Nolwenn Le Meur
email: nolwenn.lemeur@ehesp.fr

Cécile Vigneau

Mathilde Lefort

Saïd Lebbah

Jean-Philippe Jais

Eric Daugas

Sahar Bayat

Categorical state sequence analysis and regression tree to identify determinants of care trajectory in chronic disease: example of end-stage renal disease

Keywords: categorical state sequence, regression tree, discrepancy, care trajectory, endstage renal disease

Background

Patients with chronic diseases, like patients with end-stage renal disease (ESRD), have long history of care driven by multiple determinants (medical, social, economic...).

Although in most epidemiological studies, analyses of health care determinants are computed on single health care events using classical multivariate statistical regression methods. Only few studies have integrated the concept of treatment trajectories as a whole and studied their determinants.

Methods

All 18 to 80-year-old incident ESRD patients who started dialysis in Ile-de-France or Bretagne between 2006 and 2009 and could be followed for a period of 48 months after initiation of a renal replacement therapy were included (n= 5 568). Their care trajectories were defined as categorical state sequences. Associations between patients' characteristics and care trajectories were assessed using a regression tree model together with a discrepancy analysis.

Results

On average, each patient experienced 1.56 different renal replacement therapies (min=1; max=5) during the 48 months of follow-up. About 55% of patients never changed treatment and only 1% tried three or more renal replacement therapy modalities. Twelve homogeneous care trajectory groups were identified. Covariates explained 12% of the discrepancy between groups, particularly age, regions and initiation of hemodialysis with a catheter.

Conclusions

Regression tree analysis of categorical state sequence highlighted geographical disparities in the care trajectory of French patients with ESRD that cannot be observed when focusing on a single outcome, such as survival. This method is an original tool to visualize and characterize care trajectories, notably in the context of chronic condition like ESRD.

INTRODUCTION

Patients with chronic diseases have long history of care driven by multiple determinants (medical, social, economic...). For instance, end-stage renal disease (ESRD) patients need renal replacement therapy (RRT). The treatment modalities (dialysis or renal transplantation) are chosen in function of each patient's characteristics and the local healthcare offer [START_REF] Robinson | Factors affecting outcomes in patients reaching end-stage kidney disease worldwide: differences in access to renal replacement therapy, modality use, and haemodialysis practices[END_REF] . During his/her care trajectory, a ESRD patient may undergo different RRT modalities to which are added interacting events (e.g., registration to the transplantation wait-list, temporal inactive status) that could affect morbidity, mortality and quality of life 2 . Better understanding the care trajectories of ESRD patients and their determinants is therefore an epidemiological issue.

Currently most epidemiological studies of ESRD patients have analyzed the effect of one RRT modality (compared to a reference) on a given outcome (e.g., access to transplantation, graft survival or death) using classical multivariate statistical regression methods. Only few studies have integrated the concept of treatment trajectories with the aim of predicting the future healthcare demands based on a few determinants as age or diabetes status [START_REF] Couchoud | Modelling treatment trajectories to optimize the organization of renal replacement therapy and public health decision-making[END_REF][START_REF] Roderick | Simulation model of renal replacement therapy: predicting future demand in England[END_REF] . Moreover these studies accounted for determinants independently [START_REF] Fritsche | Practice variations in the evaluation of adult candidates for cadaveric kidney transplantation: a survey of the European Transplant Centers[END_REF][START_REF] Stel | Prevalence of co-morbidity in different European RRT populations and its effect on access to renal transplantation[END_REF][START_REF] Ravanan | Variation between centres in access to renal transplantation in UK: longitudinal cohort study[END_REF][START_REF] Oniscu | Equity of access to renal transplant waiting list and renal transplantation in Scotland: cohort study[END_REF] and did not integrate the potential sequence of treatments along with the possible interactions between determinants that compose a patient care trajectory.

To decipher ESRD patient care trajectory, we propose to demonstrate the use of regression tree analysis applied to categorical state sequence objects (CSS) as published by Studer et al. [START_REF] Studer | Discrepancy Analysis of State Sequences[END_REF] First developed in social sciences to characterize individual life trajectories (e.g. occupational history, professional career or cohabitation life courses), categorical sequences analysis allows transversal aggregated views of longitudinal data such as medical care trajectories. In health services research, we demonstrated that clustering analysis of care trajectory defined as CSS allowed identifying homogenous groups of care trajectories among pregnant women that were partly explained by their socio-economical environment [START_REF] Meur | Mining care trajectories using health administrative information systems: the use of state sequence analysis to assess disparities in prenatal care consumption[END_REF] . Because cluster-based approaches consist on reducing the set of sequences to a limited number of standard trajectories, one loses information about the diversity within each cluster [START_REF] Studer | Discrepancy Analysis of State Sequences[END_REF] . Furthermore, knowledge of the cluster membership alone does not inform about the distances and differences between clusters. Therefore as proposed by Studer et al. [START_REF] Studer | Discrepancy Analysis of Complex Objects Using Dissimilarities[END_REF] , we suggested to use discrepancy analysis of CSS associated with a regression tree method to quantifies the amount of variation between medical care trajectories (sequences) that can be explained by covariates or their interactions.

Discrepancy among care trajectories can be derived from their pairwise dissimilarities, which permits then to identify factors that most reduce this discrepancy. In a public health context, this approach could help showing how care trajectories are related to covariates, such as patient characteristics, healthcare offer or geographical location. The latest is of importance in France as two studies already demonstrated that after taking into account medical and non-medical factors, placement on the kidney transplant waiting list is significantly associated with the region of residence, suggesting wait-listing practice differences [START_REF] Bayat | Individual and Regional Factors of Access to the Renal Transplant Waiting List in France in a Cohort of Dialyzed Patients: Renal Transplant Waitlisting in France[END_REF][START_REF] Lefort | Facilitating access to the renal transplant waiting list does not increase the number of transplantations: comparative study of two French regions[END_REF] .

In this paper, we (i) propose the use regression tree model on CSS as an original tool to characterize and visualize care trajectories, and (II) demonstrate its application on ESRD patient care trajectories by identifying groups of patients of homogeneous care trajectories explained by a mixture of covariates.

MATERIALS AND METHODS

Data

Data were extracted from the French Renal Epidemiology and Information Network (REIN) registry [START_REF] Couchoud | The renal epidemiology and information network (REIN): a new registry for end-stage renal disease in France[END_REF] . All 18 to 80-year-old incident patients with ESRD who started dialysis in Ile-de-France or Bretagne between 01/01/2006 and 12/31/2009 were included. ESRD patients older than 80 years of age were excluded because of their extremely low probability of access to the waiting list and transplantation. For comparison purposes, selected patients had to be followed for a duration of 48 months after the first RRT. Patients who underwent RRT for less than 48 months, received preemptive graft, moved to other regions, or were lost to follow-up were excluded as their treatment data were not available. [10-12] g/dl and >12 g/dl), presence of cardiovascular diseases (0,1, 2 or ≥3), diabetes (1/0), chronic respiratory disease (1/0), hepatic disease (1/0), active malignancy (1/0), physical disabilities (ambulation impairment, paraplegia or hemiplegia, member amputation, blindness; coded as ≥1 or 0), and HIV infection (1/0). Quantitative covariates were grouped into classes, as for age and hemoglobin levels. Binary variables were coded 1 and 0 for presence or absence of the characteristic for the patient, respectively.

Care trajectory definition

A care trajectory was composed by ordered suite of RRT modalities that defined a CSS 𝑋 = (𝑥 1, 𝑥 2 , … , 𝑥 𝑛 ), where 𝑥 𝑖 is a RRT modality (Figure 1). Two extra states were used to indicate the registration in the transplantation waiting list [WAITLISTED] and the death [DIED]. Death was forced as a state to better disentangle which patients' characteristics drive care trajectory whatever the health issue (i.e. survival or death) within the 48 months of follow-up. All calendar dates were converted into time intervals in month units starting at the first RRT and ranging from 1 to 48 months. State sequences of patients from Bretagne were given a weight of 4 to account for the 1:4 ratio difference in population size between Bretagne and Ile-de-France. treatment by in-center hemodialysis for 13 months after which he started hemodialysis in medical unit for 7 months and in the meantime he was registered to the transplantation waiting list (16 months after initiation of his RRT). After hemodialysis in medical unit, he received a graft at the 26 th month but died 8 months later (34 months after RTT initiation). For patients #2772 and #1628, the dashed purple rectangles highlight the common sub-sequences taken into account by the LCS algorithm to compute their similarity (and the dissimilarity).

Discrepancy measure and Regression tree for CSS

The regression tree was built following the ANOVA principles. CSS were recursively partitioned in two subgroups based on state sequence-covariate associations that minimize within-group discrepancies and maximize between-group variations.

Discrepancies (noted S 2 ) were determined using pairwise dissimilarities between patient's state sequences (Figure 1). Pairwise dissimilarities were computed using the longest common subsequence (LCS) distance algorithm as defined and available in the R library TraMineR (version 1.8.13) [START_REF] Gabadinho | Analyzing and Visualizing State Sequences in R with TraMineR[END_REF] . LCS is a metric based on counts of common attributes occurring in the same order between state sequences [START_REF] Bergroth | A survey of longest common subsequence algorithms[END_REF] . Given two sequences 𝑋 = (𝑥 1, 𝑥 2 , … , 𝑥 𝑛 ) and 𝑌 = (𝑦 1, 𝑦 2 , … , 𝑦 𝑛 ), Z is a common subsequence of X and Y if it is a subsequence of both X and Y. 𝑍 is a longest common subsequence (LCS) of 𝑋 and 𝑌 if |𝑍| ≥ |𝑍 ′ |, for all other common subsequences 𝑍′ of 𝑋 and 𝑌 (Figure 1). Among the sequence dissimilarity measures available in TraMineR, LCS metric was chosen as is not too sensitive to timing but it presents a dependence on the sequencing and the duration spent in the distinct states, which matter most in long term RRT. Optimal matching (OM) measures [START_REF] Abbott | Optimal Matching Methods for Historical Sequences[END_REF] , frequently used in social sciences, was less justified in our context since short time deletion or substitution transformations had less meaning [START_REF] Studer | What matters in differences between life trajectories: a comparative review of sequence dissimilarity measures[END_REF] . The care trajectory of one RRT patient could hardly be considered to be the result of a transformation of a care trajectory of another patient.

The sum of weighted distances (SS) between care trajectories was then computed following Equation (1):

𝑆𝑆 = 1 𝑊 ∑ ∑ 𝑤 𝑖 𝑛 𝑗=𝑖+1 𝑛 𝑖=1 𝑤 𝑗 𝑑 𝑖𝑗 ( 1
)
where n is the number of cases, wi and wi are the weights associated to case i and j respectively, W is the total sum of weights, and dij is the LCS distance between i and j. The variance or, in more general term, the discrepancy S 2 (for non-Euclidian distances as LCS)

was then 𝑆 2 = 1 𝑊
𝑆𝑆, which is equal to half of the weighted average of the pairwise dissimilarities (Equation 2).

𝑆 2 = 1 2𝑊 2 ∑ ∑ 𝑤 𝑖 𝑛 𝑗=𝑖+1 𝑛 𝑖=1 𝑤 𝑗 𝑑 𝑖𝑗 (2)
The regression tree growing process started with the entire study sample (root).

Recursively, the tree-generating algorithm tested all values of the covariates to split the original set in two subgroups (left and right daughters) that minimize within-group discrepancies and maximize between-group variations (as standard performed for regression tree CART [START_REF] Breiman | Classification and regression trees[END_REF][START_REF] Hastie | The elements of statistical learning: data mining, inference, and prediction[END_REF] ). More precisely, at each node, each covariate and their possible binary splits of category levels were tested and the split with the highest univariate pseudo-R 2 was selected to create two child nodes. The part of the discrepancies explained by a covariate (pseudo-R 2 ) was quantified using the Huygens theorem of the ANOVA approach. The theorem states that the total sum of squares (SST) is the between (groups) sum of squares (SSB) plus the residual within (group) sum of squares (SSW is the explained discrepancy to the residual discrepancy where m is the number of groups and W the total sum of weights. The assessment of the statistical significance of the split (or strength of the association between trajectories and covariate) was performed using permutation tests on the F statistics. Within each subgroup, the F statistics was computed for the observed values of the covariates of each sequence, namely Fobs. At each permutation, the value of the covariate was assigned randomly to each sequence and a

Fperm value was computed. Five thousand permutations and a p-value threshold of 5%

were used to assess the split significance. The p-value was the proportion of Fperm values that were higher than Fobs. The regression tree growing process stopped when empirical stopping criteria were reached. We gave the arbitrary constraint that the covariates of the last partitioning step should explained at least 1% of the discrepancy between subgroups which in our case corresponded to a maximum depth of 5 leaves in the regression tree.

Only covariates that contributed significantly to partitioning the observed trajectories were selected (R 2 >= 1% and significant F permutation test).

The global quality of the tree was assess using the pseudo-F and Levene's tests that summarize the statistical significance of the obtained segmentation compared with random splits for the between-groups and within-group discrepancies, respectively. The global pseudo-R 2 was calculated as a measure of the part of the total discrepancy that was explained by the regression tree.

All computation were performed using R (version 3.3.3 -R Foundation, Vienna, Austria) [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF] , and the TraMineR library (version 1.8.13) [START_REF] Gabadinho | Analyzing and Visualizing State Sequences in R with TraMineR[END_REF][START_REF] Studer | WeightedCluster Library Manual: A practical guide to creating typologies of trajectories in the social sciences with R[END_REF] .

RESULTS

Treatment sequences during the first 48 months of RRT

We retrieved data for 6166 patients (5045 in Ile-de-France and 1121 in Bretagne). Among them, 905 were excluded because they moved to other regions or were lost to follow-up (n=357), could not be followed for 48 months (n=273), or received preemptive graft (n=310). Therefore, 5568 patients were included in the analysis (Table 1). Although care trajectories seemed heterogeneous with a diversity of switches between RTT, 72% of ESRD patients had their first RRT in-center hemodialysis (Figure 2 and Figure S1). Over the 48-month follow-up, the proportion of patients undergoing peritoneal dialysis and in-center hemodialysis decreased (essentially in favor of transplantation or because of death), while the percentage of patients undergoing hemodialysis in a medical satellite unit increased from 1% to 6%. The observation was similar in both regions (Figure S2). On average, a patient underwent 1.56 different treatments (min=1; max=5) during the 48 months of follow-up. About 55% of patients never changed RRT modality, 44% changed once or twice, and only 1% changed three or more times. Patients who tried two or more RRT modalities generally switched between the same treatments, for instance, in-center hemodialysis, then autonomous hemodialysis followed again by in-center hemodialysis and then autonomous hemodialysis, and so on (Figure S1). A patient underwent 1.64 switches on average, with a maximum of 8. When switches occurred, the most frequent transitions were from in-center hemodialysis to autonomous dialysis, from hemodialysis in a medical satellite unit to in-center hemodialysis, and from autonomous dialysis or peritoneal dialysis to graft. Over the 48 month-period after RRT initiation, patients spent on average 25 months on in-center hemodialysis, 22 months on autonomous dialysis, 20.7 months on hemodialysis in medical satellite units, or 24.5 months on peritoneal dialysis before switching to another modality (including graft), or death. Patients waited on average 8.8 months (median: 6 months) before being placed on the transplantation waiting list.

Among waitlisted patients (n=2560), 20% were registered at RRT initiation, 25% within 2 months, and 75% within the first year of RRT. Overall, 58% of waitlisted patients underwent kidney transplantation, after a mean time on the waiting list of 25 months. At the end of the 48-month follow-up, 1834 patients (33%) were dead and 50% of them within the first 18 months after RRT initiation.

Determinants of homogeneous groups of care trajectory

Twelve subgroups of homogeneous RRT trajectories were identified (Figure 3). The trajectories varied significantly more between groups than within groups (based on the results of the Levene's and pseudo F tests). The tree explained about 12% of the total discrepancy observed. A path from the root to the terminal leaf corresponded to the effects of interactions between the respective variables on discriminating patients' care trajectories. For instance, on the left side of the tree from top to bottom, patients were younger than 60 years of age AND lived in Bretagne AND underwent a first dialysis session without a catheter AND had glomerulonephritis or autosomal dominant polycystic kidney disease as primary renal disease. The first determinant was age that contributed to explain almost 6% of the differences between groups. The covariate "first dialysis session with a catheter" significantly contributed to more than one split, but at different levels. Among patients younger than 60 years of age in Bretagne, it accounted for 6% of discrepancy and seemed to separate patients who mainly underwent in-center hemodialysis (right side) from those on autonomous dialysis. Similarly, the primary renal disease contributed to two splits: one among the 60 to 69-year-old patients and one among those younger than 60 years old.

The grouping of the different modalities varied between splits. Among patients above 70 years old, physical disabilities were the primary determinant that grouped patients who underwent in-center hemodialysis, were rarely waitlisted, did not have access to kidney transplant and displayed high mortality. Among patients under 60 years old, the region of residency was the first determinant and accounted for 3% of all discrepancies. The Ile-de-France sub-group was characterized by a majority of patients starting RRT with in-center hemodialysis (75%) (Figure 3 and Figure S3). Conversely, in the Bretagne subgroup, equivalent proportions of patients started with in-center hemodialysis and autonomous dialysis (45% and 42%, respectively). In addition, by the end of the 48-month follow-up period, a higher proportion of patients had access to kidney transplantation in Bretagne (63%) than in Ile-de-France (42%) (Figure 3 and Figure S4). In Bretagne, the last two splits were driven by the "first dialysis session with a catheter" and the "primary renal disease" variables. Specifically, 85% of patients under 60 years old in Bretagne with autosomal dominant polycystic kidney disease or glomerulonephritis and who did not receive their first dialysis session with a catheter were transplanted within the study period (versus 63% for the other nephropathies). In Ile-de-France, diabetes contributed to the care trajectory discrepancies more significantly than initiation of dialysis with a catheter. In both regions, young patients (and without diabetes in Ile-de-France) who received a first dialysis session with a catheter were less likely to underwent kidney transplantation than those who did not.

DISCUSSION

While analysis of health care determinants is often computed on single health care events, we believe that monitoring care trajectories and identifying their determinants offer opportunities to highlight point of leverage for improvement of long term care [START_REF] Meur | Mining care trajectories using health administrative information systems: the use of state sequence analysis to assess disparities in prenatal care consumption[END_REF] . The formalization of care trajectories as CSS leads to an interesting and synthetic longitudinal display that allows pattern identification through cluster analysis, state transition monitoring, or trajectory analysis [START_REF] Couchoud | Modelling treatment trajectories to optimize the organization of renal replacement therapy and public health decision-making[END_REF][START_REF] Meur | Mining care trajectories using health administrative information systems: the use of state sequence analysis to assess disparities in prenatal care consumption[END_REF][START_REF] Darak | Trajectories of Childbearing among HIV Infected Indian Women: A Sequence Analysis Approach[END_REF] . Regression tree method are an innovative alternative strategy to descriptive and cluster-based analyses of CSS. As cluster-based approaches reduce the set of sequences to a limited number of standard trajectories, information about the diversity within each cluster is lost [START_REF] Studer | Discrepancy Analysis of State Sequences[END_REF] . Furthermore, knowledge of the cluster membership alone does not give information about the distances and differences between clusters. Regression tree methods overcome these limits and allow the direct analysis of the sequence-covariate links and the measurement of the relationship strength.

These methods take into account the inter-individual variability of the trajectories, while studying the relationships between the trajectories and their contexts.

This analysis of the REIN registry on ESRD patients who lived in two different regions shows care trajectory variations and the contribution of demographical, medical, and regional covariates to these differences. Though life courses of ESRD patients are specific and health care providers proposed personal care, ESRD patients had rather stable sequence of treatments and could be classified in homogenous sub-groups. Whatever the region, ESRD patients had simple care trajectories with few treatment changes.

Unsurprisingly, our study shows that the main determinant of care trajectories is age.

Whatever the region, patients older than 60 years old were less frequently on the transplant waiting list and underwent kidney transplant more rarely than younger patients [START_REF] Vigneau | Ten-years trends in renal replacement therapy for end-stage renal disease in mainland France: Lessons from the French Renal Epidemiology and Information Network (REIN) registry. Néphrologie Thérapeutique[END_REF] . Initiation of hemodialysis with a catheter is another predictable determinant of care trajectory differences. This medical procedure is associated with early mortality [START_REF] Bradbury | Predictors of early mortality among incident US hemodialysis patients in the Dialysis Outcomes and Practice Patterns Study (DOPPS)[END_REF][START_REF] Rayner | Mortality and hospitalization in haemodialysis patients in five European countries: results from the Dialysis Outcomes and Practice Patterns Study (DOPPS)[END_REF] .

This procedure does not increase the mortality risk per se (except in the rare case of infections), but it is a marker of a more complex RRT initiation at any age. It is often proposed to less compliant patients, critically ill patients, or patients not referred by a nephrologist and who need RRT in emergency. In term of care trajectories, few of these patients were waitlisted and they predominantly used in-center hemodialysis, whatever the age. Most surprisingly, region of residence is the first determinant of care trajectory among patients younger than 60 years old, before all clinical characteristics. This could be explained by regional variations in the RRT modality offer and choice. Although several RRT management changes have recently been implemented in France with the aim of developing alternatives to in-center hemodialysis to improve the quality of life of young and active patients [START_REF] Vigneau | Ten-years trends in renal replacement therapy for end-stage renal disease in mainland France: Lessons from the French Renal Epidemiology and Information Network (REIN) registry. Néphrologie Thérapeutique[END_REF] , in-center hemodialysis remains predominant, especially at initiation (Figure S2 andS3). These regional variations could also be partially explained by the higher proportion of diabetic patients in Ile-de-France. These patients have complex care trajectories. They are less likely to be registered on the transplant waiting list [START_REF] Bayat | Individual and Regional Factors of Access to the Renal Transplant Waiting List in France in a Cohort of Dialyzed Patients: Renal Transplant Waitlisting in France[END_REF] and to have access to kidney transplantation [START_REF] Lefort | Facilitating access to the renal transplant waiting list does not increase the number of transplantations: comparative study of two French regions[END_REF] .

One limitation of our result might be the small proportion of the total discrepancy explained by the computed tree. Overall, 12% of the variation observed between care trajectories was explained by the regression tree. However, as far as human behavior is involved, this level is not surprising. In the original work by Studer et al. [START_REF] Studer | Discrepancy Analysis of State Sequences[END_REF] , socio-economic and demographic variables contributed to explain 18% of the school-to-work transition in Northern Ireland. Similarly, another group showed that people activity, age, and household size explain 19% of people's daily activity-travel patterns [START_REF] Kim | Discrepancy Analysis of Activity Sequences: What Explains the Complexity of People's Daily Activity-Travel Patterns?[END_REF] . Moreno-Black et al. 28 (2016) showed that 3% of the variation of body mass index trajectories in elementary school children is explained by low socio-economic status and ethnicity. In our study, we identified homogeneous groups of care trajectories, but the within-group variation remained important. One explanation might be that although patients within a homogenous group of care trajectory used the same RRT modality with few switches, they switched between modalities at different points in time, thus increasing the variability between individuals.

Other factors not collected by REIN registry could also have influenced the switches between RRT modalities. For instance, RRT choice could be guided by the type of transportation available to the patients or the travel time between home/work place and dialysis center. Nevertheless, the regression tree analysis of CSS has the advantage to estimate the association and interaction of multiple factors along with the RRT modality sequence.

In conclusion, regression tree analysis of CSS is an original tool to visualize and characterize care trajectories in the context of chronic disease. In health services research and personalized medicine, modelling care trajectory as a whole could contribute to better assess the impact of new treatment modality or the restructuration of health care facilities on patients care trajectory 3 . In addition, this mixed method between data mining and regression could be a promising tool for the exploration of medico-administrative data or claim data that by construction collect valuable information on healthcare consumption (e.g. drug consumption, medical device usage or visits to health care professional and health care facilities) and allow care trajectory analysis [START_REF] Drezen | From medico-administrative databases analysis to care trajectories analytics: an example with the French SNDS[END_REF][START_REF] Macewan | Patterns of Adherence to Oral Atypical Antipsychotics Among Patients Diagnosed with Schizophrenia[END_REF] .

FUNDING:

Fig. 1

 1 Fig. 1 Trajectory of care as an ordered sequence of states. For each ESRD patient, the succession of renal replacement therapies (RTT) was translated into an ordered sequence of states for a 48-month period after RRT initiation. The duration of each state was the duration of each treatment phase. The death event was interpreted as an irreversible state. The event of being registered to the transplantation waiting list was defined as a punctual state with 1-month duration. Overall seven states were possible: in-center hemodialysis [CENTER] in aqua blue, hemodialysis

Fig. 2

 2 Fig. 2 Percentage of ESRD patients for each RRT modality per month during the 48-month

Fig. 3

 3 Fig. 3 Determinants of homogeneous groups of RRT sequences among ESRD patients. In each panel, each row represents one

  This study was supported by the Agence Nationale de la Recherche in the framework of the "Investment for the Future" program [grant number ANR-11 -IDEX-0005-02].

Table 1 . Characteristics of the adult ESRD patients registered in REIN between January 1, 2006 and December 3, 2009 and

 1 followed for 48 months before the study end point (December 31, 2013). (Exclusion criteria: preemptive graft, lost to follow-up, and moved to other regions)

	Bretagne	Ile-de-	All patients
	N= 1062	France	N = 5568
		N=4506

ACKNOWLEDGEMENT:

We would like to acknowledge Cécile Couchoud for organizing the extraction of the data from the REIN registry.

CONFLICT OF INTEREST:

The authors declare that they have no conflict of interest.