Power and sample size

Power and sample size computations are a little more difficult to compute than for one-way designs. 

Also, the analysis plan should identify the statistical methods that will be used and how hypotheses will be tested (e.g., a p value cutoff or a confidence interval for the difference that excludes 0). And the plan should prespecify whether interim analyses are planned, indicate how issues of multiple testing will be addressed, and predefine any subgroup analyses that will be conducted. Finally, the analysis plan should include the results of power and sample size calculations. 

Laska EM, Meisner M, Seigel C. Power and sample size in cost-effectiveness analysis. Med Decis Making 1999 19 339-43. 

Later, in Chapter 8, we will discuss power and sample size and see how to choose sample size in order to meet our objectives. We will also see in Section 3.3 how, in many circumstances, the calculation of the p-value is directly based on the signal-to-noise ratio. 

This null hypothesis is saying that the treatment difference/effect is consistent. If the p-value from this test is significant then we talk in terms of having a significant treatment-hy-centre (or a treatment x centre) interaction. Power and sample size calculations (see later chapter on this topic) will have focused... 

CH08 POWER AND SAMPLE SIZE Table 8.1 Type I and type II errors... 

Machin et al. (1997) provide extensive tables in relation to sample size calculations and include in their book the formulas and many examples. In addition there are several software packages specifically designed to perform power and sample size calculations, namely nQuery (www.statsol.ie) and PASS (www.ncss.com). The general statistics package SPLUS (www.insightful.com) also contains some of the simpler calculations. 

Dupont WD, Plummer WD. PS power and sample size program available for free on the Internet. Controlled Clin Trials 1997 18 274. 

Before - identify the primary question, primary end-point and primary statistical analysis establish equivalence limits where necessary perform power and sample size calculations. 

The implications of the disparity between empirical and nominal significance levels of the likelihood ratio test in mixed effects modeling and simulation are clear however, definitive solutions or corrections are not. While the significance of random effects is not generally the subject of interest in a simulation, the bias in hkelihood ratio test-determined p value for fixed effects could be very influential on trial simulation findings. Thus, simulation exercises should provide for determination of empirical p values to avoid faulty conclusions about power and sample size. 

Often times, the amount of attribute data needed to calculate a statistically significant proportion (e.g., fraction defective) is rather large. In this case, the sample size will be determined using MINITAB sofl ware. Assuming we are interested in detecting a difference between a sample that is 4% defective and a sample that is 1% defective (note this is a decision that the experimenter and/or company management must make), the MINITAB Power and Sample Size calculator for two proportions can be used. This results in a sample size of 568 parts per run that will have to be inspected for cracks. Fortunately, for this particular case, the visual inspection of each part takes only a few seconds to complete. So the inspection of 568 parts actually takes less than one hour. 

The a priori identification of specific risk hypotheses leads to the ability to take some of the methodology normally applied to hypothesis testing of efficacy results and apply it to safety assessment. The most important difference between these two analysis domains is that in the case of efficacy, outcomes of interest are identified a priori with great specificity, and clear statistical hypotheses are laid out in advance with complete analysis and decision rules documented in the clinical protocol. In practice, only a few efficacy variables are identified as primary, and only a few others as second-ary. Sensitivity, statistical power, and sample size are all carefully analyzed in advance to assure the trial will have a high probability of detecting differences of interest in these few critical variables. 

Mclndoe, J.X. She, Microarray experimental design power and sample size considerations, Physiol. Genomics 2003, 16, 24-28. 

Senn SJ, Bretz F (2007) Power and sample size when mnltiple endpoints are considered. Pharmaceutical Statistics 6 161-170. 

Kieser M, Rohmel J, Friede T (2004) Power and sample size determination when assessing the clinical relevance of trial results by responder analyses . Statistics in Medicine 23 3287-3305. Lindley DV (1957) A statistical paradox. Biometrika 44 187 192. 

Page, G. P., et al. (2006). The PowerAtlas a power and sample size atlas for microarray experimental design... 

The topics of statistical power and sample size estimation are intimately related. A critical part of study design is deciding upon the number of participants that will be employed in the trial. Readers are referred to other sources for detailed discussion of these topics (e.g.. Turner 2010 Teare et al. 2014 Greene 2015 Jia and Lynn 2015) at this time, pragmatic descriptions are sufficient. 

E. R. Blout and G. R. Bird, Infrared Microscopy. II, J. Opt. Soc. Am. 41, 547, 1951. Gives general considerations, performance criteria, spectral resolving power, and sample size requirements. 

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