Sample size for clinical trials

Sample sizes for clinical trials are discussed more fully elsewhere in this book and should be established in discussion with a statistician. Sample sizes should, however, be sufficient to be 90% certain of detecting a statistically significant difference between treatments, based on a set of predetermined primary variables. This means that trials utilising an active control will generally be considerably larger than placebo-controlled studies, in order to exclude a Type II statistical error (i.e. the failure to demonstrate a difference where one exists). Thus, in areas where a substantial safety database is required, for example, hypertension, it may be appropriate to have in the programme a preponderance of studies using a positive control. 

Ellenberg SS. 1989. Determining sample sizes for clinical trials. Oncology 3 39-42. 

Julious SA (2004) Tutorial in biostatistics-Sample sizes for clinical trials with normal data. Statistics in Medicine 23 1921-1986. 

Pezeshk H, Gittins J (2002) A fully Bayesian approach to calculating sample sizes for clinical trials with binary responses. Drug Information Journal 36 143 150. 

In Chapter 13 we discussed various approaches to determining the sample size in clinical trials. For trials in which there is an ethical imperative not to randomize patients... 

Statistical methods are often employed to determine the study sample size and optimize power. Outlining the methods for calculating sample size and power for clinical trials is beyond the scope of this chapter. Interested readers are referred to texts by Chow and Liu (1998), Hulley and Cummings (1988), and Shuster (1990) for specific information on sample size and power estimation methods. 

SHUSTER J J (1990) CRC handbook of sample size guidelines for clinical trials, Boston, CRC Press. 

There are of course practical considerations in clinical research. We may find patient recruitment difficult in single centre studies and this is one of the major drivers to multicentre and multinational trials. Alternatively, we may need to relax the inclusion/exclusion criteria or lengthen the recruitment period. Unfortunately, while each of these may indeed increase the supply of patients they may also lead to increased variability that in turn will require more patients. A second issue is the size of the CRD which, if it is too small, will require a large number of patients. In such circumstances we may need to consider the use of surrogate endpoints (Section S.3.3.2). Finally, the standard deviation may be large and this can have a considerable impact on the sample size - for example, a doubling of the standard deviation leads to a four times increase in the... 

Willan AR. Analysis, sample size, and power for estimating incremental net health benefit for clinical trial data. Control Clin Trials 2001 22 228-37. 

In a placebo-controlled hypertension trial, the primary endpoint is the fall in diastolic blood pressure. It is required to detect a clinically relevant difference of 8 mmHg in a 5 per cent level test. Fiistorical data suggests that CT= 10 mmHg. Table 8.4 provides sample sizes for various levels of power and differences around 8 mmHg the sample sizes are per group. 

The determination of the sample size is intimately related to the trial objectives, the inferences the researcher wants to be able to make and the error probabilities in the case of hypotheses testing or the confidence and precision in the case of estimation that the researcher is willing to tolerate. The following example illustrates the process of determining the required sample size for a clinical trial. 

Lachin JM. Introduction to sample size determination and power analysis for clinical trials. Controlled Clinical Trials 1981 2 93-113. 

Another useful interpretation of confidence intervals is that the values that are enclosed within the confidence interval are those that are considered the most plausible values of the unknown population parameter. Values outside the interval are considered less plausible. All other things being equal, the need for greater confidence in the estimate results in wider confidence intervals, and confidence intervals become narrower (that is, more precise) as the sample size increases. This last fact is explored in greater detail in Chapter 12 because it is directly relevant to the estimation of the required sample size for a clinical trial. The methods to use for the calculation of confidence intervals for other population parameters of interest are provided in subsequent chapters. 

In Chapter 6 we described the basic components of hypothesis testing and interval estimation (that is, confidence intervals). One of the basic components of interval estimation is the standard error of the estimator, which quantifies how much the sample estimate would vary from sample to sample if (totally implausibly) we were to conduct the same clinical study over and over again. The larger the sample size in the trial, the smaller the standard error. Another component of an interval estimate is the reliability factor, which acts as a multiplier for the standard error. The more confidence that we require, the larger the reliability factor (multiplier). The reliability factor is determined by the shape of the sampling distribution of the statistic of interest and is the value that defines an area under the curve of (1 - a). In the case of a two-sided interval the reliability factor defines lower and upper tail areas of size a/2. 

Suppose that one is not convinced by the arguments above which tend to show that, for the sorts of sample size usually entertained for clinical trials, given a straight choice between pooling and not pooling, the former is preferable, but wishes to explore, as fully as possible, the extent to which treatment effects differ between the sexes. Another controversy is then raised, namely whether one should test for treatment-by-sex interaction or simply study the treatment effects separately for each sex. 

Even if the clinically irrelevant difference is the same as the clinically relevant difference and not, as will usually be the case, considerably smaller, it is generally the case that equivalence trials require a larger sample size for the same power as a conventional trial. The general position is illustrated by Figure 15.2. For purposes of sample size determination it will generally be unwise to assume that the treatments are exactly equal. This would be the best possible case and this already shows an important difference from conventional trials. We plan such trials to have adequate power to detect the difference we should not like to miss, but we may of course be fortunate and be faced with an even better drug. In that case the power is better than hoped for. If we are truly interested in showing equality (and not merely that an experimental treatment... 

The number of subjects planned to be enrolled, if more than one site the numbers of enrolled subjects projected for each trial site should be specified. Reason for choice of sample size include calculations of the statistical power of the trial, the level of significance to be used and the clinical justification. 

Unfortunately, clinical trials in human volunteers usually have small sample sizes and adverse reactions are poorly documented. Also, adverse effects that have a long latency period such as carcinogenicity are difficult to account for. 

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