Predicting patient survival after deceased donor kidney transplantation using flexible parametric modelling

Abstract

Background: The influence of donor and recipient factors on outcomes following kidney transplantation is commonly analysed using Cox regression models, but this approach is not useful for predicting long-term survival beyond observed data. We demonstrate the application of a flexible parametric approach to fit a model that can be extrapolated for the purpose of predicting mean patient survival. The primary motivation for this analysis is to develop a predictive model to estimate post-transplant survival based on individual patient characteristics to inform the design of alternative approaches to allocating deceased donor kidneys to those on the transplant waiting list in the United Kingdom.

Methods: We analysed data from over 12,000 recipients of deceased donor kidney or combined kidney and pancreas transplants between 2003 and 2012. We fitted a flexible parametric model incorporating restricted cubic splines to characterise the baseline hazard function and explored a range of covariates including recipient, donor and transplant-related factors.

Results: Multivariable analysis showed the risk of death increased with recipient and donor age, diabetic nephropathy as the recipient's primary renal diagnosis and donor hypertension. The risk of death was lower in female recipients, patients with polycystic kidney disease and recipients of pre-emptive transplants. The final model was used to extrapolate survival curves in order to calculate mean survival times for patients with specific characteristics.

Conclusion: The use of flexible parametric modelling techniques allowed us to address some of the limitations of both the Cox regression approach and of standard parametric models when the goal is to predict long-term survival.

Keywords: Extrapolation; Flexible parametric model; Kidney transplantation; Multivariable analysis; Survival.

Fig. 1

Kaplan-Meier curves and log-rank tests to explore changes in patient survival between different cohorts based on year of transplant: (a) 10-year intervals (b) 5-year intervals and (c) intervals that coincide with changes to the national kidney allocation scheme

Fig. 2

Comparison of smoothed hazard function based on observed data and preliminary flexible parametric model (no covariates) fitted with spline function (2 interior knots); Weibull and loglogistic models in the accelerated-failure time (AFT) metric are also shown for comparison

Fig. 3

Comparison of Kaplan-Meier curves based on observed data (solid lines) and predicted mean survival curves based on final flexible parametric model (dotted lines) by prognostic group

Fig. 4

Extrapolated survival curves with mean predicted survival for three different patient profiles