Sample size with multiple requirements

Often there is a desire to compare responses to multiple treatments rather than simply evaluate active against a placebo control. For instance, it may be useful to evaluate several doses or to assess a product against another marketed product. Increasing the number of treatments will increase the sample size required overall, but will also increase the number of subjects required per treatment arm because the number of statistical comparisons is larger. If all between-group comparisons are to be made, the number of statistical tests increases dramatically as the number of treatment arms increases. With two groups, only one comparison is possible. With three groups, the number... 

One of the most dependably accurate methods for deriving 95% confidence intervals for cost-effectiveness ratios is the nonparametric bootstrap method. In this method, one resamples from the smdy sample and computes cost-effectiveness ratios in each of the multiple samples. To do so requires one to (1) draw a sample of size n with replacement from the empiric distribution and use it to compute a cost-effectiveness ratio (2) repeat this sampling and calculation of the ratio (by convention, at least 1000 times for confidence intervals) (3) order the repeated estimates of the ratio from lowest (best) to highest (worst) and (4) identify a 95% confidence interval from this rank-ordered distribution. The percentile method is one of the simplest means of identifying a confidence interval, but it may not be as accurate as other methods. When using 1,000... 

National and international cooperative efforts for sharing data are mandatory to achieve the large sample sizes required and allow metaanalyses of data (120,121), which can be very powerful. Study of genetic effects common to multiple diseases will also increasingly be of considerable interest (121,122). The most efficient scheme for completing a pooled association screen is for a large collaborative study of several diseases with division of microsatellites among laboratories (65). 

This approach, however, raises issues of multiplicity (see Section 7.10). Accordingly, lower p-values may be required to be able to declare a result as statistically significant. This means that an adjustment to the sample-size estimation formula is appropriate, with the precise nature of the adjustment being related to the number of outcomes to be tested. This adjustment raises the magnitude of the estimated sample size (Machin and Campbell, 2005). 

Proposal. We have recently described a procedure that we believe meets the requirements listed above.(11) More specifically, we have shown tha.t the particle size distribution can be extracted from the QELS data by a combination of a) a convergent numerical algorithm that makes use of the fact that the distribution of sizes must be non-negative (12), b) analysis of each data set with multiple but equivalent basis sets of particle sizes (13), and c) the averaging of distributions obtained from repeated, independent measurements for each sample analyzed.(11) Only a brief discussion of the procedure will be given here. More complete discussions are given elsewhere. (11,12)... 

The first step in the analysis is that loose foods must be representative and reduced down by multiple squaring to a suitably representative sample size for analysis. The wide array of foodstuffs would require different methods to achieve homogenisation. One must be applied that is practical and fits with the available resources and does not contaminate... 

During assay validation the optimal storage preservation tubes should also be determined. Low binding mbes may be preferred for optimal recovery of some analytes. Sample size/aliquot volume should be sufficient for the downstream assay requirements, because freeze/thaw may compromise sample stability (see Chapter 41 page 483) and multiple amounts/aliquots may be needed. The number of samples has to be balanced with storage costs and availabihty. 

Several different approaches to plant hormone analysis have been proposed and the appropriate method to use for each problem is not always obvious. One of the major problems in the field of development of analytical methods for lAA has been the failure to establish reference methods for the evaluation of new techniques. It was consideration of this situation that lead us to produce a multiple labeled, highly enriched, C-IAA and to develop methods for its use in routine analysis [11]. We feel that our current methods, using GC-MS, meet six important criteria 1) they are applicable to a wide variety of plant tissues with only minor modification, 2) they are highly selective in that ions specific to the target molecule are selected, 3) by use of multiple ion pairs they are self validating, 4) both in terms of tissue sample size and levels of detection these GC-MS techniques offer high sensitivity, 5) the techniques are rapid, simple, and easy to teach to those not trained in the problems of phytohormone analysis, and 6) they are absolute methods, thus requiring little complex standardization or calibration. 

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