplan-Meier and competing risks methods.** Event-free survival (EFS) and the cumulative incidence curves for death, transfer to hemodialysis (HD), and renal transplantation (RT) are stacked. The upper line (in bold) represents the sum of probabilities of the different events.

Cumulative incidence of death for two simulated dialysis populations with exactly the same probability of death, obtained by the Kaplan-Meier method

**Cumulative incidence of death for two simulated dialysis populations with exactly the same probability of death, obtained by the Kaplan-Meier method.** The only difference between the two virtual centers is whether renal transplantation (RT) is available (center 2) or not (center 1).

Cumulative incidence of death and renal transplantation for two simulated dialysis populations with exactly the same probability of death, obtained by the competing risks method

**Cumulative incidence of death and renal transplantation for two simulated dialysis populations with exactly the same probability of death, obtained by the competing risks method.** The only difference between the two virtual centers is whether renal transplantation (RT) is available (center 2) or not (center 1). Dashed vertical lines show the estimates at 2, 5, and 10 years for each center.

Sum of probabilities

Death, transfer to HD, or renal transplantation were the only three events that could occur in a given patient. In their absence, patients were still alive on PD. By definition, these four states are mutually exclusive: a patient cannot simultaneously die and be transferred to HD, or be alive on PD and have a renal transplant. Therefore, at all time points, the sum of these probabilities must be equal to one.

Simulations with or without the availability of renal transplantation

The aim was to compare the survival estimates obtained for two identical cohorts, one with the presence and the other with the absence of competing risks. Such real data are not available for dialysis, because randomized controlled trials comparing dialysis alone to dialysis plus transplantation have never been carried out for ethical reasons. We therefore simulated two different situations in two virtual centers. To simulate an intention-to-treat analysis, which is the preferred approach in the survival analysis of patients on PD, two events only were taken into account: death or renal transplantation. The simulation was based on specific characteristics (age and the presence or not of diabetes) of the 383 patients in our cohort.

In virtual center 1, renal transplantation was not available. We used a Cox-Gompertz model to simulate the survival time for each patient

In virtual center 2, patients had the same survival times as in center 1, the difference being that renal transplantation was available. It has been reported that patients on the waiting list have a higher survival time than other patients

We compared the Kaplan-Meier estimations made for the two virtual centers with the Log rank test. To avoid a biased conclusion reached on the basis of a single simulation, the latter was repeated 100 times and the results were averaged. Six different simulations (repeated 100 times) were carried out to obtain six different proportions of patients on the waiting list in center 2: 5, 10, 20, 30, 40, and 50% of the population on dialysis. Lastly, we used the Kalbfleisch and Prentice method to estimate the cumulative incidences of death and renal transplantation in the two virtual centers.

Software

All statistical calculations were carried out using R software (R Development Core Team [2009], R: A language and environment for statistical computing) with the “Survival” and “Cmprsk” packages.

Results

Patients and observed outcomes

Three hundred and eighty-three consecutive incident patients were included in the study. Patient characteristics were presented in Table

**Patient characteristics**

**Patients (n = 383)**

SD: standard deviation.

Age, yr [mean (SD)]

56.5 (18.1)

Women

160 (41.8%)

Diabetes

100 (26.1%)

Primary renal disease

Glomerulonephritis

121 (31.6%)

Diabetes

54 (14.1%)

Vascular

44 (11.5%)

Pyelonephritis

34 (8.9%)

High blood pressure

16 (4.2%)

Polycystic kidney disease

15 (3.9%)

Other

51 (13.3%)

Unknown

48 (12.5%)

Event-free survival and cumulative incidence estimations

Death was taken into account during PD only, in terms of as-treated analysis. Event-free survival, which corresponds to the probability of staying alive on PD, was estimated at 12% at five years, as shown in Figure

Cumulative incidence curves for each event estimated by the Kaplan-Meier and Kalbfleisch and Prentice methods are shown in Figure

With the Kaplan-Meier method, the 109 patients transferred to HD and the 91 renal transplantations were censored to estimate the probability of death during PD. These 200 patients (51.6%) were considered to have the same risk of dying during PD as those patients still on PD. This led to a difference in the estimation of the cumulative incidence of death between the Kaplan-Meier method and the competing risks method, which amounted to 20% at five years. The sensitivity analysis showed that the results were similar for death and transfer to HD between the early- and late-inclusion patients (data not shown).

The sums of the reported probabilities at time

Simulations

Simulations were used to compare the survival estimations obtained for two identical cohorts in different competing risks settings. We simulated two virtual centers where patients had exactly the same characteristics and the same probability of death. The only difference between these two virtual centers was whether renal transplantation was available (center 2) or not (center 1). Death was taken into account on both PD and HD, according to an intention-to-treat analysis. One hundred simulations were carried out, and the results were averaged. In virtual center 1, where renal transplantation was not available, the median survival time was 6.3 ± 0.3 years. In virtual center 2, the mean number of patients on the waiting list was 145 (38%) ± 7 patients. The median waiting time before transplantation was estimated at 2.5 ± 0.2 years.

The cumulative incidence of death estimated by the Kaplan-Meier method is shown in Figure

The influence of censoring renal transplantation in the Kaplan-Meier estimations increased with the proportion of patients on the waiting list. The gap between the two cumulative incidence curves increased from 1.5% to 18% at ten years, when the proportion of patients on the waiting list had increased from 5% to 50% (data not shown).

With the competing risks method, the cumulative incidence of death was systematically lower in virtual center 2 than in virtual center 1, as shown in Figure

Discussion

In our study, the Kaplan-Meier method overestimated the probability of each event, i.e. death, transfer to HD, or renal transplantation during PD. This approach takes only one event into account, the other events being censored

The competing risks method provided accurate estimations of event probabilities when applied to our study cohort. In particular, the sum of the estimated probabilities amounted to one at all times. Our results showed that in the PD setting, crude cumulative incidences of each event could be estimated by means of the Kalbfleisch and Prentice method. Using this approach, patients who experienced an event were no longer at risk of death during PD. Consequently, cumulative incidence curves should not be interpreted alone

The Kaplan-Meier method is frequently considered to estimate the virtual survival rate in PD, i.e. that which would be observed in the absence of any competing risk. However, the results of our simulations were not consistent with this assumption. The probability of death estimated when renal transplantation was censored (center 2) was systematically higher than that estimated when renal transplantation was not available (center 1). This was due to the independence assumption underlying the censoring process, which assumes that individuals censored at time t have the same probability of developing the event of interest beyond time t as those who remain in follow-up

The use of the competing risks method is recommended in clinical settings where dependent events are present

The efficacy of PD is frequently assessed on the basis of patient survival and technical survival, estimated by the Kaplan-Meier method. The transplantation rate varies greatly between countries or centers

We applied the Kaplan-Meier and the competing risks methods to a single-center cohort of 383 consecutive incident patients, as recommended in the literature

Randomized controlled trials comparing dialysis alone to dialysis plus transplantation are viewed as unethical, and so have never been carried out. Data on patients for whom access to transplantation would constitute the only difference are therefore not available. Our response to this situation was to make use of simulations. We used a Gompertz model, which appears to be more appropriate than the exponential or Weibull models

As the aim of our study was to compare the two methods in general, and in particular to analyze the influence of competing risks on Kaplan-Meier estimates, the question of bivariate and multivariate analysis in a competing risks setting was not addressed here.

Conclusion

Our study has shown that the Kaplan-Meier method overestimated the probability of death in the competing risks setting of PD. The use of the competing risks method is recommended in survival analysis when several dependent events are possible. This approach is used in other fields of medicine, such as hematology

Competing interests

The authors declare that there are no competing interests.

Authors’ contributions

JBB and AD designed the study. DP, EB, and CL acquired the data. JBB and DP obtained funding. JBB, JS, and AD performed the statistical analysis. JBB, DP, and AD drafted the manuscript. EB, CL, and LF revised the manuscript for important intellectual content. JBB, DP, EB, CL, JS, LF, and AD gave their final approval regarding submission for publication. All authors read and approved the final manuscript.

Acknowledgment

This study was supported by a grant from Baxter Healthcare Corp. (Deerfield, IL). This company was not involved in any way whatsoever in the study or in the preparation of the manuscript.

Pre-publication history

The pre-publication history for this paper can be accessed here: