Clinical trials null hypotheses

Clinical trials are carried out to show that the null hypothesis is false. The p value is the probability of having an effect by chance if the null hypothesis were actually true. The null hypothesis is rejected in favor of the alternative hypothesis when the p value is less than a. 

When a clinical trial has been conducted, the frequentist approach we have discussed in the book leads to certain statistical analyses being conducted. A p-value is calculated which provides information leading to the rejection of the null hypothesis or the failure to reject the null hypothesis. Additionally, the analyses lead to an estimate of the treatment effect and its associated... 

The null hypothesis is the crux of hypothesis testing. (It is important to note that the form of the null hypothesis varies in different statistical approaches. As the main type of clinical trial discussed in this book is the therapeutic confirmatory trial, we talk about this first. We then talk briefly about the forms of the null hypothesis that are used in other types of trials in Section 3.10.) As noted earlier, therapeutic confirmatory trials are comparative in nature. We want to evaluate the efficacy of the investi-... 

Assume that there are k independent groups (k > 2), each of which represents populations of interest, for example, individuals given a particular treatment. An important objective of many clinical trials is to determine if there is any difference among the treatments administered with regard to the underlying population means. The null hypothesis for such an objective is ... 

There are a number of values of the treatment effect (delta or A) that could lead to rejection of the null hypothesis of no difference between the two means. For purposes of estimating a sample size the power of the study (that is, the probability that the null hypothesis of no difference is rejected given that the alternate hypothesis is true) is calculated for a specific value of A. in the case of a superiority trial, this specific value represents the minimally clinically relevant difference between groups that, if found to be plausible on the basis of the sample data through construction of a confidence interval, would be viewed as evidence of a definitive and clinically important treatment effect. 

What is the real purpose of running a clinical trial In a confirmatory trial, the stated purpose of that trial is usually to test the null hypothesis. Clinical trials are often focused on testing the null hypothesis because there is usually an alternative model, such as that the drug does have clinically relevant activity, that can be accepted in place of the null model. Furthermore, testing the null hypothesis is an... 

Traditional (ANOVA) analysis of analgesic clinical trials (i.e., testing the null hypothesis when comparing treatment and placebo groups) have dealt inadequately with the complexities of pain relief data collected in these studies (3, 15). When patients have required rescue medication before the end of the study, scores of unobserved subsequent pain and pain relief (PR) scores have historically been imputed according to predetermined rules such as the so-called last observation... 

Now, whereas (1 - (3)/a is a monotonically increasing function of the sample size n, Li(P)/Lq(P) is not. It may increase at first, but eventually it will decline. The situation is illustrated in Figure 13.2, which takes the particular example of the trial is asthma considered in section 13.1 above and shows the likelihood for the null hypothesis (scaled to equal 1 in the case where the observed treatment difference is zero) for all possible observed treatment differences and also for the alternative hypothesis where the true treatment effect is equal to the clinically relevant difference. The situations for trials with 10 and 200 patients per group are illustrated. The critical value of the observed treatment difference for a two-sided test at the 5% level is marked in each case. For the smaller trial, a larger difference is required for significance. In the larger trial, a smaller difference is adequate. 

This has been referred to as the alpha postulate. There is a sense in which this is true also Look at Figure 13.3. Here, instead of displaying the scaled likelihood for that alternative hypothesis which corresponds to the clinically relevant difference, the alternative hypothesis for which the true treatment effect corresponds to the critical value is illustrated. For P = 0.05, the ratio of this likelihood is the same for the trial with 10 patients per group as for the trial with 200 as, indeed, it is for any trial whatsoever. But we do not know which value of the alternative hypothesis is true if the null hypothesis is false. It thus follows that for a P-value of exactly 0.05, there is always one value of the alternative hypothesis for which the likelihood is 1/0.15 or more than six times as high as for the null hypothesis. The evidence in favour of this alternative hypothesis (which hypothesis changes according to the size of the trial) is always the same. 

Size (of a test). When used in connection with hypothesis testing, the size of a test is the probability of rejecting the null hypothesis given that the null hypothesis is true. (In other words, it is the probability of committing a type I error when the null hypothesis is true.) Conventionally in clinical trials a size of 5% is used. Also called significance level. 

What if the statistical test is not statistically significant If one accepts the null hypothesis, in this case the error to be concerned about is the type II error (see Table 21.1 above). At the design stage of the trial, the statistician usually ascertains that the test to be employed at the end has high power at clinically important alternatives. Since the power is... 

Consider the implications of these errors at the end of a clinical trial. When a type I error (also known as a false positive) occurs, the researchers reject the null hypothesis, e.g., they find statistically significant efficacy when it did not truly exist. The inference from this finding, based on the sample of participants employed in this trial, is that the drug would be effective in the population from which the sample was chosen. This likely would not be the case. When a type II error... 

The most typical analytical approach to interpreting the data from scientific studies, including clinical trials, is the statistical significance test, also known as the null hypothesis significance test (NHST). This approach, which has recently come under much scrutiny and debate, formally... 

Figure 13.2 Scaled likelihood for null and alternative hypotheses for trials with (a) 10 and (b) 200 patients per gronp. Under the alternative hypothesis the clinically relevant difference obtains.

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