Sample size power

FIGURE 11.23 Power analysis.The desired difference is >2 standard deviation units (X, - / = 8). The sample distribution in panel a is wide and only 67% of the distribution values are > 8. Therefore, with an experimental design that yields the sample distribution shown in panel a will have a power of 67% to attain the desired endpoint. In contrast, the sample distribution shown in panel b is much less broad and 97% of the area under the distribution curve is >8. Therefore, an experimental design yielding the sample distribution shown in panel B will gave a much higher power (97%) to attain the desired end point. One way to decrease the broadness of sample distributions is to increase the sample size. 

FIGURE 11.24 Power curves. Abscissae is the sample size required to determine a difference between means shown on the ordinate. Numbers next to the curves refer to the power of finding that difference. For example, the gray lines show that a sample size of n = 3 will find a difference of 0.28 with a power of 0.7 (70% of the time) but that the sample size would need to be increased to 7 to find that same difference 90% of the time. The difference of 0.28 has previously been defined as being 95% significantly different. 

This latter value (tp) is given by power analysis software ancl can be obtained as a power curve. Figure 11.24 shows a series of power curves giving the samples sizes required to determine a range of differences. From these curves, for example, it can be seen that a sample size of 3 will be able to detect a difference of 0.28 with a power of 0.7 (70% of time) but that a sample size of 7 would be needed to increase this power to 90%. In general, power analysis software can be used to determine sample sizes for optimal experimental procedures. 

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. 

Reconfiguration of Data. Drug safety data from different sources are often pooled or combined in databases. Reasons for combining data vary. In the case of premarketing studies, data from different sites are routinely combined because one site may not be able to recruit enough patients for a study. Data from different studies are often combined to increase sample size and therefore statistical power for detecting an uncommon adverse event. 

A problem long appreciated in economic evaluations, but whose seriousness has perhaps been underestimated (Sturm et al, 1999), is that a sample size sufficient to power a clinical evaluation may be too small for an economic evaluation. This is mainly because the economic criterion variable (cost or cost-effectiveness) shows a tendency to be highly skewed. (One common source of such a skew is that a small proportion of people in a sample make high use of costly in-patient services.) This often means that a trade-off has to be made between a sample large enough for a fully powered economic evaluation, and an affordable research study. Questions also need to be asked about what constitutes a meaningful cost or cost-effectiveness difference, and whether the precision (type I error) of a cost test could be lower than with an effectiveness test (O Brien et al, 1994). 

Sturm R, Uniitzer J, Katon W (1999). Effectiveness research and implications for study des n sample size and statistical power. Gen Hosp Psychiatry 21, 274—83. 

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. 

Clinical trials are costly to conduct, and results are often critical to the commercial viability of a phytochemical product. Seemingly minor decisions, such as which measurement tool to use or a single entry criterion, can produce thousands of dollars in additional costs. Likewise, a great deal of time, effort and money can be saved by having experts review the study protocol to provide feedback regarding ways to improve efficiency, reduce subject burden and insure that the objectives are being met in the most scientifically sound and cost-effective manner possible. In particular, I recommend that an expert statistician is consulted regarding sample size and power and that the assumptions used in these calculations are reviewed carefully with one or more clinicians. It is not uncommon to see two studies with very similar objectives, which vary by two-fold in the number of subjects under study. Often this can be explained by differences in the assumptions employed in the sample size calculations. 

Power Calculator provides sample size programs for various models, including normal, exponential, binomial, and correlation models http //home. stat.ucla.edu/ calculators/powercalc/... 

Power Analysis for ANOVA Designs can be used to calculate sample size for one and two-way factorial designs with fixed effects http //evall.crc.uiuc.e du/ fp o wer. html/... 

Growing experience with complex disease genetics has made clear the need to minimize type I error in genetic studies [41, 109]. Power is especially an issue for SNP-based association studies of susceptibility loci for phenomenon such as response to pharmacological therapy, which are extremely heterogeneous and which are likely to involve genes of small individual effect. Table 10.2 shows some simple estimation of required sample sizes of cases needed to detect a true odds ratio (OR) of 1.5 with 80% power and type I error probability (a) of either 0.05 or 0.005. 

Tab. 10.2 Sample size requirements for case control analyses of SNPs (2 controls per case detectable difference of OR >1.5 power=80%) (reprinted with permission from Palmer and Cookson 2001 [16])...

Polymorphisms of the beta adrenergic receptors have also been studied in patients with heart failure and cardiomyopathy, or other complex and rather ill-defined phenotypes. In patients with heart failure due to ischemic or idiopathic dilated cardiomyopathy, the Thrl64Ile polymorphism in the />2-adrerioreceplor was significantly associated with survival rate at one year [62]. Similarly, the Ser49Gly polymorphism of the /Vadrenoreceptor gene has been linked to the improved survival of patients with idiopathic cardiomyopathy [63]. However, sample size was limited in those studies and results need to be confirmed in adequately powered studies. 

No definitive conclusions can be drawn concerning a possible role of rifaximin in preventing major complications of diverticular disease. Double-blind placebo-controlled trials with an adequate sample size are needed. However, such trials are difficult to perform considering the requirement of a large number of patients. Assuming a baseline risk of complications of diverticular disease of 5% per year [2], a randomized controlled trial able to detect a 50% risk reduction in complications should include 1,600 patients per treatment group considering a power of 80% (1 - (3) and an a error of 5%. 

Dynamic rheological measurements have recently been used to accurately determine the gel point (79). Winter and Chambon (20) have determined that at the gel point, where a macromolecule spans the entire sample size, the elastic modulus (G ) and the viscous modulus (G") both exhibit the same power law dependence with respect to the frequency of oscillation. These expressions for the dynamic moduli at the gel point are as follows ... 

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