The objective of a multiregional bridging trial is to show the efficacy of a drug in various global regions, and at the same time to evaluate the possibility of applying the overall trial results to each region. However, to apply overall results to a specific region, the result in that region should be consistent with either the overall results or the results of other regions. This article discusses methods of sample size allocation to regions by introducing statistical criteria for consistency between regional and overall results. Specifically, three rules of sample size allocation are discussed: (1) allocating equal size to all regions, (2) minimizing total sample size, and (3) minimizing the sample size of a specific region. Some total and regional sample sizes calculated under each allocation rule are illustrated.
A neural network system has been developed on a personal computer to identify 1129 infrared spectra. The system is composed of two steps of networks. The first step classifies 1129 spectra into 40 categories, and each unit of the output layer is connected to one of the 40 networks in the second step, which identify each spectrum. Each network is composed of three layers. The input, intermediate, and output layers are composed of 250, 40, and 40 units, respectively. Intensity data at 250 wavenumber points between 1800 and 550 cm−1 of the infrared spectra are entered into the input layer of each network. The training of the networks was carried out with the spectral data of 1129 compounds stored in the SDBS system, and thus the networks were successfully constructed. On the basis of the results, the system has been developed by preparing pre- and post-processing programs. The system can identify each unknown spectrum within 0.1 s, and is quite efficient for identifying infrared spectra on a personal computer.
A rapid and intact method has been developed for predicting polyethylene density by near-infrared spectroscopy combined with neural network analysis. Near-infrared spectra in the region of 1.1-2.2 µm wavelength were measured using pellets or powders of twenty-three kinds of polyethylene (PE) with different densities (0.898-0.962 g cm-3). The spectra were used for training a back-propagation neural network after normalized and second-derivative treatments to predict PE density. Although only a small number of spectral data were used for training, a leave-one-out test of neural network analysis has demonstrated good results. In comparison, principal component regression (PCR) analysis and partial least-squares (PLS) regression analysis were applied. The correlation coefficients (R) were calculated to be 1.000, 0.968 and 0.983 for neural network, PCR and PLS analysis, respectively. The root mean square errors of prediction were found to be 0.00026, 0.0043 and 0.0031 g cm-3 , respectively. It is found that near-infrared spectroscopy combined with neural network analysis is useful for the efficient and accurate determination of PE density.
Structure identification of chemical substances from infrared spectra can be done with various approaches: a theoretical method using quantum chemistry calculations, an inductive method using standard spectral databases of known chemical substances, and an empirical method using rules between spectra and structures. For various reasons, it is difficult to definitively identify structures with these methods. The relationship between structures and infrared spectra is complicated and nonlinear, and for problems with such nonlinear relationships, neural networks are the most powerful tools. In this study, we have evaluated the performance of a neural network system that mimics the methods used by specialists to identify chemical structures from infrared spectra. Neural networks for identifying over 100 functional groups have been trained by using over 10 000 infrared spectral data compiled in the integrated spectral database system (SDBS) constructed in our laboratory. Network structures and training methods have been optimized for a wide range of conditions. It has been demonstrated that with neural networks, various types of functional groups can be identified, but only with an average accuracy of about 80%. The reason that 100% identification accuracy has not been achieved is discussed.
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