Biological data, variability

Any set of quantitative biological data may be employed as the dependent variable. 

Structure-activity relationships are generally applied in the pharmaceutical sciences to drug molecules. The value of any structure-activity correlation is determined by the precision of the biological data. So it is with studies of the interaction of nonionic surfactants and biomembranes. Analysis of results is complicated by the difficulty in obtaining data in which one can discern small differences in the activity of closely related compounds, due to i) biological variability in tissues and animals, ii) potential differential metabolism of the surfactants in a homologous series (2), iii) kinetic and dynamic factors such as different rates of absorption of members of the surfactant homologous series (2) and iv) the typically biphasic concentration dependency of nonionic surfactant action (3 ). 

There are of course many mathematically complex ways to perform a risk assessment, but first key questions about the biological data must be resolved. The most sensitive endpoint must be defined along with relevant toxicity and dose-response data. A standard risk assessment approach that is often used is the so-called divide by 10 rule . Dividing the dose by 10 applies a safety factor to ensure that even the most sensitive individuals are protected. Animal studies are typically used to establish a dose-response curve and the most sensitive endpoint. From the dose-response curve a NOAEL dose or no observed adverse effect level is derived. This is the dose at which there appears to be no adverse effects in the animal studies at a particular endpoint, which could be cancer, liver damage, or a neuro-behavioral effect. This dose is then divided by 10 if the animal data are in any way thought to be inadequate. For example, there may be a great deal of variability, or there were adverse effects at the lowest dose, or there were only tests of short-term exposure to the chemical. An additional factor of 10 is used when extrapolating from animals to humans. Last, a factor of 10 is used to account for variability in the human population or to account for sensitive individuals such as children or the elderly. The final number is the reference dose (RfD) or acceptable daily intake (ADI). This process is summarized below. 

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

The correlation coefficient r is a measure of quality of fit of the model. It constitutes the variance in the data. In an ideal situation one would want the correlation coefficient to be equal to or approach 1, but in reality because of the complexity of biological data, any value above 0.90 is adequate. The standard deviation is an absolute measure of the quality of fit. Ideally s should approach zero, but in experimental situations, this is not so. It should be small but it cannot have a value lower than the standard deviation of the experimental data. The magnitude of s may be attributed to some experimental error in the data as well as imperfections in the biological model. A larger data set and a smaller number of variables generally lead to lower values of s. The F value is often used as a measure of the level of statistical significance of the regression model. It is defined as denoted in Equation 1.27. 

Gao et al. [36] used binary QSAR based on topological descriptors and indicator variables (including one for the phenolic hydroxyl group) to derive a classification model that separates active from inactive compounds. The model was trained on 410 diverse molecules, and it demonstrated its predictive power on a test set of 53 randomly selected molecules from which 94% were correctly classified. The biological data were selected from four different laboratories, so there might be some inconsistency with respect to the classification of the model. 

A cursory review of most introductory statistics texts will usually reveal a section on inferential analysis that explains how one can make a qualified leap from a sample to a population then it will dutifully caution that a p-value should only be viewed as one type of evidence in evaluating that leap of faith. It is designed to be one of many ingredients leading to a rich, deep understanding of the phenomenon under study, when that phenomenon is surrounded by unexplained variability. Inferential statistics and the jo-value are particularly useful when it is not possible to understand or control some of the sources of variability, and this clearly applies to human biological data. 

The procedure used to obtain data is important to the outcome. Experiments consist of controls and variables. A control is the experiment run under normal conditions. The variable includes a factor that is changed. In biology, the variable may be light, temperature, pH, time, etc. The differences in tested variables may be used to make a prediction or form a hypothesis. Only one variable should be tested at a time. One would not alter both the temperature and pH of the experimental subject. 

Fig. (14). A Experimental vs. calculated pIC o values from a QSAR model for inhibitory effect of 28 STLs on NF-kB activation (biological data from [59], structures see Fig. (12)). The model was generated by GA-PLS analysis (number of latent variables 3) from the 8 descriptors shown in the loading weights plot (B). This plot illustrates the impact of each descriptor on the first two latent variables (PCI and PC2) explaining 54 % and 27 % of the variance in the Y data (pIC o), respectively.

Method Suggested minimum ratio of Compounds variables Biological Data Interpretability... 

The correlations in this table are the highest that were observed in the analysis. The activities in the last column are the biological response variables that were most highly associated with the fint canonical variable of the biological data. 

Regression analysis [388, 389, 571] correlates independent X variables (e.g. physicochemical parameters, indicator variables) with dependent Y variables e.g. biological data) (Figure 30). The dependent variables contain error terms e, while the independent variables are supposed to contain no such error. In reality, this is only an approximation, because the physicochemical parameters of a QSAR equation indeed contain experimental error however, in most cases this error is much smaller than the error in the biological data. Only Free Wilson (indicator) variables are error-free terms. 

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