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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Ren Fail. Author manuscript; available in PMC 2011 May 12.
Published in final edited form as:
PMCID: PMC3093108
NIHMSID: NIHMS286430

Analyses of renal outcome following transplantation adjusting for informative right censoring and demographic factors: A longitudinal study

Abstract

Demographical factors such as race, vital status, gender and age could affect the final renal outcome of patients who undergo renal transplantation. These demographical factors could be assessed at a recipient and donor levels. Repeated measures for blood urea nitrogen (BUN) are typically recorded for each patient following renal transplantation, as a biomarker to assess renal progress. However, once a patient develops renal failure due to graft rejection, no measurement of BUN can be registered and the patient goes back to dialysis. This causes loss of follow-up and incomplete data on BUN measurements, a problem referred to as informative right censoring. If this problem is ignored inaccurate and biased estimates will be generated. In this study unbiased estimates for rate of change for BUN levels over time adjusted for informative right censoring and demographical factors were acquired using a sophisticated model of analysis. Our results demonstrated that BUN levels for Caucasians were decreasing at a greater rate than African-Americans (P<0.0001). When donors are deceased, African-American recipients showed an increase instead of a decrease in their BUN levels following transplantation. Moreover, African-Americans showed a decrease in their BUN levels when donors were African-Americans compared to when donors were Caucasians (P=0.03). Our results also showed that BUN levels were decreasing at a greater rate when donors and recipients were of different gender than when they were of same gender (P = 0.009). These results suggest that success of renal transplantation is impacted by donor/recipient demographical factors.

Keywords: BUN rate of change, Renal transplant, Longitudinal data, Informative missing Values

Introduction

Renal transplant is an increasing therapy of choice for patients with end-stage renal disease (1,2). However several demographical factors that could affect the success of renal outcome following transplantation include race, gender and age of the recipient (3,4). Likewise the donor’s race, gender as well as vital status (deceased or living) could have a significant impact on short and long-term outcomes (57). Thus, the appropriate matching of the donor and the recipient is a key factor for successful renal outcome following renal transplantation (8,9).

Blood Urea Nitrogen (BUN) and serum creatinine are biomarkers that are typically measured repeatedly over time for patients who had undergone renal transplantation (10). These biomarkers provide an evaluation of how well the kidneys are functioning following renal transplantation. In this study we were interested in in evaluating the rate of change of BUN levels that are regularly recorded for each patient over time following renal transplantation. However, it is not unusual for patients to experience renal failure following renal transplantation that is usually attributed to graft rejection. In this case, patients with graft failure go back on dialysis, and as a result, no more measurements on BUN can be attained. This will leave the patient with incomplete set of BUN measurements for analyses, a problem that is referred to as informative right censoring. If informative right censoring is ignored in the data analysis then this will result in biased estimates of the rate of change of BUN, and hence inaccurate evaluation of renal outcome (1113).

Although evaluating the rate of change of BUN over time gives a powerful quantitative assessment of renal outcome following transplantation, generating such an estimate for the rate of change can be a complex issue because of the problem of informatively missing values, a common occurrence among patients that undergo renal transplantation and experience graft failure. Therefore, an appropriate statistical approach that accounts for informative missing values is essential in assessing renal outcome following transplantation among the different groups of patients (11,12).

Therefore, in this study valid estimates of the rate of change for BUN levels were generated over a period of three years following renal transplantation using advanced statistical models that adjust for informative missing values (14). Thus obtaining accurate and unbiased estimates of the rate of change for BUN over time for each patient adjusted for informative right censoring and demographical factors, will enable us to assess the impact of these demographical factors on the temporal changes of BUN levels following renal transplantation.

Methods

Study Population

The study population included 103 patients who had undergone renal transplant in the year 2000 at the Medical University of South Carolina (MUSC). Registry information includes demographic information for both donor and recipient as well as follow-up kidney function after transplant. BUN levels for each patient were recorded at baseline and post-transplant. Seven measurements of BUN were recorded at 0 (baseline measure preceding transplantation), 1, 3, 6, 12, 24, and 36 months following renal transplant; i.e., three-year follow-up measurements were collected on BUN between the years 2000 to 2003. Twenty one patients had informative missing values due to graft failure. A normal BUN level ranges between 8 mg and 25 mg per 100 ml of blood. Whereas, the mean BUN values of the patients prior to transplantation is 90 ± 30 mg per 100 ml of blood.

Statistical Approach

A sophisticated statistical model that adjusts for informatively right censored dadat when generating estimates for the rate of change ([beta]) of BUN levels for the renal transplant patients was employed in this study (14, statistical model described in the appendix). [beta], denotes the rate of change (increase or decrease) in mg per 100 ml of blood for BUN levels every month. NLMIXED SAS procedure was employed to generate the rate of change ([beta]) for BUN levels (15). In order to achieve linearity, a logarithmic transformation was applied on the BUN values and the measurement time points (0, 1 months, 3 months, 6 months, 12 months, 24 months, and 36 months) following the transplant. The rate of change in BUN levels were estimated for each group of patients that were categorized according to:

  1. Recipients characteristics:
    1. Gender (males vs. females).
    2. Race (Caucasians vs. African-Americans).
    3. Age (<= 50 vs. > 50).
  2. Donors characteristics:
    1. Gender (males vs. females).
    2. Race (Caucasians vs. African-Americans).
    3. Vital status (living vs. deceased).
  3. Donors-Recipients characteristics:
    1. Same gender vs. different gender.
    2. Same race vs. different race.

Due to multiple comparisons and to avoid inflated type I errors, Bonferroni correction was conducted on the significance level. Accordingly the P-values we are reporting are adjusted using Bonferroni correction.

This study was approved by the MUSC Institutional Review Board.

Results

Donor/recipient profile

The renal transplant recipient patients included 46 Caucasians, and 57 African Americans. As for gender distribution, the study population included 44 females and 59 males. Among donors, 80 were Caucasians and 23 were African-Americans. There were 36 female donors and 67 male donors. Of the donors 84 were deceased and 19 donors were living. As for donors-recipients race match the distribution was as follows: 42 Caucasian donors-Caucasian recipients, 38 Caucasian donors-African-American recipients, 19 African-American donors/African-American recipients, and 4 African-American donors-Caucasian recipients. As for the gender donor-recipient profile, there were 15 female donors-female recipients, 21 female donors-male recipients, 38 male donors- male recipients, and 29 male donors-female recipients.

Influence of recipient gender, race and age

Analyses identified the significant influence of the recipient’s gender, race and age on the estimates of the rate of change of BUN levels; i.e., it illustrated the impact of the recipient’s characteristics on the success of the renal transplant. The estimated rate of change ([beta]) of BUN levels for each of the recipient groups (grouped according to gender, race and age) are shown in Table 1. The results indicate that the estimated rate of change of BUN levels for female recipients ([beta]= −0.099, P<0.0001) and for male recipients ([beta]= −0.057, P<0.0001) were both significantly decreasing with time following renal transplant. However, the decrease in the rate of BUN levels was significantly greater in female recipients compared to male recipients (P<0.05).

Table 1
Shows the rate of change over time ([beta]) for BUN levels at a log scale of recipients of kidney transplant, standard error (SE) by gender, race and age.

Similar analyses determined effect of the recipient’s race (Table 1). In this context, the estimated rate of change for BUN levels for both Caucasian recipients and African-American recipients are decreasing with time following renal transplant (Caucasian: [beta]= −0.148, P<0.0001; African-American: [beta]= −0.041, P=0.0004, Table 1). However, the decrease in the rate of BUN levels was significantly greater in Caucasian recipients compared to African-American recipients (P<0.0001). As for the effect of age on the outcome of renal transplant, no significant difference was observed between the recipients below the age of 50 inclusive, and those above the age of 50 (P = 0.38, Table 1).

Influence of donor gender, race and vital status (living/deceased)

The influence of donor gender (female versus male), donor race (Caucasian versus African-American) and donor vital status (living versus deceased) on the rate of change of BUN levels was also assessed. Our results showed that there was no significant effect of the gender and race of the donor on the rate of change of the BUN levels among recipients (P = 0.079, and P = 0.33 respectively) However, there was a significant impact of the vital sign of the donor (living versus deceased) on the outcome of renal function following transplant. In this regard, our results showed that although the estimated rate of change for BUN levels for recipients of kidneys from both living and deceased donors are decreasing with time following renal transplant (living: [beta]= −0.196, P<0.0001; deceased: [beta]= −0.061, P<0.0001), the decrease in the rate of BUN levels was significantly greater in recipients of kidneys from living donors than recipients of kidneys from deceased donors (P<0.0001). Thus our results indicated that only the donor’s vital status influenced the rate of change for BUN levels and the advantage was to the group of recipients from living donors as compared to deceased donors. Nonetheless, there was no significant effect of either gender or race of the donors.

Influence of donor-recipient characteristics

Table 2 presents the estimated rate of change for BUN for recipients having different gender from the donors ([beta]=−0.106, P<0.0001) and for recipients having the same gender as their donors ([beta]=−0.061, P<0.0001). For both groups, the rate of change of BUN levels was towards decreasing with time following renal transplant. However, the decrease in the rate of BUN levels was significantly greater in recipients having different gender than their donors compared to recipients having same gender as their donors (P=0.009).

Table 2
The rate of change ([beta]) for the BUN levels at a log scale of recipients of kidney transplant, standard error (SE) by race of donor-recipient.

As for matching donors and recipients based on race, our results (Table 2) suggested that the estimated rate of change of BUN level for the group of recipients who had the same race as their donors ([beta]=−0.121) was decreasing at a greater rate compared to those recipients who had a different race as their donors ([beta]=−0.040), P<0.0001. Accordingly, our results suggested significant effect of matching donors and recipients on the rate increase or decrease of BUN levels following transplantation.

Influence of donor-recipient gender

Matching donors and recipients based on gender and race was investigated further in our study. Our results presented in Table 3 suggested that when the donor was male, the estimated rate of change for BUN levels for female recipients ([beta]= −0.14) decreased at a significantly greater rate (P<0.0005) than male recipients ([beta]=−0.052). However, with female donors there was no significance difference between female and male recipients. In addition, our results also showed that females receiving kidneys from male donors ([beta]=−0.14) had a greater decrease in BUN levels (P=0.005) compared to males receiving kidneys from female donors ([beta]=−0.061).

Table 3
The rate of change over time ([beta]) for the BUN levels at a log scale of recipients of kidney transplant, standard error (SE) by donor-recipient gender. The estimated rate of change correspond to the recipients that are: 1) females and have ...

Influence of donor-recipient race

The results in Table 4 revealed that when donors are Caucasians, Caucasian recipients had a greater decrease in BUN levels than African-American recipients (P<0.0005) with estimated BUN rate of change [beta] = −0.151 and [beta] = −0.03 respectively. However, when donors were African-Americans, the decrease in the estimated rate of change in BUN levels for the Caucasian recipients ([beta] = −0.138) was not significantly greater than that of African-American recipients ([beta] = −0.089), P=0.145. Thus Caucasian recipients had a greater decrease in BUN compared to African-American recipients when donors are Caucasians. This is not the case when Donors are African-Americans.

Table 4
The rate of change over time ([beta]) for the BUN levels at a log scale of recipients of kidney transplant, standard error (SE) by donor-recipient race. The estimated rate of change corresponds to the recipients that are: 1) Caucasian and ...

The results of Table 4 also showed that there is no statistically significant difference for Caucasian recipients whether their donors are Caucasian or African-Americans (P=0.3). Unlike Caucasian recipients, African-American recipients showed a greater decrease in BUN levels (about 23%) when their donors were also African-Americans than when their donors were Caucasians (P = 0.03). Thus for African-American recipients rate of change of BUN is impacted by whether their donors are African-Americans or Caucasians.

Finally, the results in Table 4 also demonstrate that the group of Caucasian donors-recipients had a greater decrease in BUN than the group of African-American donors-recipients, P=0.05.

Influence of donor vital status (living/deceased) and recipient race

When donors were deceased, the BUN levels for Caucasian recipients decreased by 0.108, whereas, that for African-Americans recipients increased by 0.0989, P<0.0005 (Table 5). Accordingly, with respect to African-American recipients, our results suggested that kidney transplantation from deceased donors resulted in an increase in BUN levels after transplantation by an amount of 1.1 mg per 100 ml of blood a month. With regard to living donors, no significant difference was observed between Caucasian and African-American recipients (P= 0.075).

Table5
The rate of change over time ([beta]) for the BUN levels at a log scale of recipients of kidney transplant, standard error (SE) by donor type (living/deceased) and by recipient race. The estimated rate of change corresponds to the recipients ...

With respect for deceased donors, we conducted further analysis to assess the effect of deceased donors on the recipient’s race. The results demonstrated that when the donors were deceased Caucasians, Caucasian recipients had a greater decrease in their BUN levels (66% decrease) compared to African-Americans (p-value = 0.004). Similarly, when the donors were deceased African-Americans, Caucasian recipients still performed better than African-American recipients (P = 0.04).

The results in Table 5 also suggested that Caucasian recipients who received kidneys from living donors had a greater decrease in their BUN levels (54% decrease) compared to Caucasians who received kidneys from deceased donors, P<0.0005. Same result was also observed for African-American recipients, since they displayed a significant decrease in their BUN levels when their donors were living compared to when their donors were deceased (P<0.0005). Therefore, regardless of the recipient race, recipients of kidneys from living donors appear to have a greater decrease in BUN levels compared to recipients of kidneys from deceased donors.

Discussion

In the current study significant demographic factors were identified that could affect the rate of change of BUN levels and thus the outcome of renal transplant over time following the transplant. Female recipients were observed to have a greater decrease in their BUN levels than males. These results confirm earlier studies with similar conclusions (49). The better renal outcomes were attributed to the protective effect of estrogen (16). From the current study, race appeared to have a significant impact in the sense that Caucasian recipients’ BUN levels appeared to be decreasing at a greater rate than African-Americans. No significant effect of age was found when dichotomized by age above 50 and below 50 inclusive.

As for donors, it was shown that no significant impact of donor’s gender on the BUN levels can be detected. This result confirms previously reported study by [empty]ien C. et al. (17) who showed no significant effect of donor’s gender on graft failure despite the earlier studies that speculated that female donors had poorer effect than male donors on the outcome of kidney transplants (16). These early studies based their speculation on nephron underdosing in females caused by their smaller kidney weight compared to males, resulting in fewer nephrons and nephron overload (2, 18). The lower nephron number is supported by results from Lackland et al., where low birth weight babies were significantly more likely to develop end-stage renal disease (19). However, follow-up studies have inconsistent findings when the kidney size was corrected for the total body surface area (20).

No significant impact of donor’s race on the BUN rate of change was detected. Nonetheless, donor’s vital sign, whether living or deceased, had a great impact on the rate of change of BUN levels. In this regard, recipients of kidney from living donors had a greater decrease in BUN than those of deceased donors.

Matching donors and recipients was also shown to have a great impact on the BUN levels. In this regard, we realized that recipients having the same race as their donors had a significantly greater decrease in BUN levels than those having different races. As for matching based on gender, the opposite was observed. When recipients and donors were of opposite gender, the associated BUN levels decreased at a greater rate than those of same gender.

In this study, our results showed that African-American recipients had significantly better renal outcomes as assessed by the rate of decrease in BUN levels over time when their donors were also African-Americans. In turn, Caucasian recipients had better renal outcome than African-Americans regardless of the donor’s race. African-American kidney function was significantly poorer when donors were deceased since their corresponding rate of change for BUN levels was shown to increase with time.

The clinical implications of these findings would include the race and vital status of the donated kidney, as well as the recipient’s race. For African-American recipient, the preferred donor would be African-American and living. For Caucasian recipients, it was less relevant whether their donors were Caucasian or African-American. Nonetheless, Caucasian recipients did better when their donors were living.

The strength of this study lies in the longitudinal repeated measures for a period of three years for patients who underwent kidney transplantation. These repeated measures enabled us to monitor and assess the rate of change for BUN levels over time following transplantation for each group of patients. In addition, since the problem of informative right censoring due to graft failure was common in this longitudinal study, implementing a sophisticated analytical model to generate unbiased and accurate estimates for the BUN rate of change by adjusting for this censoring problem was of great advantage. However, a limitation of this statistical model is that it does not allow for incorporation of covariates and adjusting for them in our statistical modeling. We are in the process of extending our statistical model to allow for adjustments of covariates in our analysis. Furthermore, it would be interesting to conduct a study that will use other known renal biomarkers such as eGFR as well as serum creatinine. Moreover, adjusting for factors such as immunosuppression and number of previous transplantations would also provide important information regarding the final outcome of renal function following transplantation.

In summary, our findings identified that the success of renal transplantation is affected by race, donor vital status and gender. It is important to take these factors into consideration when matching donors with recipients in order to achieve optimal outcomes following renal transplantation.

Acknowledgement

This research was supported by Award Number UL1RR029882 from the National Center for Research Resources and by a grant from the National Institutes of Health HL55782.

Appendix

Statistical Approach

The Model: Consider a set of i=1,…,n independent subjects, with outcome yik at measurement times k=(ti1, ti2,…,timi), where mi is the number of observations for subject i, which is assumed to be greater than 1 for all subjects in the study (2 ≤ mip). The underlying model for yik is assumed to be

equation M1
(1)

with random effects αi and βi, and random error eik, which is assumed to be normal with mean zero and variance equation M2. The random effects αi, βi, and eik are all assumed to be mutually independent. Then, given αi and βi, yik is normal with mean αi + βi tik and variance equation M3. Ordinary least squares (OLS) estimate of βi are,

equation M4
(2)

where ti is the sample mean of the observation times for subject i. Further, given αi and βi,

equation M5
(3)

for each individual subject the following model was assumed (Mori et al, 1994):

  1. equation M6
    (4)
  2. mii ~ Truncated geometric with Pi = F01βi);
    equation M7
    (5)
  3. equation M8
    (6)

Assumption 1) states that the underlying individual subjects’ slopes βi ’s are normally distributed with a mean β and variance equation M9. Assumption 2) states that the number of observations for each individual is dependent on the individual’s true rate of change. The truncated geometric distribution follows the probability model: Pr(M=mi)={1−F01βi)}mi−2{F01βi)}Ri, mi=2,3,…,p with p being the number of the prespecified time points. equation M10, where Ri is an indicator variable that takes the value 1 if censoring occurred and zero otherwise, and γ1 is the censoring parameter that is zero if the censoring process is non-informative and different from zero if the censoring process is informative. The geometric distribution used in this model is left-truncated since at least two observations are required to estimate the slope, and right-truncated since the study may terminate before the withdrawal of every subject is observed.

Assumption 3) states that the observed OLS slope for each individual bi,ols (i = 1, 2,…,n) follows a normal distribution with mean βi and variance equation M11. Then a joint distribution of mi, βi and bi,ols was presented. The joint distribution did not include the response vectors yi ’s since the interest was in the rate of change. The missing value mechanism was assumed to depend on the random effects βi of the distribution of bi,ols. Accordingly, βi functions both as a parameter and as an unobserved observation.

The corresponding likelihood function was presented as:

equation M12
(7)

Maximization of the Likelihood Function

In our study we propose the following maximization approach:

Since βi is not observed, we integrated the likelihood over βi to get a marginal likelihood,

equation M13
(8)

Thus, we maximize the marginal likelihood, integrated over the unobserved random βi to obtain the maximum likelihood estimate of population slope β, γ0 and γ1. However, we also use empirical Bayes method to predict βi for each individual. The Empirical Bayes estimates of the individual random slopes are obtained via an approach similar to Ten Have and Localio (1999) 21. Note that the likelihood is also a function of the unknown parameters equation M14 which is the unknown parameter in Var(bi,ols) and equation M15.

Conditional on the αi and βi from all individuals, the unbiased OLS estimate of equation M16 is

equation M17
(9)

which can then be plugged in the likelihood function (eq. 8) to obtain consistent estimates of the other parameters of interest (β, γ0, γ1, equation M18).

Footnotes

The authors have nothing to declare.

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