Data analysis, planning experiments

Phase IV studies can also take the form of retrospective pooled analyses which are designed to reflect the totality of clinical research experience with a new drug which is usually obtained via analysis of pooled clinical trial databases. Such data-mining efforts should not be considered inferior to data obtained from the conduct of an individual clinical trial. In fact, there are substantial benefits of such an approach, as the results of a given trial, especially if the end point is not prespecified to be primary because of power limitations, can be a function of chance. To assure that the results obtained from pooled analyses are not biased, a prespecified data analysis plan is often formulated as the first step, outlining the clear goals of the proposed analysis as well as its methodology. Key to this type of analysis is the definition of the outcome measure. Both efficacy and safety measures can be the focus of these types of analyses. 

Because earlier experimental results and data analyses (3-10) had led us to anticipate the inadequacy of the simple approach considered above, we also planned and carried out (2) a second order factorial design of experiments and related data analysis. Mathematical analysis (of the results of 11 experiments) based on the second order model showed that all of these results could be represented satisfactorily by an equation of the form... 

The level of validation to be undertaken must be chosen considering scientific and economic constraints. All data have some value, and results from the development phase can all be pressed into service for validation. Separate planned experiments might lead to better and more statistically defensible results, but when this cannot be done, then whatever data are at hand must be used. The best use can be made of experiments to be done by understanding what is required. For example, in a precision study, if the goal is to know the day-to-day variability of an analysis, then duplicate measurements over 5 days would give more useful information than 5 replicates on day 1, and another 5 on day 5. The strategy would be reversed if variations within a day were expected to be greater than between days. 

However, it should be emphasized that the statistical methods presented here are no cures for poor data. Irrelevant or erroneous measurement and poorly planned experiments will still be irrelevant, erroneous and poorly planned in spite of any statistical analysis. There are, however, many examples of excellent data that have been seriously mutilated by poor statistical analysis. The aim of this chapter is to present multivariate statistical methods for design and... 

As we may remember from Sections 2.3 and 2.4.10, the ANOVA technique is useful in cases where the number of results in each cell is different (but see below ). This may happen sometimes when single experiments fail or, in environmental analysis, when some samples are exhausted more quickly than others or when sampling fails. We also recognize ANOVA to be a valuable technique for the evaluation of data from planned (designed) environmental analysis. In this context the principle of ANOVA is to subdivide the total variation of the data of all cells, or factor combinations, into meaningful component parts associated with specific sources of variation for the purpose of testing some hypothesis on the parameters of the model or estimating variance components (ISO 3534/3 in [ISO STANDARDS HANDBOOK, 1989]). 

Practical science should not start with collecting data it should start with a hypothesis (or several hypotheses) about a problem or technique, etc. With a set of questions, one can plan experiments to ensure that the data collected is useful in answering those questions. Prior to any experimentation, there needs to be a consideration of the analysis of the results, to ensure that the data being collected are relevant to the questions being asked. One of the desirable outcomes of a structured approach is that one may find that some variables in a technique have little influence on the results obtained, and as such, can be left out of any subsequent experimental plan, which results in the necessity for less rather than more work. 

Two types of experiments can produce the data needed to establish statistical models. Passive experiments refer to the classical analysis of an experimental process investigation. They occur when the sets of experiments have been produced (in an industrial or in a pilot unit) either by changing the values of independent process variables one by one or by collecting the statistical materials obtained with respect to the evolution of the investigated process. Active experiments will be produced after the establishment of a working plan. In this case, the values of each of the independent variables of the process used for each planned experiment are obtained by specific fixed procedures. 

The observational areas and the oceanographic sampling plan used in this experiment are described here. The choice of the appropriate statistical methods to use in data analysis generally is dependent on the nature of the data and how the data were taken. 

On a practical level, the heuristic approach includes first collecting all the possible data during the experiments as a function of the parameters which are deemed to be important, i.e. concentrations, temperature, pressures, pH, catalyst concentration, volume, etc. Then the rate constants are estimated by regression analysis and the adequacy of the model is judged based on some criteria (like residual sums and parameter significance, which will be discussed further). If a researcher is not satisfied, then additional experiments are performed, followed by parameter estimation and sometimes simulations outside the studied parameter domain. The latter procedure provides the possibility to test the predictive power of a kinetic model. The kinetic model is then gradually improved and the experimental plan is modified, if needed. This process continues until the researcher is satisfied with the kinetic model. 

It must be noted that if the experiments are carefully planned, relatively simple data analysis techniques (variance analysis, linear regres.ston, etc.) can be used. Conversely, if the experiments are not carefully planned, it is often necessary to use much more complex mathematical and statistical tools (factorial analyses, clas.siflcations. etc,) without even being sure of the re.sulLs. 

This book is intended to serve as a reference and/or textbook on the topic of impedance spectroscopy, with special emphasis on its application to solid materials. The goal was to produce a text that would be useful to both the novice and the expert in IS. To this end, the book is organized so that each individual chapter stands on its own. It is intended to be useful to the materials scientist or electrochemist, student or professional, who is planning an IS study of a solid state system and who may have had little previous experience with impedance measurements. Such a reader will find an outline of basic theory, various applications of impedance spectroscopy, and a discussion of experimental methods and data analysis, with examples and appropriate references. It is hoped that the more advanced reader will also find this book valuable as a review and summary of the literature up to the time of writing, with a discussion of current theoretical and experimental issues. A considerable amount of the material in the book is applicable not only to solid ionic systems but also to the electrical response of liquid electrolytes as well as to sohd ones, to electronic as well as to ionic conductors, and even to dielectric response. 

The chapters are ordered in a logical sequence, the sequence in which data analysis might be carried out—from planning an experiment through... 

The important messages to remember from this chapter are to think carefully about the discovery experiment first. Put together a solid team with the skills necessary to accomplish the project. Think carefully about the question that is being asked Is it reasonable and achievable Plan the project well and listen to potential problems and challenges so that the question can be answered satisfactorily. Focus on the question being asked and do not get sidetracked until there is an answer to the initial question there is always an opportunity to investigate the data further after the question has been answered. Simplify each step in the biomarker discovery experiment as much as possible so that the data analysis results are as clear as possible. 

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