| کلیدواژههای انگلیسی مقاله |
Kidney transplantation, Graft survival, Survival analysis, Longitudinal studies, Multivariate analysis, What&,rsquo s Known After kidney transplantation, key markers are measured longitudinally over time to prevent the risk of kidney failure due to the allograft rejection. These markers are correlated to ensure accurate assessment of kidney function. Previous studies focused mainly on joint modeling of one longitudinal marker and time-to-event (allograft rejection) data. What&,rsquo s New The effect of multiple markers, such as serum creatinine and blood urea nitrogen, on allograft survival was evaluated by using multivariate joint models. The results showed that the blood urea nitrogen marker played a more important role than serum creatinine in preventing allograft rejection. IntroductionChronic kidney disease causes gradual loss of kidney function, leading to the so-called end-stage renal disease (ESRD). At this advanced stage, kidney transplantation is the main treatment modality to improve patients&,rsquo quality of life and reduce mortality. 1, , 2, Considering the high prevalence of ESRD, it is important to address the social impact and financial burden of this medical condition. 3, Kidney transplantation is performed under specific conditions, as it is often difficult, and at times impossible to find a compatible kidney for patients in need of a transplant. Therefore, it is important to identify risk factors associated with graft failure, most of which are predictable and preventable. One such risk factor is the rejection of a donated kidney due to the renal allograft failure. 4, To assess the progression of renal disease in transplant patients, kidney markers such as blood urea nitrogen (BUN), serum creatinine, and glomerular filtration rate (GFR) are measured periodically after transplantation. 5, , 6, These markers are measured over time to monitor changes in their levels and to prevent the risk of kidney failure due to allograft rejection. While some tend to give a prognosis solely based on the baseline measure of these markers, the advantages of repeated measurements over an extended period of follow-up have been reported. 7, The true potential of a marker in determining severity of the disease and subsequent prognosis can only be illustrated with longitudinal measurements. 8, In fact, physicians require access to both baseline and follow-up data to accurately determine the progress of a disease and provide an accurate prognosis. 9, However, the main challenge is to correctly relate longitudinal measurements of kidney markers to the prognosis. A useful tool to analyze such data is the time-dependent Cox model. 10, In this model, it is assumed that longitudinal outcomes are measured over time and without error. However, given that longitudinal outcomes are measured periodically, and the generated errors are not considered, the hypotheses of this model are violated. 11, An alternative method is to use joint models of longitudinal and time-to-event data. Joint models calculate the dependence between the longitudinal and survival process and provide estimates with reduced standard error. With a more accurate estimate of parameters, valid conclusions can be drawn regarding the impact of covariates on the longitudinal and survival process. 12, A previous study, using theoretical and simulated data, demonstrated the advantages of joint models over the time-dependent Cox model. 13, In practice, the collected data often have a more complex structure, including several longitudinal responses. 14, , 15, There are some advantages in simultaneous modeling of multiple longitudinal responses in joint models over individual modeling of each longitudinal response. First, for correlated longitudinal responses, the adjusted estimation of each longitudinal response is more appropriate with the risk of occurrence of the event. 16, In other words, by measuring multiple longitudinal variables, the relationship between a longitudinal variable and time-to-event data with or without the effect of other longitudinal variables may vary greatly. Second, the predictive ability of joint models would significantly increase when the correlation between longitudinal variables is taken into account. 16, , 17, Several studies also showed bias in the estimated parameters, if the correlation between longitudinal variables and the separate fitting of joint models for each longitudinal outcome is ignored. 6, , 14, The multivariate joint model has become an attractive tool in medical research, as it provides physicians with a good insight in the dynamics of the underlying disease and to opt for the most appropriate treatment at any given time during follow-up.Accurate assessment of kidney function requires a correlation between the measured serum creatinine and BUN markers, since each marker can be influenced by the demographic and physiological characteristics of a patient. 18, , 19, Current studies on renal diseases have mainly focused on methodological development and clinical application of the multivariate joint model. 5, , 15, , 16, , 20, , 21, To the best of our knowledge, no study has previously evaluated the effect of multiple markers and other risk factors on allograft survival. Hence, using the multivariate joint model, this study aimed to determine the simultaneous longitudinal effects of serum creatinine and BUN markers, in combination with other risk factors on allograft survival after kidney transplantation.Materials and MethodsIn a retrospective cohort study, medical records of 731 recipients of kidney transplants, dated July 2000 to December 2013, from various transplant centers in Mashhad (Iran) were examined. An accurate estimate of allograft survival was anticipated, since the patients were followed up for two years after kidney transplantation. Initial assessment of the records led to the exclusion of 113 patients, because they had less than three months of follow-up, had other types of organ transplants, or had kidney transplants more than once. Eventually, the medical records of 618 recipients of kidney transplants were included in the study. Allograft failure was defined as creatinine levels &,gt 6 mg/dL for more than three months or clinical diagnosis, and the need for peritoneal dialysis or hemodialysis. The records showed that the serum creatinine and BUN levels of the patients were measured longitudinally over time. These repeated measurements (longitudinal variables) were important indicators in the analysis of allograft survival and were used as response variables in the longitudinal sub-model of the joint modeling process. The included risk factors of the recipients were age, sex, donor source, history of hypertension (systolic hypertension &,gt 140 mmHg or diastolic hypertension &,gt 90 mmHg), serum creatinine level within one month after transplantation, duration of dialysis, types of immunosuppressant drugs (patients receiving prednisolone, CellCept&,reg , and cyclosporine were assigned to group A, and those receiving prednisone, cyclosporine, and imuran to group B), and body mass index (BMI) on the last visit. Patients with BMI &,lt 18.5 were considered as underweight, 18.5&,le BMI&,le 24.9 as normal, and &,gt 24.9 as overweight.To analyze longitudinal and survival data, multivariate mixed-effects models were used for longitudinal multivariate responses, and the Cox model for the time-to-event response was used to evaluate the relationship between explanatory variables and response variables. 11, Longitudinal ModelsThe l-th longitudinal data sub-model is given by, y l ( t i ) = y l * ( t i ) + &,#1013 il = X l T ( t i ) &,beta l + Z l T ( t i ) b il + &,#1013 il (1)Where y l * = ( y l ( t i1 , y l ( t i2 ) , ... , y l ( t ini ) ) T is the corresponding true underlying longitudinal measures of l&,#8210 th biomarker (l=1, ..., L) for the i&,#8210 th subject (i=1, ..., n) at time points tij (j=1, ..., n), where n and ni are the number of subjects and number of longitudinal repeated measures for each subject respectively. X l T ( t i ) is the design matrix of fixed effects Z l T ( t i ) is the design matrix for the random effects, b i = ( b i1 , b i2 , ... , b iL ) T &,#8275 N ( 0, D ) measurement error is distributed as &,#1013 il &,#8275 N ( 0 , &,sigma l 2 I ni ) . In the variance-covariance matrix of random effects D, the between- and within-subject correlations for longitudinal markers are represented.The Survival Model Let T i * be the true event time and Ci be the censoring time for the i-th subject, respectively. The observed event time is T i = min ( T i * , C i ) , and the event indicator is &,delta i = min ( T i * , C i ) . The hazard function can be written as, h ( t i ) = h 0 ( t ) exp { &,gamma T w i + &,sum l=1 L &,alpha l y l * ( t i ) } (2)Where h 0 ( t ) denotes the baseline hazard function, and &,alpha 1 and &,gamma are coefficients for the function of the l-th biomarker and baseline risk factors. The correlation between the multivariate mixed-effects models and time-to-event sub-models is induced by the shared random effects through y l * ( t i ) .In addition, a separate joint analysis of each of the longitudinal markers was considered for the survival response. An important assumption in using mixed-effects models is that the observations of longitudinal responses are normal. Due to the lack of normal distribution of BUN marker observations, we used the square transformation of this marker. In the analysis of joint models, if one or more observations are missing for any of the variables used in the analysis for an individual, then all the relevant information for that individual is excluded from the study, ultimately leading to a reduction in sample size and bias in the results. Therefore, the estimation of missing observations was initially conducted using the multiple imputation method. Parameter estimates and inferences were then made using the maximum likelihood method, and based on the expectation-maximization algorithm. The R package joineRML (version 3.3.2) was used to implement the joint models. P values &,lt 0.05 were considered statistically significant. The study was approved by the Ethics Committee of Mashhad University of Medical Sciences, Mashhad, Iran (code, IR.MUMS.REC.1395.232).ResultsA total of 618 medical records of recipients of kidney transplants were analyzed. Among the patients, who were followed up during the 13 years, 35 (5.66%) cases had irreversible transplant rejection leading to dialysis and death occurred in 7 (1.13%) of the cases. The median time of patient follow-up was 6.36&,plusmn 4.97 years. The demographic and clinical characteristics of the patients are presented in table 1,.For each patient, the longitudinal profiles of the square root of BUN and serum creatinine with respect to the event status are presented in figure 1,. The fitted curves represent moderate population profiles for the event and non-event groups using linear mixed-effects models. We observed that the mean population of BUN and serum creatinine markers measured over time was larger in the event group than the non-event group. This indicated the potential association between the risk of occurrence, and the longitudinal measurements of BUN and serum creatinine. The difference in marker values at the beginning of the study was negligible between the groups. Therefore, by only using the baseline values of BUN and serum creatinine markers, the analysis may not detect any relationship between the marker values and the risk of allograft failure.Figure 1. Longitudinal profiles of the square root of BUN and serum creatinine with respect to the event status. The curves represent moderate population profiles for the event and non-event groups. The mean population of BUN and serum creatinine markers measured over time was larger in the event group than the non-event group. This indicated the potential association between the risk of occurrence and the longitudinal measurements of BUN and serum creatinine.VariablesEventNon-eventTotal VariablesEventNon-eventTotal N (%)NN (%)N Sex Male25 (59.52)316 (54.86)618Donor sourceLiving donor 27 (67.50)393 (71.07)593Female17 (40.48)260 (45.14)Deceased donor13 (32.50)160 (28.93)Age &,le 4035 (85.37)374 (66.20)606BMIUnderweight6 22.22)27 (7.28)398&,gt 406 (14.63)191 (33.80)Normal15 (55.56)182 (49.06)Serum creatinine after transplantation&,le 1.624 (57.14)479 (83.16)618Overweight6 (22.22)162 (43.66)&,gt 1.618 (42.86)97 (16.84)Months of pre-transplantation dialysis&,le 2433 (82.50)414 (76.24)583HypertensionYes26 (61.91)243 (42.19)618&,gt 247 (17.50)129 (23.76)No16 (38.09)333 (57.81)Types of immunosuppressant drugsA36 (85.71)546 (94.79)618B6 (14.29)30 (5.21)BMI, Body Mass Index A, Patients receiving prednisolone, CellCept&,reg , and cyclosporine B, Patients receiving prednisone, cyclosporine, and Imuran |