Statistical analyses, sequential

We decided to examine only one sample size for the design, 4096. Abt et al. (6) examined sample size, among other factors, when studying sequential screening. Yi et al. (20) also used a sample size of 4096 when studying the optimization of a statistical analysis method for this dataset. Both studies indicated that relatively small sample sizes of 5000 to 10,000 compounds could be used to produce useful trees. Clearly, large sample sizes should lead to better... 

Clinical trials, with almost no exception, are longitudinal (Chow and Liu, 2004). This means that data are accumulated sequentially over time. From the perspective outlined so far in the book, the statistical analysis takes place once the number of subjects stated in the study protocol have been enrolled, randomized, and completed their participation in the trial. This approach can be called the Fixed design or fixed sample design approach. Another design of interest in clinical trials is the group sequential design, in which interim analysis plays a crucial role. 

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 amount of EBT present in Showa Denko tryptophan varied markedly in the period 1987-89 (Figure 5), presumably reflecting alterations in the manufacturing conditions. It is likely that levels of all of the contaminants varied with time. These data are consistent with the hypothesis that a contami-nant(s) in tryptophan is responsible for EMS and for the sporadic cases of EE between 1986 and 1988. Recent statistical analyses of EBT, adjusted for serial autocorrelation (to take into account that sequential lots of tryptophan may be related), revealed that higher levels of EBT are still associated with EMS, but the association (p = 0.120) did not achieve statistical significance. Nonetheless, the results do not vindicate EBT as a cause of EMS because mis-classification of lots as case or control could weaken the association and the methods used to account for the lack of independence of observations over time probably reduce the power of the statistical analysis. 

An approach based on the sequential use of Monte Carlo simulation and Quantum Mechanics is suggested for the treatment of solvent effects with special attention to solvatochromic shifts. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. This is a totally discrete model that avoids the use of a dielectric continuum. Statistical analysis is used to obtain uncorrelated structures. The radial distribution function is used to determine the solvation shells. Quantum mechanical calculations are then performed in supermolecular structures and the spectral shifts are obtained using ensemble average. Attention is also given to the case of specific hydrogen bond between the solute and solvent. 

The statistical analysis of data requires a proper design of experiments to prove or disprove a certain hypothesis which has been formulated in advance. From the viewpoint of a puritanical statistician most QSAR analyses are forbidden , because they are retrospective studies and, in addition, many different hypotheses (i.e. combinations of independent variables) are tested sequentially. Indeed, many problems arise from the application of regression analysis in ill-conditioned data sets. Only in later stages of lead structure optimization are certain hypotheses, e.g. on the influence of more lipophilic, electronegative, polar, or bulky substituents in a certain position, systematically tested, now fulfilling the requirements for the proper application of statistical methods. 

Fig. 10.14(a), trace 1 includes the statistical analysis of the data for the bacterial reduction of E. coli. No regrowth was observed after the first inactivation cycle for ZrNO and ZrNO-Ag samples. Fig. 10.14(b) shows the bacterial inactivation of E. coli by ZrNO-Ag samples under low-intensity actinic light. Within about 115 min, complete bacterial reduction was observed. Fig. 10.14(c) shows that ZrNO-Ag co-sputtered for 90 s on polyester led to a 6 logm bacterial reduction within 45 min. The co-sputtered Ag-ZiON for 90 s led to the complete loss of cultivability within 40—45 min (Fig. 10.14(c), trace 1). This time was much shorter than to the time needed by the sequentially sputtered ZrNO (90 s)-Ag (10 s) sample shown in Fig. 10.1(b). 

Today a trend can be seen to computer aided experimentation. Not only the operation and control of the reactor but also automatic data sampling, analysis and statistically based sequential design of the experiments are performed by micro-computers /23,24,25/. In general, the experimental effort is appreciable and any method is welcome which can reduce the number of necessary experiments without loss of required accuracy. 

The analysis of the properties of mesityl oxide in aqueous solution was based on the continuous and discrete models of the solvent. Here, we used the polarizable continuum model (PCM) [32, 33], and for the discrete model of the solvent, we performed the sequential use of quantum mechanics and molecular mechanics methods, S-QM/MM [20, 21]. In the S-QM/MM procedure, initially the liquid-phase configurations are sampled from molecular simulations, and after statistical analysis, only configurations with less than 10 % of statistical correlation are selected and submitted to quantum mechanical calculations. In our study, we used the Monte Carlo method (MC) with... 

For the performance analysis, the computer sequentially acquires the signal from each instrumentation channel, and performs statistical analysis on this data. Signal errors and probability distribution functions are computed and compared with the reference errors. 

In passing we remark that there are well-known statistical methods of hypothesis testing and parameter estimation used in decisionmaking. Sequential analysis is a method of sampling used to decide whether to accept or reject a lot with defective items, or whether to continue sampling. Also, there are various statistical methods used in quality control of a manufacturing process, to decide on how much the quality should be improved to be acceptable. 

Table 5.9 summarises the main features of FTIR spectroscopy as applied to extracts (separated or not). Since many additives have quite different absorbance profiles FTIR is an excellent tool for recognition. Qualitative identification is relatively straightforward for the different classes of additives. Library searching entails a sequential, point-by-point, statistical correlation analysis of the unknown spectrum with each of the spectra in the library. Fully automated analysis of... 

An approximate analysis of polymer adsorption as a set of sequential reactions leads to a simple equation for the adsorption isotherm expressed in terms of three parameters. Comparison of the model with recently published statistical theories reveals remarkable agreement in both the general shape of the isotherms and the predicted effects of molecular weight. The problems of applying such models to experimental data are discussed. 

Cluster analysis is simply a method to group entities, for which a number of properties or parameters exist, by similarity [292, 308-313]. Various distance measurements are used, and the analysis is performed in a sequential manner, reducing the number of clusters at each step. Such a procedure has been described for use in drug design and environmental engineering research as a way to group substituents that have the most similarity when various combinations of the electronic, steric, and statistically derived parameters are considered. 

The concentration data obtained from each sample analysis were expressed as fractional parts and normalized to sum to 100. The normalized data were statistically analyzed, and three principal components (A=3, Equation [1]) were calculated. The PCB constituents (varlbles) are numbered sequentially and correspond to peak 1, peak 2,. .. to peak 105. The structure and retention index of each constituent in the mixture were reported by Schwartz et al. (9). The tabular listing of the data is availedile from the present authors. 

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