Proximity to transplant center and outcome among liver transplant patients

In the United States, distance from liver transplant center correlates with worsened outcomes; the effects of geography elsewhere are unassessed. We performed a national registry analysis of United Kingdom listings for liver transplantation (1995‐2014) and assessed whether travel time to transplant center correlates with outcome. There were 11 188 listings assessed (8490 transplanted), with a median travel time to center of 60 minutes (range 36‐86). Of the national population, 3.38 × 107 (55.1%) reside ≥60 minutes from a center, and 7.65 × 106 (12.5%) >119 minutes. After competing risk analysis, increasing travel time was associated with an increased risk of death after listing (subdistribution hazard ratios relative to <60 minutes of 1.33 for 60‐119 and 1.27 for >119 minutes; P < 0.001) and reduced likelihood of transplantation or recovery (0.94 and 0.86; P < 0.001). Among those transplanted, travel time was not associated with retransplant‐free survival (P = 0.532). We used our model to examine optimal placement of a new center and identify a single site with a total travel time reduction of ≈10%. Our findings of disparities in accessibility of liver transplantation showed worse outcomes following listing in those distant from their transplant center, and our description of a method to model a new center complement existing data and support similar analyses of other networks.

The United Kingdom National Health Service (UK NHS) has a well-established liver transplant program, and represents the only option for liver transplantation within the United Kingdom. Since 1992, the NHS provision of care has been split between 7 centers.
Recent analyses of the provision of national liver transplant services have emphasized reducing disparity and considering the building of new transplant center(s) to do so. [11][12][13][14] In addition to potential effects on patient outcome, it is reported that proximity to treating transplant center is identified as a factor important to many liver transplant patients. 15 To date, however, the roles of distance and travel time in UK liver transplantation have not been formally assessed.
In this analysis, we sought to describe the geographic distribution of UK patients using liver transplantation services, assess whether current variations in travel time are associated with differences in outcome, and to assess where a potential new liver transplant center might be best placed to minimize travel time.

| MATERIAL S AND ME THODS
The NHS Blood and Transplant national registry was queried for all patients ≥18 years old listed for liver transplantation in the United Kingdom from 1995 to 2014 inclusive; approval for the study was given by the UK Transplant Registry. Patients listed for repeat transplants, those listed on a "super-urgent" basis, those listed for simultaneous multi-organ transplantation, and those listed from postal codes (postcodes) outside England, Scotland, or Wales were excluded ( Figure 1). Those resident in Northern Ireland were excluded because of the incomplete availability of Census data, incomplete availability of data on population liver-related mortality, and the distorting effects of air travel. Data sources are summarized in Table S1.
To preserve anonymity, only the first portion of each patient's postcode was available describing the "postcode district." The longitude and latitude for the centroid of each of 2736 postcode districts ( Figure S1) and the precise location of each renal or liver transplant center was then entered into the Google Maps API (Alphabet, Palo Alto, CA). The shortest driving distance and travel time, unadjusted for traffic conditions, were then calculated from each postcode district to each transplant center. Centers with a preexisting renal transplant center were chosen as a proxy for the presence of sufficient infrastructure to support a new liver transplant center. Travel times were divided into 3 groups: <60 minutes, 60-119 minutes, and >119 minutes. Population estimates for postcode districts were obtained from the 2011 UK National Census; adjusted standardized mortality ratio (ASMR) estimates for liver disease were obtained for 2011 from national agencies. Geographic boundaries of the organizational subunits for which ASMR was available were overlaid with postcode districts and each postcode district was assigned the ASMR for the healthcare administrative area with the most shared area. Mapping was performed using Quantum GIS v2.18.7 (https://qgis.osgeo.org).
For the assessment of outcome from listing, death on the waiting list and de-listing for worsening condition were treated as outcomes, with patients censored if they received a transplant or were de-listed because of an improvement in their condition. For the assessment of outcome from transplantation, retransplant-free survival was assessed. Here, the outcomes of interest were mortality and the receipt of a second transplant, with patients censored at the end of follow-  (17 186) were listed for liver transplantation from 1995 to 2014 inclusive. After application of the exclusion criteria, an analysis cohort of 11 188 was generated with missing data in 1 or more categories were excluded from the univariable analyses in question and entirely from multivariable analyses.
Univariable analyses were used to compare differences between the 3 travel time categories: the nptrend test in Stata for continuous variables, 16 the Mann-Whitney U test to compare travel time between 2 categorical variables, and the Kruskal-Wallis test to compare 3 or more categorical variables. To assess for outlying contributors of listings for liver transplantation, the relative contribution of different postcode areas-each including multiple postcode districts-to listings for liver transplantation, rates, and confidence intervals were calculated to generate a funnel plot according to the method of Spiegelhalter. 17 To assess outcome from the point of listing for transplantation, competing-risks regression models according to the method of Fine and Gray were constructed. 18 Analyses were constructed both with death as the primary outcome and transplantation or recovery as a competing risk, and also with attaining transplantation or recovery as a primary outcome and death or all other outcomes as a competing risk. To assess outcome following liver transplantation, a Cox proportional hazards model was constructed with the incidence of either death (of any cause) or retransplantation considered a failure.
In both competing risk and Cox models, variables other than travel time were selected for inclusion in the final model with a backwards stepwise approach with a cut-off of P < .1. Visual inspection was used to ensure no crossover of Kaplan-Meier survival plots for each categorical value. For Fine-Gray competing risk models, cumulative sums of residuals were used to confirm the appropriateness of the model constructed for each variable; for Cox models, Martingale and Cox-Snell residuals were calculated. 19 For skewed values with poor fit, logarithmic transforms were used (this was required in 2 instances: intensive treatment unit stay duration and international normalized ratio). A value of P < .05 was assumed to be representative of statistical significance. Statistical analyses were conducted using StataMP v15.0 (StataCorp, College Station, TX) using the University of Birmingham's BlueBEAR High Performance Computing Cluster.
After exclusions, 11 188 were included in subsequent analysis  Those who did not attend their nearest center were primarily resident in areas of near equidistance between centers, or in the northwest or southwest of England ( Figure S3).
To assess whether there was a correlation between mortality from liver disease with travel time to nearest liver transplant center, we plotted ASMR for each postcode district against travel time. This revealed a negative correlation −3.51 ASMR points per 100 minutes   Wales, and around urban centers in northern England. We then repeated this procedure but adjusted values according to the ASMR for that postcode district normalized to the average ASMR nationwide ( Figure S7). After this adjustment, the largest values of "person minutes" were evident in the northwest of England.

| Travel time is significantly correlated with worsened outcome from the point of listing for liver transplantation and a lower likelihood of receiving a liver transplant
To assess outcome after listing of transplant patients, we first divided patients into 3 groups: <60 minutes, 60-119 minutes, and >119 minutes .003 by log-rank test), with a hazard ratio of 1.21 (95% CI: 1.03-1.41, P = .020) for the >119 minutes vs <60 minutes groups. However, this did not account for the rates of transplantation or recovery, which were also found to differ significantly across the groups, being lowest in the >119 minutes group (HR: 0.91; 95% CI: 0.85-0.96, P = .002, Figure 5B). As such, competing risks analyses were performed, to consider both of these outcomes simultaneously. These models also accounted for other confounding factors, in order to account for the baseline differences observed between the 3 travel time groups.
When considering death as the primary outcome (

| Travel time is not significantly correlated with outcome following liver transplantation
We next looked for differences in outcome after transplan-

| The optimum site for an additional UK transplant center to reduce patient travel time is Bristol
Having demonstrated a correlation between increasing travel time and worsened outcome, we modeled the effect on total  Figure 6B), for the total population ( Figure 6C), and for the total population with adjustment for ASMR ( Figure 6D).
In each case, the greatest overall reduction in patient travel time was achieved by modeling the addition of a new center in Bristol.

| D ISCUSS I ON
Here we show that there is a significant disparity in travel time to  to liver transplantation. In addition, we cannot account for possible regional variations in the approach to listing or delisting patients. Indeed, differences in the general behavior of clinicians and/or patients further from transplant centers may also explain some of the variation in outcome we describe. Such variation might be amenable to educational approaches. However, major differences in behavior might also be expected to have effects on posttransplant outcomes, and these were not evident in this study.
In contrast to work from the United States, we do not, however, Although our data set is relatively large with excess of 11 000 listings considered, one potential concern is that with the multiple variables examined, an otherwise statistically significant outcome signal from travel time posttransplantation might be lost. This is made less likely by significant differences in HRs for posttransplant outcome in risk factors in other studies (eg, increased mortality in those receiving organs from deceased after cardiac death donors, those receiving grafts from older donors or with longer cold ischemic times, and those with renal failure at listing). 23,24 Weaknesses of this analysis include the moderate imprecision introduced by only using the first part of the postal code, although this was necessary to preserve relative anonymity, and these factors represent potential confounders of our findings.
This imprecision also precludes estimates of social status and income based on place of residence, although we note that population rates of mortality from liver disease tend to be lower with greater travel time. Importantly, we only considered those who reached the point of listing for transplantation and are therefore unable to account for geographic variations in ability to access assessment for possible liver transplantation. We have, however, attempted to account for this in our geographic analysis by using ASMR as a proxy for total liver disease. It is notable, however, that a large proportion of liver-related death in the United Kingdom is alcohol related and that these patients are often not referred for consideration of transplantation. 12 In addition, we only considered mortality and a requirement for retransplantation as outcomes; it is possible that patient experience, loss of productive work, financial cost, and other variables are affected by distance from transplant center. We were also unable to ascertain which patients changed their address; patient migration for the purposes of transplantation is reportedly common in the United States. 25 We recorded variation in outcome between centers in the United Kingdom both from the point of listing and from the point of transplantation. However, for the reasons explored above and because of the lack of information about the denominator population including those who are not accepted for listing, further work would be necessary to understand this variation.
Finally, in our modeling we do not consider the addition of more than one center to the current network.
The issue of how best to approach the provision of liver transplantation in the United Kingdom is challenging. We highlight disparity in access to liver transplant centers and demonstrate a correlation between greater distance from transplant center and outcome from the point of listing for transplantation, although we do not prove causation. Further careful analysis will be required to guide future decisions on both the number and geographical distribution of liver transplant centers, including the consideration of factors other than simple mortality and chance of attaining transplantation.

ACK N OWLED G M ENT
The authors wish to thank the statistical team of NHS Blood and Transplant for their assistance with data provision.

D I SCLOS U R E
The authors of this manuscript have no conflicts of interest to disclose as described by the American Journal of Transplantation.

CO NTR I B UTI O N S
GJW originally conceived the study, which was then modified in response to suggestions from each of the other authors. The analysis was performed by GJW and JH. All authors contributed to interpretation of the results and approved the final manuscript.

D I SCL A I M ER
This report presents independent research funded by the National