Patent Application: US-25948405-A

Abstract:
described are methods of predicting graft survival based on pre - transplant variables . a logistic regression and / or a tree - based model are used to identify predictors of graft survival and to generate prediction algorithms . both the logistic regression model and the tree - based model may be used in clinical practice for long term prediction or graft survival based on pre - transplant variables . the invention is also directed to computer software , which includes a logistic regression model and / or a tree - based model to select pre - transplant variables and generate a graft survival algorithm and to calculate a graft survival probability , and for selecting appropriate organ donors and recipients to optimize the graft survival probability .

Description:
it will be appreciated that the following detailed embodiments and examples described herein are illustrative only and do not limit the invention which is defined by the claims . the present invention is a method of estimating the probability of organ and tissue graft survival using pre - transplant variables . the methods of the present invention use a logistic regression model ( lm ) and a tree - based model ( tbm ). several features make tbm a powerful tool for building a prediction algorithm that can be successfully used in practice . tbm works when the regression variables are a mixture of categorical and continuous variables , it is often able to uncover complex interactions between predictors , which may be difficult or impossible to do using traditional multivariate techniques . the algorithm is non - parametric , so no assumptions are made regarding the underlying distribution of values of the predictor variables . tbm identifies splitting variables based on an exhaustive search of all possibilities , even in problems with many hundreds of possible predictors . simultaneously , it requires relatively little input from the analyst . this graphical algorithm , presented as a collection of simple binary rules , is much simpler to interpret by a non - statistician than the multivariate lm . thus can be used in the decision making without doing any additional calculations , and therefore is more likely to be followed in clinical practice . patients were selected with end - stage renal disease ( esrd ) that underwent kidney or kidney - pancreas transplantation and were listed on the us scientific registry of transplant recipients supplied by unos . the dataset includes transplants performed in infants and young children ( minimal age , & lt ; 1 year ; maximum age 98 years ). independent variables ( see table 4 ) available for analysis included : age , gender , race , height , and weight for both donor and recipient , recipient cause of esrd ( table 1 ), type of pre - transplant renal replacement therapy , number of previous kidney transplants and pre - transplant blood transfusions , recipients &# 39 ; most recent creatinine and donors &# 39 ; terminal creatinine , history and duration of diabetes and htn in the donor , number of hla match and mismatch , cold ischemia time , kidney or kidney - pancreas transplant , and transplant center code . one of skill in the art will recognize that the independent predictor variables are exemplary only and may be added to or modified as necessary or desired . statistical analysis . bivariate analysis was performed using cross - tabulation and comparison of graft survival in the subgroup using the chi - square test . the friedman supersmoothing method was used to fit the curve in bivariate analysis . discrimination was determined by area under receiver operating characteristic ( roc ) curve and chi - square for lm models . model calibration was assessed using the hosmer - lemeshow goodness - of - fit test . for the purpose of prediction analysis , all records were randomly assigned either to a training set ( n = 25 , 000 ), used for knowledge acquisition and model development , or to a testing set ( n = 12 , 407 ), used to validate the models . predicted probabilities of three - year graft survival were generated on a testing set and compared with the actual patient outcomes . the predicted probability of the graft survival with group - average observed graft survival was used to compare the performance of the models . also 2 × 2 contingency tables were used to determine positive and negative predictive values ( pv ). statistical methods used in the current invention include lm and classification trees . in certain situations , traditional statistical methods are poorly suited for complex interactions or detecting patterns in the data . many possible predictor variables may violate the normality assumptions necessary for parametric analysis . in addition , the results of traditional methods sometimes may be difficult to use . therefore , along with a traditional regression model that assumes linear relationship between predictors and the outcome , a tbm was used , which does not require the linearity assumption , and was used in clinical prediction before ( 28 ). tbm is an exploratory technique for uncovering structure in data , which generates a collection of many rules displayed in the form of binary tree ( 29 ). bivariate analysis — donor and recipient characteristics . donor and recipient characteristics . young and old donors and recipients have lower three - year graft survival ( p & lt ; 0 . 001 ) ( fig1 , panels a and b ). there were differences in outcome associated with donor and recipient gender ( table 2 ) and race ( table 3 ) ( p values presented in the tables ). kidneys from the donors with both diabetes mellitus ( dm ) and htn had the worst three - year survival ( 59 . 3 %), while those from the donors without either had the best outcome ( 76 . 3 %). kidneys from either diabetic or hypertensive donors were roughly in the middle ( 66 . 2 and 64 . 3 %, respectively ) ( p & lt ; 0 . 001 ). increased duration of htn and / or diabetes ( from 1 to 5 years by one - year increments ) in the donor was associated with worse outcome ( p & lt ; 0 . 001 for both ). there is no relationship between donors terminal creatinine and graft survival . there were differences in outcome associated with different etiologies of renal failure ( data not shown ). patients with no dialysis history ( pre - emptive transplant ) had the best three - year graft survival ( 81 . 3 %, n = 1 , 940 ) followed by those with history of peritoneal dialysis ( 76 . 1 %, n = 4 , 591 ) and then hemodialysis ( 73 . 0 %, n = 11 , 542 ) ( p , 0 . 001 ). a previous transplant worsened three - year survival in almost a linear fashion with 76 . 7 % survival in the recipient with no previous transplant history , 70 . 9 , 62 . 1 , and 56 . 9 % in those with one , two and more than two previous transplants , respectively ( p & lt ; 0 . 001 ). number of pre - transplant transfusions did not significantly affect graft survival in bivariate analysis . transplant procedure , matching donor and recipient . the three - year survival improves and declines in linear fashion with increasing number of matched and mismatched antigens , respectively ( p & lt ; 0 . 001 ). donor / recipient bmi vs . three - year graft survival looks almost like a bell - shape curve with the best outcome associated with the donor / recipient bmi = 1 ( fig2 , panel a ). the worst survival was in grafts from relatively small donors to large recipients ( p & lt ; 0 . 001 ). transplant centers with a low volume of transplants had variable outcome , while in those with high number of transplants the outcome was relatively uniform ( fig2 , panel b ). there was slight downward trend in relation of three - year graft survival to cold ischemia time ( fig2 , panel c ). recipients of kidney - pancreas transplants had better three - year kidney survival ( 82 . 5 %, n = 3 , 243 ) than those receiving a single ( 75 . 7 %, n = 33 , 526 ) or en - bloc kidneys ( 68 . 2 %, n = 638 ) ( p & lt ; 0 . 001 ). multivariate analysis — logistic regression model ( lm ). using stepwise forward selection , a significance level of 0 . 05 was set for independent variables to enter the model . the variables and model information are presented in table 4 . odds ratios with 95 % confidence intervals ( ci ) for the binary variables identified by the model are presented graphically ( fig4 ). causes of esrd ( table 1 ) in categories that demonstrated & lt ; 70 % three - year survival are : membranous nephropathy ( 66 . 2 %), cyclosporin nephrotoxicity ( 68 . 3 %), analgesic nephropathy ( 68 . 8 %), type ii insulin - dependent dm ( 65 . 6 %), henoch - schonlein purpura ( 69 . 7 %), mesangio - capillary type 1 glomerulonephritis ( 68 . 5 %), hemolytic uremic syndrome ( 54 . 8 %). model discrimination using the c index ( area under the receiver operating characteristic curve ) was 0 . 653 . this is the probability that for a randomly chosen pair of patients , the predicted and observed graft survival are concordant . model calibration was assessed using the hosmer - lemeshow goodness - of - fit test . as the p value , p = 0 . 63 , of this test was not significant , the model &# 39 ; s estimated probabilities of three - year graft survival are not significantly different from the actual survival of patients over groups spanning the entire range of probabilities . prediction analysis — logistic regression ( lm ). to identify predictors of three - year graft survival and develop a prediction model using lm , 25 , 000 records were randomly selected as the training set , while the remaining 12 , 407 records were designated as a testing set and were used to compare predicted and observed three - year allograft survival . a lm model was again generated on the training set only . this model was 65 % concordant , 34 . 5 % discordant , and the c index was 0 . 653 . using the variables and parameter estimates generated with the training set , we calculated the probability of three - year graft survival in the testing set . all records were divided into ten groups based on deciles of predicted probability of graft survival ( 0 - 10 %, & gt ; 10 - 20 %, & gt ; 20 - 30 %, etc .). the observed percentage of three - year graft survival was calculated for each group , and the observed graft survival was compared with the expected survival . as there was only one patient in the & gt ; 10 - 20 % group , that group was combined with the & gt ; 20 - 30 % group to produce a & gt ; 10 - 30 % group . the midpoint of each group &# 39 ; s probability range was used as the expected percent survival . as shown in fig4 the prediction of the probability of graft survival from the training model achieved a very good match with the observed survival of the testing set , with a chi - square value of 6 . 15 and p = 0 . 63 , which shows no significant difference between observed and predicted category , and a correlation of r = 0 . 998 . the predicted allograft failure probability was converted into a binary variable ( graft survival =“ yes ” or “ no ”) using a cut - point of 50 % probability . the results were compared by means of a 2 × 2 contingency table . the positive pv of allograft survival with the model was 76 % and the negative pv was 63 %. prediction analysis — tree - based model . a tbm was used to identify predictors of three - year graft survival and develop a prediction model . the outcome of cross - validation procedure in the form of deviance plotted against number of terminal nodes ( tree size ) was analyzed and the optimal size of the tree was determined to be equal to 54 terminal nodes . to identify predictors of the outcome , the initial tree was constructed on the whole dataset and pruned to 54 terminal nodes . the following 17 predictors of outcome ( in order from the root of the tree to the terminal nodes ) were identified by the tbm : recipient race , donor age , recipient weight , cold ischemia time , recipient height , previous number of transplants , recipient age , number of matched hla antigens , donor race , cause of esrd ( table 1 ), recipient gender , number of mismatched hla antigens , recipient bmi , recipient weight , presence of diabetes and / or htn , donor height , donor / recipient bmi . the residual mean deviance of the model is 1 . 03 and misclassification error rate was 0 . 23 . the new tbm was built upon a training set and validated on the testing set . using the model generated with the training set , the probability of three - year graft survival was calculated in the testing set . all records were divided into ten groups based on deciles of predicted probability of graft survival ( 0 - 10 %, & gt ; 10 - 20 %, & gt ; 20 - 30 %, etc .). the observed percentage of three - year graft survival was calculated for each group . the observed graft survival was compared with the expected survival . as there were only six patients in the 0 - 10 % and & gt ; 10 - 20 % groups together , those groups were combined with the & gt ; 20 - 30 % group to produce a 0 - 30 % group . for the same reason groups & gt ; 30 - 40 % and & gt ; 40 - 50 % were combined to produce & gt ; 30 - 50 % group . the midpoint of each group &# 39 ; s probability range was used as the observed percent survival ( fig6 ). the prediction of the probability of graft survival from the training model achieved a good correlation with the observed survival of the testing set ( r = 0 . 984 ). the predicted allograft failure probability was converted into a binary variable ( graft survival =“ yes ” or “ no ”) using a cut - point of 50 % probability ( fig6 ). the graph represents the model in a form of dichotomous tree , where each node presents a question regarding the value of a single independent variable . if the answer to the question is “ yes ” users move to the next node by way of the left branch ( or right branch , if the answer is “ no ”) until it reaches the terminal node , which predicts three - year graft survival ( y or n ). the results were compared by means of a 2 × 2 contingency table . the positive pv of the allograft survival with the model was 76 . 0 % and the negative pv was 53 . 8 %. 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