Non-Parametric Statistical Analysis of Rare Events in Healthcare: Case of Histological Outcome of Kidney Transplantation

Non-Parametric Statistical Analysis of Rare Events in Healthcare: Case of Histological Outcome of Kidney Transplantation

Soheila Nasiri (University of Ottawa, Canada) and Bijan Raahemi (Unviersity of Ottawa, Canada)
DOI: 10.4018/978-1-5225-2515-8.ch009
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Abstract

The assumption of Gaussian distribution of population does not always hold strongly in health studies. The sample size may not be large enough due to the limited nature of observations such as biopsies taken during kidney transplantation, the distribution of sample may not be Gaussian, or the observation may not even be possible for the far ends of a Gaussian distribution. In such cases, an alternative approach, called nonparametric tests can be applied. In this study, a non-parametric single center retrospective analysis of adult kidney transplant is performed to compare histological outcomes among three different groups of deceased kidney donors, based on the biopsies taken before and after kidney transplant at months 1, 3, and 12. A total of 107 transplants were observed in this study with 310 surveillance biopsy taken then classified based on the Banff 97 adequacy assessment. It is concluded that the recipient's internal condition after kidney transplant is as important as the donor's risk factors.
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Introduction

Statistical analysis of sampled data has been extensively applied in many areas of health studies. The majority of the traditional statistical tests, such as ANOVA and the t-test, assume that the sampled data are from a population with a Gaussian (bell-shaped), or approximately Gaussian, distribution. However, the assumption of a Gaussian population distribution does not always hold, especially in biology and health studies. The sample size may not be large enough, due to the limited nature of available observations, such as for kidney transplants performed in a particular state or country. Further, observation may not be possible for the far ends of a Gaussian distribution when examining biological tests. In such cases, an alternative approach, called non-parametric tests, can be applied, which do not assume that data follow a Gaussian distribution. In a non-parametric approach, instead of considering the actual values, they are ranked from low to high, and analysis is based on the distribution of ranks. This approach ensures that the test is not affected much by outliers, and does not require the assumption of any particular distribution.

In this study, we perform a non-parametric single-center retrospective analysis of consecutive deceased-donor adult kidney transplants. The goal is to compare histological and clinical outcomes among three different groups of deceased kidney donors, namely expanded criteria donor (ECD), standard criteria donor (SCD), and donation after cardiac death (DCD). We report on a study of 107 cadaveric kidney transplants with regard to histological changes, based on protocol biopsies taken before the transplant (month 0), and 1, 3 and 12 months after the transplant. The transplant recipients were selected based on a waiting list and histological compatibility, regardless of donor physiological characteristics. In some cases, the recipients’ ages in the ECD, SCD, and DCD groups were the same. Consequently, we had the opportunity to compare the graft outcomes in the three groups of SCD, ECD and DCD, without considering age as a constraining factor.

It is observed that the relative increase in the Banff summation score, as an indicator of histological change, was similar among the SCD and ECD groups over the 12 months. However, in the DCD group, despite better organ condition at transplantation, its mean score was higher than that of the ECD group. It is further observed that the similar ages of recipients among the three groups highlights the influence of recipient’s age on the outcome. We conclude that a recipient’s internal condition after kidney transplant is as important as the donor’s risk factors. In other words, it is not only the risk factors associated with donors that play a significant role in the outcome, but also the risk factors of recipients.

Key Terms in this Chapter

Kruskal-Wallis Test: This non-parametric test is analogous to one-way ANOVA. This test first ranks the data from low to high, and then characterizes the distribution of the ranks among groups.

Expanded Criteria Donor (ECD): Defined as any brain-dead donor aged 60 years or more, or a donor aged 50 years or more with two of the following conditions: a history of hypertension, terminal serum creatinine level > 1.5 mg/dL, or death resulting from a cerebrovascular accident.

Banff Score: A standardization of a renal allograft biopsy to establish an objective end-point for clinical trials. Banff 97 was developed by investigators using the Banff Schema and the Collaborative Clinical Trials in Transplantation (CCTT) modification, for diagnosis of renal allograft pathology.

Mann-Whitney Test: A non-parametric test used to compare two unpaired groups, to compute a P -value for the null hypothesis that the distribution of ranks is totally random. Under the null hypothesis, it would be equally likely for either of the two groups to have the larger mean ranks.

Biopsy (Protocol Biopsy): A routine sampling of kidney tissue (with the use of biopsy needles and bioptic devices to obtain tissue cores, using ultrasound guidance for the biopsy procedure), particularly within the first few months of post-transplantation, to investigate potential rejection of a transplanted kidney. Multiple tissue samples are recommended for adequate sampling.

Standard Criteria Donor (SCD): Defined as a donor who is under 50 years of age and suffered brain death from any cause, including traumatic injuries or medical problems such as a stroke.

Donation After Cardiac Death (DCD): Defined as coming from a donor who has suffered irreversible brain injury and who may be near death, but who does not meet formal brain death criteria. In these cases, when the patient’s heart stops beating, and with the permission of the family, the organs are then recovered in the operating room to be used for transplantation.

Gaussian Distribution: The Gaussian distribution is also commonly called the “normal distribution,” and is often described as a “bell-shaped curve.” If the number of events is very large, then a Gaussian distribution may be used to describe physical events. The normal distribution is useful because of the central limit theorem, which states that averages of random variables independently drawn from independent distributions become normally distributed when the number of random variables is sufficiently large.

Non-Parametric Tests: A family of methods which makes no assumptions about the population distribution. Non-parametric methods most commonly work by ignoring the actual values, and, instead, analyzing only their ranks. This approach ensures that the test is not affected much by outliers, and does not assume any particular distribution. The clear advantage of non-parametric tests is that they do not require the assumption of sampling from a Gaussian population. When the assumption of Gaussian distribution does not hold, non-parametric tests have more power than parametric tests to detect differences.

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