Statistical Analysis of Biochemical Data

All numerical data are subject to uncertainty for a variety of reasons but because decisions will be made on the basis of analytical data, it is important that this uncertainty be quantified in some way. Variation between replicate measurements 11 

The sum of all deviations from the mean — that is, Z (xt — 3c) —will always equal zero. Summing the absolute values of the deviations from the mean results in a quantity that expresses dispersion about the mean. This quantity is divided by n to yield a measure known as the mean deviation or the standard error of the mean (SEM), which expresses the confidence in the resulting mean value  

An approach to eliminate the sign of the deviations from the mean is to square the deviations. The sum of the squares of the deviations from the mean is called the sum of squares (SS) and is defined as 

As a measure of variability or dispersion, the sum of squares considers how far the Xt s deviate from the mean. The mean sum of squares is called the variance (or mean squared deviation), and it is denoted by a2 for a population  

Dividing the sample sum of squares by the degree of freedom (n — 1) yields an unbiased estimate. If all observations are equal, then there is no variability and s2 = 0. The sample variance becomes increasingly large as the amount of variability or dispersion increases. 

---

This chapter is aimed at introducing the concepts of biostatistics and informatics. Statistical analysis that evaluates the reliability of biochemical data objectively is presented. Statistical programs are introduced. The applications of spreadsheet (Excel) and database (Access) software packages to analyze and organize biochemical data are described. 

Henderson PJF (1978) Statistical analysis of enzyme kinetic data. Techniques Prot Enzyme Biochem B113 1 3... 

The terms bioinformatics and cheminformatics refer to the use of computational methods in the study of biology and chemistry. Information from DNA or protein sequences, protein structure, and chemical structure is used to build models of biochemical systems or models of the interaction of a biochemical system with a small molecule (e.g., a drug). There are mathematical and statistical methods for analysis, public databases, and literature associated with each of these disciplines. However, there is substantial value in considering the interaction between these areas and in building computational models that integrate data from both sources. In the most... 

Chemometrics is the discipline concerned with the application of statistical and mathematical methods to chemical data [2.18], Multiple linear regression, partial least squares regression and the analysis of the main components are the methods that can be used to design or select optimal measurement procedures and experiments, or to provide maximum relevant chemical information from chemical data analysis. Common areas addressed by chemometrics include multivariate calibration, visualisation of data and pattern recognition. Biometrics is concerned with the application of statistical and mathematical methods to biological or biochemical data. 

This chapter presents a brief summary of the essentials of statistics that are particularly appropriate for handling biochemical data. This is followed by a section on the quantitative analysis of experimental results which deals chiefly with binding processes and enzyme kinetics. The chapter concludes with a brief discussion of methods of sequence analysis and databases, including a description of the FASTA and Needleman and Wunsch algorithms which form the basis of most of the sequence alignment methods currently in use. 

An important extension of our large validation studies involves the use of data bases from field studies in the development of improved statistical methods for a variety of problems in quantitative applications of immunoassays. These problems include the preparation and analysis of calibration curves, treatment of "outliers" and values below detection limits, and the optimization of resource allocation in the analytical procedure. This last area is a difficult one because of the multiple level nested designs frequently used in large studies such as ours (22.). We have developed collaborations with David Rocke and Davis Bunch (statisticians and numerical analysts at Davis) in order to address these problems within the context of working assays. Hopefully we also can address the mathematical basis of using multiple immunoassays as biochemical "tasters" to approach multianalyte situations. 

M. C. Ortiz, S. Sanchez and L. Sarabia, Quality of analytical measurements statistical methods for internal validation, in Comprehensive Chemometrics Chemical and Biochemical Data Analysis, ed. S. D. Brown, R. Tauler and B. Walcazack, Elsevier, Amsterdam, 2009. 

From a chemical and biochemical point of view, biomarker discovery use a range of familiar techniques and tools that have been around for a long time such as SDS-PAGE, HPLC, mass spectrometry, etc. What is new is the number of samples and the data analysis that are often new and complicated. Biological systems especially involving human subjects are highly variable and lack a much of the consistency that is seen in other experimental systems such as animal models. Thus, it is important to choose methods that can be applied to large numbers of samples in order to deal with the statistical requirements of human samples. In a cfinical study it is not uncommon to think of hundreds or thousands of samples to vahdate a biomarker. This will require the use of bioinformatics to analyze and interpret data and to keep track of the vast amount of data and information that will be used in the process of biomarker discovery and validation. 

Ferrer A. Statistical control of measures and processes. In Brown SD, Tauler R, Walczak B, editors. Comprehensive chemometrics chemical and biochemical data analysis. Amsterdam Elsevier Ltd. 2009. 

---