ISSN: 2378315X BBIJ
Biometrics & Biostatistics International Journal
Research Article
Volume 5 Issue 2  2017
Using the Logistic Regression to Predict Saudi’s Kidney Transplant Rejection Patients
Ezz H Abdelfattah^{1}*, Marzog S Al Nasser^{2}, Ahmed S Ali^{3} and Mai A Abdul Sattar^{3}
^{1}Statistics Department, King Abdulaziz University, Saudi Arabia
^{2}Armed Forces Hospital, Saudi Arabia
^{3}Clinical Pharmacology Department, King Abdulaziz University, Saudi Arabia
Received: December 02, 2016  Published: February 15, 2017
*Corresponding author:
Ezz H Abdelfattah, Statistics Department, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia, Email:
Citation:
Abdelfattah EH, Nasser MSAl, Ahmed SA, Sattar MAA (2017) Using the Logistic Regression to Predict Saudi’s Kidney Transplant Rejection Patients. Biom Biostat Int J 5(2): 00129. DOI:
10.15406/bbij.2017.05.00129
Abstract
Background: Many factors may affect rejection in kidney transplant patients. Tacrolimus is immunosuppressive agent used for the prevention of the rejection in kidney patients which has narrow therapeutic range and variable pharmacokinetics. Many other factors like age, gender, Nephrotoxicity (NT), Fluid Retention (FR) may affect the rejection.
Objectives: To build a predictive model based on the Binary Logistic Regression that can identify the kidney Transplant Rejection Patients that contains only the significant factors only out of all variables measured on Saudi Patients.
Method: The research population consisted of 100 SKTP at the Armed Forces Hospital in the Southern Region (AFHSR) treated with Tacrolimus and followedup for a period of 24 months (2012 till 2014). Many other variables were measured on these patients.
Results: A significant Binary Logistic model that can be used to detect the factors affect the rejection and the probability of rejection. The significant factors (based on the stepwise logistic regression) where found to be Nephrotoxicity (NT), Fluid Retention (FR) and Tacrolimus trough level (after more than 180 days) (TTL). The Probability of rejection for the kidney can be calculated based on the equation: $$\text{Prob(rejection)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}{e}^{z}}$$
where z = 1.004 + 2.769× NT + 24.234× FR .856× TTL
Keywords: Logistic regression; Tacrolimus; Kidney transplant; Saudi
Abbreviations
SKTP: Saudi Kidney Transplant Patients; AFHSR: Armed Forces Hospital in the Southern Region; CYP3A: Cytochrome P450 3A System; TDM: Therapeutic Drug Monitoring; ANOVA: Analysis of Variance; CI: Confidence Interval
Introduction
Organ transplantation requires lifelong pharmacotherapy with combination of immunosuppressant drugs which include a steroid, and immune modulator (e.g. mycophenolate mofetil, and a calcineurin inhibitor (CNI) like cyclosporine A and Tacrolimus [1].
Tacrolimus became an essential component of immunosuppressant regimens in most transplant centers. Its mechanism involve selective suppression of Tlymphocyte and its pharmacokinetic is quite variable among individuals and influenced by so many variables, race, time after transplantation, and other chronic illness. It is extensively metabolized in the liver by cytochrome P450 3A system (CYP3A), which is subject to considerable interindividual variation and drug interaction [2]. It produces many adverse reactions which include including infections and malignancies, nephrotoxicity, hypertension and diabetes mellitus [3]. Furthermore, Tacrolimus is liable for several drug interactions, primarily with agents affecting the cytochrome P450 system which include food, and herbal medicines. These interactions may lead to serious toxicity or rejection of the transplanted organ [3]. Tacrolimus has narrow therapeutic window; under dosing is associated with an increased risk for rejection, whereas overdosing is associated with higher incidence of dose related toxicity [4].
Marzouk et al. (2017) show that there is a significant relationship between Tacrolimus trough level and incidence of kidney rejection was remarkably found only after 180 days posttransplantation. During this period, Tacrolimus mean trough level (ng/ml) was 7.4 ± 0.2 in SKTP with no rejection, 5.3 ± 0.7 for those with acute rejection, and 3.8 ± 0.4 for those with chronic rejection. Furthermore, the coefficient of variation (CV %) which reflects fluctuation in Tacrolimus trough level, was obviously high in SKTP with acute rejection in all postkidneytransplant periods.
The aim of present study is to build a predictive model based on the Binary Logistic Regression that can identify the kidney Transplant Rejection Patients that contains only the significant factors measured on Saudi Patients [5,6].
Method
A retrospectively was done during 2012 till 2014, all adult Saudi kidney transplant patients who were followedup in Kidney Transplant Center in Armed Forces Hospital in the Southern Region are legible for inclusion in the present study.
All adult patients of either sex, in the age group of 1860 years, recipient of only first renal transplant and those on immunosuppressant therapy comprising of Tacrolimus, MMF and Prednisolone only were included in the study. Patients with more than one kidney transplant procedure. or who use other immune suppression regimen, or Cyclosporine based immunosuppressive therapy . Also patients who show poor drug compliance record or not attend regularly for follow up as scheduled were excluded.
At the AFHSR in Khamis Mushait (Saudi Arabia), the initial Tacrolimus orally dose taken is 0.1 mg/kg/day (two divided doses) and subsequently adjusted as guided by assessment of the patients which includes scheduled Tacrolimus trough level determination (in view of international; guidelines). the following target of Tacrolimus trough level were implemented in SKTP which depend on post transplantation time: 114 days (1012 ng/ml), 1528 days (810 ng/ml), 29 days to 180 days (68 ng/ml) and from 180 days onward (57 ng/ml).These reference range according to transplant protocol which approved by kidney transplant center in AFHSR .
Parameters used for measurement of outcomes in this study included: acute and chronic rejection kidney rejection as indicated by clinical manifestations (i.e. graft enlargement, fever, malaise, hypertension, oliguria and decreased renal clearance), biopsy test and histopathological findings. Furthermore, posttransplant NODM, hypertension, nephrotoxicity, and neurotoxicity were recorded.
The following data were retrieved by the researcher from patients medical record (classic file and computerized system) and recoded in A data collection form which involved for example following items: Demographics: Age, height, weight and BMI. Medical profile: Source of transplanted kidney, Etiology of ESRD, type of induction therapy, current immunosuppressant medication doses, other medications, adverse effects associated with immunosuppressant therapy, incidence of rejection episodes and all relevant lab investigation including Tacrolimus blood trough level (C0), Lab test: chemistry, hematology, serology and immunology test [7].
Statistical analysis
This research uses SPSS 24 software. The findings were processed through descriptive statistics (i.e. mean, SD, and coefficient of variation etc.) and inferential statistics (i.e. testing for significance, using the Chisquare test, ttest, one way Analysis of Variance (ANOVA), correlation and logistic regression). Data are expressed by means ± SE were p value < 0.05 is considered significant.
Results
Demographic characteristics and relevant clinical data are presented in Tables 1 & 2, to allow precise comparison with other similar studies. Out of 100 SKTP enrolled in the present study 59 were males and 41 were females, the mean age ± SD of the patients was 37.4±14.2 years. The median age was 34.5 years, the age ranged between 18 and 60 years, the mean BMI ±SD of the patients was 27.3±6.6 Kg/m^{2}. The BMI ranges between 16.4 and 47.4 Kg/m^{2}. The median BMI was 26.9 Kg/m^{2}.
Statistics 
Age (Years) 
Height
(m) 
Weight
(Kg) 
BMI
(Kg/m2) 
Mean ± SD 
37.4±14.2 
1.58±0.08 
68.8±18.4 
27.3±6.6 
Table 1: Demographic data for the sample of SKTP (41 male, 59 female, total 100).
Parameter 
Relevant Findings 
% 
Place of transplantation 
AFHSR (Khamis Mushate) 
81 
Other places 
19 
Etiology of kidney failure * 
Hypertensive nephropathy 
69 
Small kidney +other reasons 
13 
Diabetes mellitus nephropathy 
11 
Induction Therapy 
Unknown 
7 
Yes 
89 
Not reported 
11 
HBAg 
nonreactive 
97 
Reactive 
3 
HCV 
nonreactive 
96 
Reactive 
4 
HIV 
nonreactive 
100 
CMV G 
Positive 
100 
CMV M 
Negative 
100 
Type of Donor 
Nonrelative 
23 
Relative 
59 
Deceased 
18 
Table 2: Relevant clinical variable in SKTP (n=100).
Kidney Transplantation for the majority of the patients (81%) was in AFHSR Khamis Mushait. Records showed that most of the patients (89%) received induction therapy before transplantation. Tacrolimus initial dose was 0.1 mg/kg/day (twice daily). Limited numbers of the patients were reactive for HBAg and HCV (3 % and 4% respectively). While all patients were negative for HIV and CMVM; but they were positive for CMVG.
Regarding documented etiology of ESRF; hypertension represented the major cause for kidney failure (69%). Followed by diabetes mellitus (14%). Glomerulonephritis among other kidney disorders were also documented as less common reasons for kidney failure.
59% of the patients in the present study received kidney from first grade relative and 23% of them received kidney from living nonrelative donors and 18% of the transplanted kidneys were obtained from deceased persons.
Although no significant statistical relationship between the type of donor and incidence of kidney rejection in SKTP (chisquare and Fisher exact tests pvalues were > 0.05). The results provided an impression that SKTP received kidney from living related donor showed a relatively lower incidence of rejection episodes compared to those received cadaveric kidney.
Table 3 summarizes Tacrolimus mean trough level (ng / ml) in different post kidney transplant periods in SKTP classified according to incidence of rejection episodes.
Time Post Transplantation 
No Rejection
N= 90 
Acute Rejection
N=8 
Chronic Rejection
N=2 
P Value 

Mean ± SD 
CV % 
Mean ± SD 
CV % 
Mean ± SD 
CV % 

0 – 14 days 
12.12 ±2.69 
22.2 
11.71±5.84 
49.9 
10.50±2.33 
22.2 
> 0.5 
15 – 28 days 
10.23±2.15 
21.0 
9.69±5.12 
52.8 
8.65±1.77 
20.5 
>0.5 
29 – 180 days 
8.77±2.29 
26.1 
8.16± 2.48 
30.4 
6.65± 1.34 
20.2 
>0.5 
> 180 days 
7.37±1.87 
25.4 
5.34±2.03 
38.0 
3.75±0.54 
14.4 
0.001 
Table 3: Mean Tacrolimus trough level at various time post transplantation in SKTP and its relation to incidence of rejection episodes during 24 month follow up period.
It was noted that the significant relationship between Tacrolimus trough level (ng/ml) and incidence of kidney rejection was only established in the period after 180 days post transplantation. (Pvalue = 0.001). In this period, Tacrolimus trough level was 7.4 ± 0.2 in patients who showed no rejection; 5.3 ± 0.7 for those who suffered acute rejection episodes and 3.8 ± 0.4 for those subjected to chronic rejection (Kidney loss). The CV % which reflects variation between the Tacrolimus level was shown to have its greatest value in SKTP showed acute rejection in all different post kidney transplant periods.
Table 4 shows that 95% confidence interval (CI) Tacrolimus trough level for the patients who showed no rejection episodes.: from 1  14 days, the range was 11.5  12.7 (ng/ml); from 15  28 days, it was 9.7  10.6 (ng/ml); for the 29th180 days, it was 8.2  9.2 (ng/ml) and for more than 180 days, the proposed range was 6.9  7.8 (ng) (Figures 1 & 2).
Time Post
Transplantation 
Mean
Tacrolimus Trough Level 
95 % CI Of (TTL) 
0 – 14 days 
12.12 
11.5 
12.7 
15 – 28 days 
10.23 
9.7 
10.6 
29 – 180 days 
8.77 
8.2 
9.2 
More than 180 days 
7.37 
6.9 
7.8 
Table 4: 95 % confidence interval (CI) of Tacrolimus trough level (TTL)(ng /ml) in SKTP showed no rejection during 24 follow up period.
Figure 1: Correlation between type of donor and incidence of renal rejection in SKTP.
Figure 2: Box blot for median Tacrolimus trough level (ng / ml in the period 624 month after transplantation.
Logistic Regression
When the dependent variable is binary or has only two values (yes, no), the regression method is known as binary logistic regression. Before this, a method of discreminatnt analysis was also in practic but this allows direct prediction of group membership but the assumptions of multivariate normality if independent variables is required for prediction rule to be optimal. Logistic regression model requires fewer assumptions than discriminant analysis and even when the assumptions required for discriminant analysis are not met, logistic regression, still performs well. In logistic regression one can directly estimate the probability of an event where as in linear regression it is not possible as they do not fall in the interval 0 to 1.
The method of logistic regression has become the standard method of analysis for the last three decades, when the dependent variable is binary or dichotomous (yes, no). The difference between logistic and linear regression lies both in the choice of a model and assumptions. Once the difference is accounted for, then logistic method of analysis follows the same general principles as used in linear regression. Stepwise regression is a method of fitting regression models in which the choice of predictive variables is carried out by including only significant variables to the rmodel in many steps based on the number of variables to be including to the model. In each step, a variable is considered for addition to or subtraction from the set of explanatory variables.
We applied the binary logistic regression by considering having a kidney rejection as a depaendent variable and all other variables are considered as independent variables. A significant Binary Logistic model can be used to detect the factors affect the rejection and the probability of rejection. The significant factors (based on the stepwise logistic regression) where found to be Nephrotoxicity (NT), Fluid Retention (FR) and Tacrolimus trough level (after more than 180 days) (TTL). The Probability of rejection for the kidney can be calculated based on the equation [828]:
$$\text{Prob(rejection)}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}{e}^{z}}$$
where z = 1.004 + 2.769× NT + 24.234× FR .856× TTL
The following table summarize the variables coefficients and the corresponding odds ratios (Table 5):
Variables Affecting Kidney Survival 
Symb. 
Model Coefficient 
Odds Ratio 
Nephrotoxicity 
NT 
2.769 
15.949 
Fluid Retention 
FR 
24.234 
33462461965.163 
Tacrolimus trough level (after more than 180 days) 
TTL 
.856 
.425 
Constant 
Constant 
1.004 
2.728 
Table 5: The variables coefficients and the corresponding odds ratios.
Interpretation of Odds Ratio
A value of 15.9 of odds ratio for Nephrotoxicity means that with the existence of Nephrotoxicity , there is a chance about 16 times for the kidney rejection in compare of non existence provided all other factors are kept constant.
Also A value of 33.46E9 of odds ratio for Fluid Retention means that with the existence of Fluid Retention, there is a confirmed kidney rejection in compare of non existence provided all other factors are kept constant.
With the increase of one ng/ml in Tacrolimus trough level (after more than 180 days) the risk of rejection is decreased 0.425 times provided all other factors are kept constant.
As an example on how to use the logistic regression equation for prediction, suppose that a patient has the following measurements: NT= yes, FR= No and TTL=3, Then
z = 1.004 + 2.769× 1 + 24.234× 0 .856× 3 = 1.205
Hence, the probability of rejection:
$$Prob\text{}\left(rejection\right)=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{1}{1\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}{e}^{1.205}}=0.77$$
Examples for different possibilities
Nephrotoxicity 
F.R. 
Conc. 
Probability of Rejection 
Yes 
Yes 
3 
1 
Yes 
Yes 
8 
1 
Yes 
No 
3 
0.77 
Yes 
No 
8 
0.04 
No 
Yes 
3 
1 
No 
Yes 
8 
1 
No 
No 
3 
0.17 
No 
No 
8 
0.00 
Conclusion
Trough level monitoring during the 1st 6 month post transplantation and achievement of target level couldn’t solely exclude the risk of incidence of rejection. After a period of 180 days posttransplantation, inadequate Tacrolimus trough level (< 5 ng/ ml can lead to chronic rejection (graft loss). Fluctuation in Tacrolimus trough is a major risk factor in incidence of rejection. Monitoring trough level is a valuable tool to adjust the Tacrolimus after 6 month post transplantation and its recommended to keep within 58 ug/ ml. Further studies are recommended to evaluate the utility of the LSS for TDM of Tacrolimus in SKTP first 6 months post transplantation. The significant factors (based on the stepwise logistic regression) where found to be Nephrotoxicity (NT), Fluid Retention (FR) and Tacrolimus trough level (after more than 180 days) (TTL).
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