Data sources and measurements
This retrospective cohort study was conducted on registry data of liver patients who underwent surgical liver transplantation at Namazi Hospital, Shiraz between 2004 and 2019. According to the purpose of the study, the criteria for inclusion in the study were liver transplants performed at Namazi Hospital. Patients were admitted to the hospital from 2004 to 2019, resided in one of the 31 provinces of Iran, and the patient’s age at the time of transplantation was 18 years or older. Therefore, out of a total of 3,332 liver transplant patients from 2004 to 2019, 47 patients living abroad, 68 patients without registered residence, and 33 children under 26 months of age were excluded. the study. The remaining 3,148 of his patients were included in the study and no patients were excluded from the study (Figure 1). Data were collected using a checklist of patient information from medical records: age, donor and recipient sex and blood type, place of residence, date of transplantation, MELD score (predicting 3-month mortality A prognostic scoring system based on test parameters used to determine (by liver disease) and disease information such as cause of liver disease, year and exact date of transplant, presence of diabetes, and vital status.
Flowchart of participants analyzed in this retrospective cohort study on liver transplantation.
Four main causes of liver disease: primary sclerosing cholangitis (677 people), hepatitis B and C (835 people), inherited liver diseases (604 people), and other liver diseases (1005 people) Patients with the disease were included in the study. Most patients (3066) received a complete liver transplant, 78 patients received a split liver transplant, 1 received a partial liver transplant, and 2 received a domino transplant. Of these, 3,147 came from brain-dead donors, and only one came from a living donor. donor. The outcome variable was the number of days from the date of transplantation to the date of death due to disease.
From 2008 to 2004, 83 patients underwent transplantation, from 2009 to 2013, 1079 patients underwent transplantation, and from 2014 to 2019, 1997 patients underwent transplantation.
Vital status information was confirmed through active contact with patients or their families until March 20, 2019. Written informed consent was obtained from the patient. Patients who did not die from the disease, died during the study, or died from unrelated causes were considered censored observations.
To ensure the accuracy and consistency of data collected during the study period, data collectors were periodically briefed on how to retrieve information from their files and record it on checklists. The data collector did not change during the information collection process and the checklist used was the same throughout the process.
statistical analysis
Cox regression models were used to determine the influence of predictors on mortality risk. A survival model with spatial random effects was used because the patients were from different provinces in Iran and people living in the same or neighboring regions share common or similar health services and environmental risk factors. Add spatial effects to the Cox model to adjust for group relatedness for patients living in the same region and neighborhood relatedness for patients living in adjacent regions. Spatial effects indicate that mortality risk may vary across states. Spatial models fall into two general categories depending on the structure of the data. Data with point references (geostatistics) are used for precise geographic locations (latitude and longitude), and spatial data (grids) are used to divide the study area. It is divided into several spatial units with clearly defined boundaries and the status of each area relative to other areas. This study used a grid approach to map the spatial risk of post-transplant mortality in each state.28. Spatial effects are typically proxies for many unobserved influencing factors, some of which have strong spatial structure and some of which may be local.29. We aimed to distinguish between two types of influencing factors by estimating structured and unstructured effects. We assumed a Markov random field for smooth spatial effects and completely independent Gaussian distributions for uncorrelated effects.30,31,32.
In accordance with our study objectives, we also wanted to investigate the nonlinear effects of the variables age and MELD score on survival time. To investigate nonlinear effects of variables, we used splines, which are used to fit nonlinear relationships. A spline is a piecewise polynomial function restricted to certain control points called knots (points where the spline changes from one polynomial to another).31,32. Splines are sensitive to the number and location of knots, and unlike polynomials, splines allow a more local fit to the data.31, 33, 34.
In general, there are three ways to estimate splines. Smooth splines, polynomial splines, and penalized splines. Evaluation results show that penalized splines are more accurate in representing the relationship between explanatory variables and the log hazard function. Penalized cubic splines use a penalty term to reduce the number of knots and control the smoothness of the spline. By adjusting the penalty parameter, you can better fit your data and avoid overfitting or underfitting. Penalized cubic splines are similar to smoothing splines, but give you more flexibility in choosing knot locations and degree of smoothness.twenty three,33,34,35. Therefore, the penalized cubic spline method was used in this study.
A generalized additive model (GAM) is a generalized linear model in which the response variable depends linearly on unknown smoothing functions of some predictor variables, and we are interested in making inferences about these smoothing functions and a response that follows an exponential family distribution. is concentrated. This study considered four different generalized Cox additive models for the risk of death at time t based on the following study objectives:
model 1 Investigating the impact of structured spatial effects on post-transplant mortality risk without covariates
$$h\left( t \right) = h_{0} \left( t \right)exp\left( {f_{str} \left( {\text{k}} \right)} \right)$$
model 2 Separation of structured and unstructured spatial effects
$$h\left( t \right) = h_{0} \left( t \right)exp\left( {f_{str} \left( {\text{k}} \right) + f_{unstr} \ left( {\text{k}} \right)} \right)$$
model 3 Model based on univariate analysis results adjusted for other covariates
$$\begin{aligned} h\left( t \right) & = h_{0} \left( t \right)exp\left( {\gamma_{1} {\text{gender}} \cdot {\text {Donor}} + \gamma_{2}\,cause\,of\,diseas1 + \gamma_{3} \,cause\,of\,diseas2} \right. \\ & \quad + \;\gamma_{4 } \,Cause\,of\, Illness 3 + \gamma_{5}\,Transplant\,Date 1 + \gamma_{6} \,Transplant\,Date 2 \\ & \quad \left. { + \;f \left( {age \cdot donor} \right) + f\left( {age \cdot recipient} \right) + f\left( {MELD} \right) + f_{str} \left( {\text{ k}} \right) + f_{unstr} \left( {\text{k}} \right)} \right). \\ \end{Align}$$
model 4 Model 3 without age covariates searches for location-correlated variables based on the non-significance of spatial effects in the presence of other variables.
$$\begin{aligned} h\left( t \right) & = h_{0} \left( t \right)exp\left( {\gamma_{1} {\text{gender}}. {\text{ Donor}} + \gamma_{2} \,Cause\,of\, Disease 1 + \gamma_{3} \,Cause\,of\, Disease 2} \right. \\ & \quad + \; \gamma_{ 4} \,Cause\,of\, Illness 3 + \gamma_{5} \,Transplant\,Date 1 + \gamma_{6} \,Transplant\,Date 2 \\ & \quad \left. { + \; f\left( { MELD} \right) + f\left( {age \cdot donor} \right) + f_{str} \left( {\text{k}} \right) + f_{unstr} \left( {\text{k }} \Oh yeah). \\ \end{Alignment}$$
In all models,\(h_{0} \left( t \right)\) was an arbitrary baseline hazard function. Also, \(\gamma_{1} , \gamma_{2} , \gamma_{3} , \gamma_{4} , \gamma_{5} , \gamma_{6}\) were the regression parameters corresponding to the observed explanatory variables: gender, class of primary cause of disease, and class of date of transplantation.
In these models, \(f\left( {age} \right)\) and \(f\left( {MELD} \right)\) are unknown functions of nonlinear effects, and these unknown functions were estimated using a quadratic spline basis and a penalized spline with a quadratic penalty.31,32,33,34.
\(f_{str} \left( {\text{k}} \right)\) Structured spatial effects in the k-th region assuming a Markov random field, and for uncorrelated effects \(f_{unstr} \left( {\text{k}} \right)\)we assumed that the Gaussians are uniformly independent distributions.31,32. Details of model construction are provided in Appendix A.
In a penalized cubic spline, the coefficients of the linear and nonlinear effects of the knot are maximized by the penalized partial likelihood function by adding a vector λ (a smoothing parameter, which controls the trade-off between the data). estimated by the method. Fitting and Smoothness) from a nonlinear variable such as a z vector to the second derivative of an unknown function f as follows:
$$l_{{p + }} \lambda \mathop \smallint \limits_{0}^{\infty } \left\{ {f^{\prime\prime } \left( z \right)} \right\} ^{2} \; zu$$
where \(l_{p }\) is the logarithm of the partial likelihood, \(f^{\prime \prime } \left( z \right)\) was the second derivative of f(z). Generalized cross validation (GCV) was also used to select the smoothing parameters.31, 33, 34 (Appendix A).
Analyzes were performed using R software version 4.1.3 and the mgcv package.
Ethics approval
Data were collected from patients’ medical records at the hospital. Written informed consent was obtained from the patient. All methods were performed in accordance with relevant guidelines and regulations, and the study was approved by the Ethics Committee of Hamadan University of Medical Sciences (Ethics code: IR.UMSHA.REC.1401.277).
consent to participate
Written informed consent was obtained from the participants. It was approved by the ethics committee of Hamadan University of Medical Sciences (ethics code: IR.UMSHA.REC.1401.277).
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