Nominal significance level

In the fixed sample clinical trial approach, one analysis is performed once all of the data have been collected. The chosen nominal significance level (the Type I error rate) will have been stated in the study protocol and/or the statistical analysis plan. This value is likely to be 0.05 As we have seen, declaring a finding statistically significant is typically done at the 5% p-level. In a group sequential clinical trial, the plan is to conduct at least one interim analysis and possibly several of them. This procedure will also be discussed in the trial s study protocol and/or the statistical analysis plan. For example, suppose the plan is to perform a maximum of five analyses (the fifth would have been the only analysis conducted had the trial adopted a fixed sample approach), and it is planned to enroll 1,000 subjects in the trial. The first interim analysis would be conducted after data had been collected for the first fifth of the total sample size, i.e., after 200 subjects. If this analysis provided compelling evidence to terminate the trial, it would be terminated at that point. If compelling evidence to terminate the trial was not obtained, the trial would proceed to the point where two-fifths of the total sample size had been recruited, at which point the second interim analysis would be conducted. All of the accumulated data collected to this point, i.e., the data from all 400 subjects, would be used in this analysis. 

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. 

The fully parameterized model elucidated thus far was subject to the backward elimination procedure to achieve parsimony. When a parameter was removed from the model, an objective function value increase of at least 7.88, corresponding to a nominal significance level of 0.005, was required for retention of the covariate relationship quantified by the parameter. Ultimately, the effect of RACE on Kant was removed, as was the effect of gestational age on PRE and The influence of bronchopulmonary dysplasia was also determined to be insignificant. Removal of these covariates resulted in the final PD model as follows ... 

First, the statistician and physician together need to identify a particular outcome variable Including the particular time-point (or combination) which will be used. Next the statistician must identify an appropriate statistical test. A size of this test, or nominal significance level, (see Chapter 4) must also be identified. It will also be important to have obtained from previous trials, or some appropriate source, an estimate (sometimes no more than a guesstimate) of the likely variability of the particular measure chosen. The statistician also needs to establish a working alternative hypothesis. This is not a... 

Figure 19.2 Nominal significance level at each look for three group sequential schemes.

The error estimate based on replicates at nominal level results in underestimated critical effects, and consequently a high number of effects is considered significant, which practically are not relevant, e.g., the effects of A, C, D, I, E, and J on response Rs at significance level a = 0.05 (Table 10). A possible reason is that the replicates are measured under repeatability conditions. For duplicated design experiments, a similar problem might occur. However, in Table 11 it is not the case or the critical effect is only slightly underestimated. In case underestimation occurs for a response related to the quantitative aspect, the method would incorrectly be considered non-robust, since effects considered significant occur. This is fundamentally not a problem, because one will react when it is not necessary. It just leads to a waste of time and money. The opposite situation is worse. 

Then, in choosing the tabular value of the F-criterion, it is necessary to consider degrees of freedom for bigger and smaller variances and for the chosen significance level. Associated degrees of freedom are mostly known, since nominators in formulas for determining associated variances are Sad and Sy2. The problem of lack of fit of a model may become clearer if we look at Fig. 2.41. 

For the determination of the significance level of fixed effects, the LRT is known to be anti-conservative, i.e., the empirical p value will be greater than the nominal p value [35]. Generally, as the number of parameters (degrees of freedom) being tested increases, the more anti-conservative the test. 

The Type I error (rejection of the reduced model in favor of the full model) that would result from the use of the theoretical critical value was assessed for each of the designs considered, and for three alternative NONMEM linearization methods first-order (FO), first-order conditional estimation (FOCE), and first-order conditional estimation with interaction (FOCEI). Type I error rates were assessed by empirical determination of the probability of rejection of the reduced model, given that the reduced model was the correct model. Data sets were simulated with the reduced model (FO, 1000 data sets FOCE/FOCEI, 200 data sets) and fitted using the full and reduced models. The empirical Type I error was determined as the percentage of simulated data sets for which a LRT statistic of 3.84 or greater was obtained. The 3.84 critical value for the LRT statistic corresponds to a significance level of 5%, for a distribution with 1 degree of freedom (for the one extra parameter in the full model). The LRT statistic was calculated as the difference between the NONMEM objective function values of the reduced and full models. The results of these simulations were also used to determine an empirical critical value that would result in the Type I error rate equal to the nominal 5% value. 

Number of nominally constant parameters, p Number of sampled data points in transient Significance level for F-test ajd. 1 + ajd. 2... 

Bonferroni correction A commonly adopted approach to controlling false-positive results due to multiple comparisons. Under this approach, the statistical significance level is set to be the ratio between the global nominal level and the number of statistical tests conducted. 

Finally, before the results were aggregated between these two methods of data collection for further analysis, one extra check of the reliability of the assumption was performed. To check for differences on individual items between the internet and face-to-face surveys, a Chi-square tests for every individual guideline was conducted. The Chi-square test can be used to check for a relation between two variables of nominal measurement level. Table 2 presents the results of these individual Chi-square tests per item by presenting the Chi-squared value, the degrees of freedom and the significance level. Since there is no significant relationship between the data collection method and the number of correct responses the assumption that there is no effect for the method of data collection is supported. 

Further incentives to use energy-efficient motors are provided by various cost rebate programs offered by utilities based on norsepower rating and efficiency level. Another factor that will have a significant impact is the Energy Policy Act of 1992, in which the U.S. Congress established limits on the lowest level of nominal efficiency that certain classes of motors of standard design can have after 1997. 

The final estimation of the value of ay may appear tedious and several assumptions are made in its derivation, but experimental evidence suggests that it may be used with reasonable accuracy to assess the levels of potentially damaging cavitation erosion. In small valves with nominal bores up to 65 mm cavitation inception occurs in intermittent bursts when the value oy is approximately unity. The cavitation becomes continuous and audible as Oy is reduced to about 0.6, but the risk of damage does not become significant until the value falls below 0.4. As a design criterion the condition of light, steady noise has been described by Tullis as the critical level and is sug-... 

ID-ICP-MS [425,426], Certified values for the 4 PE/Cd materials (VDA-001 to -004) with nominal Cd concentrations of 0.35 to 3.6mmolkg 1 were established by IDMS, using an enriched mCd spike [427]. The results did not show significant differences between bottles at the 300-mg level. For the sample with the highest Cd content (VDA-004 407 ppm) the measurement reproducibility was worse, which stands in relation to heterogeneity problems, as confirmed by GF-ZAAS results. 

For cases where equation (4.17) is true, the change from the nominal to the alternative level is significant. However, the results of the test will be misleading if the factors investigated are not independent. Such a study may be used to set the level of control that should be applied at particular stages of the method, e.g. adjust the pH to 6.5 0.2. It is also possible to study the effect of potential interferences by using this approach. 

Relative to body weight, humans have a much lower respiratory rate and cardiac output than rodents. These are the two primary determinants of systemic uptake of volatile chemicals. Therefore, at similar nominal concentrations, rodents absorb substantially more cyanide than primates. From a pharmacokinetic view, lower hepatic rhodanese levels in primates will not be significant at high, acute HCN exposures. It should be noted that Barcroft s subject withstood a 1 min and 31 s exposure at approximately 500 to 625 ppm without immediate effects (Barcroft 1931), whereas mice suffer asphyxia during a 2 min exposure at 500 ppm (Matijak-Schaper and Alarie 1982). Compared with rodents, the respiratory tracts of humans and monkeys are more similar in gross anatomy, the amount and distribution of types of respiratory epithelium, and airflow patterns (Barrow 1986 Jones et al. 1996). 

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