Analysis data sets common types

The analysis of quality control samples is an important activity for laboratories and to make the most of the data, control charts should be used. This chapter has discussed a number of common types of control chart and described how they are set up and interpreted. 

Principal component analysis is most easily explained by showing its application on a familiar type of data. In this chapter we show the application of PCA to chromatographic-spectroscopic data. These data sets are the kind produced by so-called hyphenated methods such as gas chromatography (GC) or high-performance liquid chromatography (HPLC) coupled to a multivariate detector such as a mass spectrometer (MS), Fourier transform infrared spectrometer (FTIR), or UV/visible spectrometer. Examples of some common hyphenated methods include GC-MS, GC-FTIR, HPLC-UV/Vis, and HLPC-MS. In all these types of data sets, a response in one dimension (e.g., chromatographic separation) modulates the response of a detector (e.g., a spectrum) in a second dimension. 

Validation The use of TMAs enables analysis of large data sets, however this does not by any means suggest that the data set is not skewed. This skewing may be the result of the institution s location (population distributions with regards to race, ethnicity, access to health care), type of practice (community hospital versus referral center). These collectively might influence the tumor size, grade and subtype composition of the cases in the dataset. Such abnormalities of the dataset need to be compensated the involvement of a biostatistician from the start (i.e from case selection) helps to prevent the creation of biased TMAs. It is useful to perform common biomarker analysis on sections from the created TMA to confirm the normal distribution of known parameters. Comparison of this data with prior clinical data (e.g. ER analysis) obtained from whole section analysis is particularly useful to validate utility of the TMA. Alternatively the incidence of expression of a number of biomarkers in the TMA should be compared to that in published literature (using whole sections). 

The principal components do not (necessarily) have any physical meaning, they are simply mathematical constructs calculated so as to comply with the conditions of PCA of the explanation of variance and orthogonality. Thus, PCA is not based on any statistical model. Factor analysis (FA), on the other hand, is based on a statistical model which holds that any given data set is based on a number of factors. The factors themselves are of two types common factors and unique factors. Each variable in a data set is composed of a mixture of the common factors and a single unique factor associated with that variable. Thus, for any variable Xu in an A-dimen-sional data set we can write... 

A Weibull distribution is a generalized distribution, as each type of product population provides different types of information about the life of the product, and different life data analysis method may vary. It is quite normal that life will be in unit of time but it may not be the case always, for example, life of lubrication in automobile is dictated by kilometers miming of the vehicle and not in time units. Time is a common measure of life, so often referred to as times-to-failure. There could be different (e.g., three) types of life data, each type provides different information about the life of the product with complete data, the exact time-to-failure for the unit is known (e.g., the unit failed at 100 h of operation). With suspended or right censored data, the unit operated successfully for a known period of time and then continued (or could have continued) to operate for an additional unknown period of time (e.g., the unit was still operating at 100 h of operation).With interval and left censored data, the exact time-to-failure is unknown but it falls within a known time range [5] . Based on statistical methods, characteristic parameters are calculated to fit a life disnibution to a patticulat data set. Fot futthet details on this generalized statistical distribution, a standard book on statistics may be referred to. After the same is done one can use to get the following results ... 

Another approach to using spectra to identify cell type is a method called principal component analysis (PCA). This method is commonly used in multivariate analysis to reduce the number of variables and allow visualization of complex data sets in two or three dimensions [16,17]. We use our Raman spectra as examples and give a geometric interpretation of PCA to explain the process. We first assume that each of the 1340 spectral channels is a dimension in a 1340 hyperspace. As a result, any spectmm can be represented by a single point in this space. The distance between points in this hyperspace is determined by calculating the Euclidian distance... 

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