Sample size inputs required

Sample size estimation requires the input of a number of specialists involved with the development of new drugs. The estimate of the standard deviation can be informed by exploratory therapeutic trials of the same drug or by literature reviews of similar drugs. Synthesis of these data from a number of sources requires statistical and clinical judgments. As was seen in Figure 12.1 the estimate of the standard deviation has an important effect on the sample size. Study teams should understand the sources of variability in... 

In summary, sample size estimation requires the input of a number of disciplines involved in the design of clinical trials. 

Indicator and sample selection are not the only choices a researcher has to make when using MAXCOV. A decision also has to be made about interval size, that is, how finely the input variable will be cut. Sometimes it is possible to use raw scores as intervals that is, each interval corresponds to one unit of raw score (e.g., the first interval includes cases that score one on anhedonia, the second interval includes cases that score two). This is what we used in the depression example. This approach usually works when indicators are fairly short and the sample size is very large, since it would allow for a sufficient number of cases with each raw score. In our opinion, this is the most defensible method of interval selection and should be used whenever possible. However, research data usually do not fit the requirements of this approach (e.g., the sample size is too small). Instead, the investigator can standardize indicators and make cuts at a fixed distance from each other (e.g.,. 25 SD), thereby producing intervals that encompass a few raw scores. 

Most pharmaceutical firms have pipelines fofaling less than 1000 developmental compounds, and often no more than 40. Handling these smaller sample sizes requires an approach, which is capable of affaching individual characteristics to xmique, discrete elements. Such models are called "agent-based " they establish a simulation environment in which individual agents represent actual NCEs in the pipeline, complete with unique characteristics that can be compound-specific. In addihon, the small numbers of items tracked dictate that they must be "discrete event " model inputs must have a range of... 

One algorithm for blindly approximating physical states has already been proposed [36], although the method requires the number of states to be input. In work to be reported soon, Zhang and Zuckerman developed a simple procedure for approximating physical states that does not require input of the number of states. In several systems, moreover, it was found that sample-size estimation is relatively insensitive to the precise state definitions (providing they are reasonably physical, in terms of the timescale discussion above). The authors are therefore optimistic that a "benchmark" blind, automated method for sample-size characterization will be available before long. 

The first four basic factors above constitute the primitive inputs required to determine the fifth. In the formula for sample size, n is a function of a, (3, A and a, that is to say, given the values of these four factors, the value of n is determined. The function is, however, rather complicated if expressed in terms of these four primitive inputs and involves the solution of two integral equations. These equations may be solved using statistical tables (or computer programs) and the formula may be expressed in terms of these two solutions. This makes it much more manageable. In order to do this we need to define two further terms as follows. 

In practice, the sample size calculation is not done by hand, but by computer programs (such as the free G Power ), which lets you choose a statistical test, asks for the necessary inputs (i.e., a, P, variance, and effect size), and gives you the minimum required sample size. They can also be used to determine the power of your test given the sample size, a, S, and effect size. Because of all these unknowns, it is a good idea to consult a biostatistician on these matters if possible. 

Metamodel or response surface-based methods perhaps provide the best balance between computational intensity and information about the partial variances due to input parameter imcertainties. In many cases, the development of an accurate metamodel can be achieved using a far smaller sample size than that required by FAST or Sobol s basic method. The metamodel is then used for calculating global sensitivity indices. In common with the Sobol method, HDMR, for example, is based on the analysis of variance. Where higher-order terms (>2) in the HDMR expansion are weak, global sensitivity indices can be achieved using a relatively small quasi-random sample even for large parameter systems. 

Line size and length must be small enough to meet transporttime requirements without excessive pressure drop or excessive bypass of sample at the analyzer input. 

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