6.1. Introduction
Why are nonparametric statistical methods important to pharmaceutical research? To really address this question, we first must begin by looking at the nature of pharmaceutical research. The goal of pharmaceutical research is to discover and develop new medicines that are able to cure or moderate various disease symptoms or conditions. The disease response (i.e., physiological trauma) can vary greatly from individual to individual because of a complex inherent genetic variability. The corresponding statistical phenomenon associated with this genetic variation to disease response is that measurements collected on such a cohort can be skewed by the extreme response of a small portion of the individuals under consideration.
Consider, as an example, the search for a new anti-inflammatory agent. Inflammatory response (e.g., swelling) can vary greatly in untreated subjects. Some individuals can have a very extreme response to a biological insult producing an inflammatory response, causing the distribution of those responses to be very "heavy" or "long-tailed" in the upper direction (e.g., a great deal of swelling). The common summary statistic for continuous responses in such a setting, the mean, is greatly influenced by the presence of a small number of high responses and "over-represents" the location of the untreated subjects' distribution (we will see that a similar phenomenon can also occur in the study of novel antibacterial drugs).
A similar phenomenon can occur, but this time, in treated subjects, in the study of the toxicology of new agents. The genetic variability of individuals can vary greatly as the body responds to higher and higher levels of a compound. Some subjects in a high dose group of a toxicology study may exhibit very high or very low responses that skew the distribution. In both cases (the study of efficacy and toxicology), it becomes apparent that traditional Gaussian (normal) statistical methods may fail because of the required assumption of symmetry. Nonparametric, or distribution-free, statistical methods liberate us from the need to assume symmetry in response. We no longer impose an assumption on our inference that may not be verifiable (because of small sample sizes) or observable.
This chapter is an introduction to popular nonparametric statistical methods in the analysis of studies in the pharmaceutical industry. It provides a review of some new statistical methods for inference and an introduction to some fairly infrequently used techniques that have existed "below the radar" for several years.
Section 6.2 will be devoted to the two-sample setting, exploring both the equal and unequal dispersion cases. Section 6.3 will discuss aspects of the one-way layout and associated multiple comparison procedures. Section 6.4 will introduce one approach to sample size determination in a "nonparametric" sense, using data from pilot studies. Each section also contains a mixture of SAS/STAT procedures and some original macros to perform elementary nonparametric data analyses.
Throughout this chapter, the discussion of topics will be motivated by providing some real or simulated examples of data from studies in medical research. In either situation, the purpose of the example is not to make a medical claim (efficacy or safety of an anonymous compound) but to illustrate a feature of data critical to the outcome of the statistical inference.
To save space, some SAS code has been shortened and some output is not shown. The complete SAS code and data sets used in this book are available on the book's companion Web site at http://support.sas.com/publishing/bbu/companion_site/60622.html.