Statistics power calculations

The protocol should present statistical power calculations, estimates of anticipated precision, or both. This is particularly relevant to studies of rare events, for which the interpretation of elevated relative risks that are not statistically significant creates challenges. 

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. 

The number of subjects per cohort needed for the initial study depends on several factors. If a well established pharmacodynamic measurement is to be used as an endpoint, it should be possible to calculate the number required to demonstrate significant differences from placebo by means of a power calculation based on variances in a previous study using this technique. However, analysis of the study is often limited to descriptive statistics such as mean and standard deviation, or even just recording the number of reports of a particular symptom, so that a formal power calculation is often inappropriate. There must be a balance between the minimum number on which it is reasonable to base decisions about dose escalation and the number of individuals it is reasonable to expose to a NME for the first time. To take the extremes, it is unwise to make decisions about tolerability and pharmacokinetics based on data from one or two subjects, although there are advocates of such a minimalist approach. Conversely, it is not justifiable to administer a single dose level to, say, 50 subjects at this early stage of ED. There is no simple answer to this, but in general the number lies between 6 and 20 subjects. 

Clinical trials generate vast quantities of data, most of which are processed by the sponsor. Assessments should be kept to the minimum that is compatible with the safety and comfort of the subject. Highest priority needs to be given to assessment and recording of primary endpoints, as these will determine the main outcome of the study. The power calculation for sample size should be based on the primary critical endpoint. Quite frequently, trials have two or more evaluable endpoints. It must be stated clearly in the protocol whether the secondary endpoints are to be statistically evaluated, in which case power statements will need to be given, or are simply... 

The clinical endpoint is a clinically meaningful measure of how patients feel, function or survive. Investigator-rated or self-assessed rating instruments are the most frequently used clinical endpoints. A primary endpoint is the main outcome that a study protocol is designed to evaluate. The statistical power and the sample size calculation of a particular trial are determined by the primary endpoint. Depending on the purpose of a study the primary endpoint can be... 

Although the results of these studies mostly support the notion that yogurt has immunostimu-latory effects, poor study design, lack of appropriate controls, and short duration of most of the studies limit the value of the conclusions that can be drawn from them. Most early animal and human studies included too few animals or subjects in each group and most did not include statistical analysis. Although more recent studies addressed these points, none provided the statistical basis for the selected number of subjects that is, it seems that no power calculations were performed. 

The Wilcoxon s Rank-Sum Test (WRST) is a non-parametric alternative. The WRST is robust to the normal distribution assumption, but not to the assumption of equal variance. Furthermore, this test requires that the two groups of data under comparison have similarly shaped distributions. Non-parametric tests typically suffer from having less statistical power than their parametric counterparts. Similar to the /-test, the WRST will exhibit false positive rate inflation across a microarray dataset. It is possible to use the Wilcoxon test statistic as the single filtering mechanism however calculation of the false positive rate is challenging (48). 

In the previous example, the two samples differed slightly in size. This does not invalidate the f-test The calculation of the test can incorporate such inequalities without difficulty. The only reason we normally use balanced designs (equal numbers in both groups) is that, for any total number of observations, statistical power is greatest if they are split equally. In this case the imbalance is so small that any loss of power will be trivial. However, if imbalance leads to one of the groups being quite small, the loss of power may make the whole exercise futile. 

If it turns out that the ideal sample size is actually available, so much the better. However, sample sizes ranging around the one agreed to by the clinicians should be worked out, and the values for varying statistical power (the probability of detecting a given difference if it truly exists) should be calculated. If the sample size calculated to be optimal is unworkable because the largest N feasible in the real world is smaller, then the statistician must have the other team members consider the following four alternatives ... 

If a claim is to be made for superiority of a drug preparation over another such product, power calculations must be performed to support this claim of statistical significance. Similarly, any claim of therapeutic equivalence between a study drug and another product must be supported by appropriate power calculations. 

In the planning of a trial it is necessary to calculate the number of persons needed to be able to detect a predefined difference. In many countries, e.g. in Denmark, ethical approval is not given if a proper statistical power analysis is not given. 

Benchmark Dose (BMD) modeling is an alternative method to the NOAEL/ LOAEL approach (Cmmp, 1984 Dourson et al., 1985 Barnes et al., 1995 U.S. EPA, 2000a). The method fits flexible mathematical models to the dose-response data and then determines the dose associated with a specified incidence of the adverse effects. Once this dose is estimated, then an RfD is estimated with the use of one or more uncertainty factors or Chemical Specific Adjustment Factors (CSAF) as described above. Advantages over the NOAEL/LOAEL approach include (1) the BMD is not limited to the tested doses (2) a BMD can be calculated even when the study does not identify a NOAEL and (3) unlike the NOAEL approach, the BMD approach accounts for the statistical power of the study. Numerous examples of BMD use in the dose-response assessment part of the risk assessment process are available on the U.S. EPA s Integrated Risk Information System (IRIS) (2004b). 

External reports are most likely going to be manuscripts submitted to peer-reviewed journals. Placement of pharmacoeconomic articles in nonspecialty journals is important but difficult. Some editors do not understand the intrinsic properties of pharmacoeconomic data, and some reviewers will blindly apply statistical constraints that are inappropriate or not valid to humanistic outcomes (e.g. power calculations to measures of the adverse effects of drugs on QOL measures). 

Hence, CTS cannot answer the question WiU this trial succeed but rather answers the question What is the probability of this trial succeeding One outcome frequently reported from a CTS is that of statistical power—the probability of declaring the null hypothesis (the hypothesis of no difference) false. Power is computed from a stochastic simulation by counting the number of times the null hypothesis is rejected divided by the total number of replicates used in the simulation. For example, if 88 runs out of 1000 reject the null hypothesis, the power of the trial design is 8.8%. Since this type of analysis is binomial (the trial either fails or it succeeds), the (1 - a)% confidence interval for the power of the trial may be calculated using the normal approximation as... 

There is at least one important caveat to the power considerations discussed above. Standard power calculations for the linear model setting are based on the assumption of a tme linear relationship between exposure and outcome. In a real world dose-response setting, such as encountered for MeHg, there is likely to be some nonlinearity. That means that the observed level of statistical significance in a study might depend less on the total sample size than on the spread of the exposure... 

Statistical Methods. The planned sample size and the formula for sample size and power calculations should be provided, (a) Statistical and Analytical Plans. Discuss the planned statistical analyses and any changes made while the trial was conducted. Emphasis should be placed on which analyses and comparisons are planned, not on the specific statistical techni ques to be used, (b) Interim Analyses. The frequency and nature of any planned interim analyses and any circumstances under which the trial may be terminated should be discussed. Include any statistical adjustments to be used because of interim analyses. 

Reduction refers to efforts to minimise the number of animals used during an experiment, as well as the prevention of unnecessary replication of previous experiments. To satisfy this requirement, statistical design of experimentation (SDE) methodology and other mathematical calculations of statistical power are employed to determine the minimum number of animals that must be used to get a statistically significant experimental result. 

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