Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 10

Empirical Likelihood Methods in Clinical Experiments

Albert Vexler, Alan D. Hutson and Jihnhee Yu

10.1 Introduction

Testing-statistical hypotheses based on the t-test or its different modifications is one of the traditional instruments used in medical experiments and drug development. Despite the fact that these tests are straightforward with respect to their utilization in clinical trials, it should be noted that there is a huge literature on the criticism of t-test-type statistical tools. One major issue, which has been widely recognized, is with respect to the significant loss of efficiency of these procedures under different distributional assumptions. The legitimacy of t-test type procedures also comes into question in the context of inflated type I errors when data distributions differ from normal and the number of observations is fixed. This can pose serious problems when data based on biomarker measurements are evaluated via statistical testing. The recent biostatistical literature has addressed well the arguments that show that values of biomarker measurements tend to follow skewed distributions, for example, a lognormal distribution [28], and hence the use of t-test-type techniques in this setting is suboptimal as well as accompanied by strong difficulties to control the corresponding type I error.

When the forms of data distributions are assumed to be known, the likelihood principle is a central tenet for developing powerful statistical inference tools for ...