Determining the Sample Size

Hain t we got aU the fools in town on our side and aint that a big enough majority in any town  

Statistical Issues in Drug Development, 2nd Edition. Stephen Senn 2007 John Wiley Sons, Ltd. ISBN 978-0-470-01877-4 

In what follows we shall assume that the sample size is going to be determined as a function of the other factors. We shall take the example of a two-arm parallel-group trial comparing an active treatment with a placebo for which the outcome measure of interest is continuous and will be assumed to be Normally distributed. It is assumed that analysis will take place using a frequentist approach and via the two independent-samples t-test. A formula for sample size determination will be presented. No attempt will be made to derive it. Instead we shall show that it behaves in an intuitively reasonable manner. 

We shall present an approximate formula for sample size determination. An exact formula introduces complications which need not concern us. In discussing the sample size requirements we shall use the following conventions  

This magnitude is the difference we should not care to miss.) 

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These estimates are for a national distribution and will increase depending upon the number of subpopulation groups for which frequency distribution data is desired. Determining the sample size, therefore, requires decisions regarding the percentile of interest and level of accuracy needed, and balancing these against the costs of the required sample. 

In most cases we will be interested in determining the sample size for a given type-11 error, which is typically fixed at values of 0.1 or 0.2. 

Determining the sample size is often a difficult decision, and sometimes has to be made without sufficient information. If there is uncertainty, sometimes a quick small informal test of the system may help decide what is the best way to proceed. 

The normal Gaussian distribution df coarse HMX impact sensy is used to estimate the increased sensy of coarse HMX contg various amounts of fine ( <63 microns) airborne grit by a statistical modeled expt. The exptl results were then used in a BemoulUan confidence level eqtn to determine the sample size required to accurately estimate the sensy of any grit contg HMX sample with a K % level of confidence. A sample of the type of K table derived is shown for HMX in Table 5]... 

The general objective of this study was to determine the sample size limits of each of the above mills. Factors which affected mill efficiency and grind times were also evaluated. In some cases, the grind times required to reduce the sample particle size to less than three microns were determined as a function of grind media type, grind media charge and sample size. All particle size analyses were carried out on a Coulter Counter (Model TA II). 

Step 5 Determine the sample size for each individual experimental run. 

The number of subjects to be included in the study will be determined by the inherent variability in drug substance pharmacokinetics, the magnitude of effects that are of interest, the desired confidence in conclusions, costs, time, ethical aspects and where relevant, regulatory guideline recommendations. Three different situations may be identified that require different algorithms to determine the sample size ... 

The statistical analysis of this data will determine the sample size and frequency of later routine checking by indicating ... 

To return to our discussion of experiments, a good experiment is one which may reasonably be expected to be salient. Obviously, other things being equal, a large experiment is better than a small one, and one which is too small is unlikely to be salient. Hence the belief has arisen that the major function of the statistician in designing an experiment is to use his theories to determine the sample size. In fact, sample size is only one aspect of the problem and its importance has been overrated. 

In both of these examples, the task of the statistician has widened considerably beyond that of simply determining the sample size. Of course, some of the points the statistician made to the physician could have been appreciated without his help. No one profession has a monopoly of logic. The point is that these sorts of matters are more likely to be discovered and explored if statistician and physician work together on all aspects of trial design and the statistician s responsibility is not narrowly defined. 

Some further issues regarding interpretation of significance results and P-values are covered in the next chapter on determining the sample size. Here a specific issue regarding replication probabilities is discussed. 

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... 

A similar formula is also available for determining the sample size in situations that require determination of actual time to perform a task. For example, for a staffing study in a call center, one may need to estimate average time needed to service a phone call. 

There are two methods of determining the sample size the statistical method and the nomogram method ... 

Type II errors are more difficult to predict. The concept of a Type II error is important to determine the sample size of an experiment to detect a difference of stated magnitude. 

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