Introducing hypothesis tests

Essential Statistics for the Pharmaceutical Sciences Philip Rowe 

---

The simplest possible experimental design would almost not be recognized as an experimental design at all, but does serve as a prototype situation (as we like to use for pedagogical purposes). The situation arises when there is one variable (factor) to investigate, and the question is, does this factor have an effect on the property studied We have introduced this situation earlier, in our discussion of hypothesis testing, as in... 

This chapter introduces basic concepts in statistical analysis that are of relevance to describing and analyzing the data that are collected in clinical trials, the hallmark of new drug development. (Statistical analysis in nonclinical studies was addressed earlier in Chapter 4.) This chapter therefore sets the scene for more detailed discussion of the determination of statistical significance via the process of hypothesis testing in Chapter 7, evaluation of clinical significance via the calculation of confidence intervals in Chapter 8, and discussions of adaptive designs and of noninferiority/equivalence trials in Chapter 11. 

It first introduces the reader to the fundamentals of experimental design. Systems theory, response surface concepts, and basic statistics serve as a basis for the further development of matrix least squares and hypothesis testing. The effects of different experimental designs and different models on the variance-covariance matrix and on the analysis of variance (ANOVA) are extensively discussed. Applications and advanced topics such as confidence bands, rotatability, and confounding complete the text. Numerous worked examples are presented. 

We have already met P values in the context of significance testing and it is singularly unfortunate that the same letter should be introduced for a second important function, but then that is statistics for you. (To achieve some clarity. I will use lower case p for proportion and upper case P in hypothesis testing.)... 

The hypothesis-testing approach for using mass-balance models to understand groundwater geochemistry, introduced by Plummer et al. (1983),... 

In this book all research questions are addressed and then answered via the construction of two research hypotheses, commonly called the null hypothesis and the alternate hypothesis. (Although another name for the alternate hypothesis, the research hypothesis, has its own appeal, we employ the commonly used term "alternate hypothesis" in this book.) Both of these hypotheses are key components of the procedure of hypothesis testing. This procedure is a statistical way of doing business. It is described and discussed in detail in Chapter 6, but it is beneficial to introduce the main concept here. 

A probability value can be represented as a fraction or as a decimal value. In addition, it is common in some aspects of Statistics to multiply the decimal expression of a particular probability by 100 to create a percentage statement of likelihood. A probability of 0.5 would thus be expressed as a 50% chance that an event would occur. Percentage statements of likelihood are a central component of hypothesis testing, which is introduced later in the chapter. 

We discuss the former method, confidence intervals, first, after a necessary introduction to the concept of sampling variation. The latter method (hypothesis testing) is discussed later. First, however, it is useful to introduce a few other ideas. 

This is an appropriate point at which to describe the relationship between the various parameters used in practice to specify the statistical criteria used in decisions on hypothesis tests on data sets that are too small to justify using the unmodified Gaussian model. (The parameters and P , that were introduced in Section 8.2.3 can be regarded as special cases of the parameters discussed in the following, but will not be referred to again in this... 

The probability value (p-value) of a statistical hypothesis test is closely related to the significance level a the p-value is the critical value of the statistical parameter (z or m in the Gaussian case in Section 8.2.3, or the Student-t introduced in Section 8.2.5) for which H, would be only just rejected for a given value of a. That is, the p-value is the threshold value for false positives (type I... 

The previous chapter provided examples of statistical analyses that are used to assess efficacy in clinical trials. In this and the following chapter, the focus moves to assessments of safety. As will be seen in the first part of this chapter, general safety assessments are conducted quite differently from those for efficacy, in that descriptive statistics are used as opposed to hypothesis testing. However, in the domain of cardiovascular safety, hypothesis-testing approaches are employed to investigate the potential occurrence of specific cardiac and cardiovascular adverse events. In the language introduced in this chapter, these can be regarded as adverse events of special interest. 

Hypothesis testing is an involved procedure, which we have briefly introduced here. It is outside the scope of this chapter to discuss hypothesis testing in more depth. The interested reader is referred to Bethea [3] and Ostle et al. [4J for further discussion. 

The simpler PEP300 was introduced" to test a hypothesis that torsional terms around single bonds in saturated compounds are not needed provided non-bonded interactions are treated adequately. This was indeed so. 

It is important to keep in mind that statistically based studies by themselves can never prove the e.xistence of a cause and effect relationship. However, such obseix ations may be used to generate or to test a hypothesis. Many possibilities exist for introducing bias in this type of investigation, and statistical correlations may be fortuitous. 

---