Probability of chance correlation

In order to obtain reliable models (minimize the probability of chance correlations) it is necessary to consider the ratio /Jdf/v ... 

Clark, M. and Cramer III, R.D. (1993). The Probability of Chance Correlation Using Partial Least Squares (PLS). Quant.Struct.-Act.Relat., 12,137-145. 

Clark, M. and Cramer, R.D., III (1993) The probability of chance correlation using partial least squares (PLS). Quantitative Structure-Activity Relationships, 12, 137-145. 

Clark M, Cramer RD III. The probability of chance correlation using PLS. Quant Struct-Act Relat 1993 12 137-145. 

Timer et al. (1983) used the intraperitoneal dosing data from Williams et al. (1982) to develop 3 QSARs for the Pearson and Mawby softness parameter (Op) that predicted mouse LD50 values for groups of 8,11, and 14 divalent cations (Table 5.1). The coefficients of determination, standard deviations, and probabilities of chance correlations for groups of 8, 11, and 14 divalent cations decreased as the number of divalent cations increased (Table 5.17). The Timer et al. (1983) QSAR for 14 divalent cations is identical to the Williams et al. (1982) mouse QSAR for 14 divalent cations (Table 5.1). The test system used to develop the Timer et al. (1983) QSARs is listed in Table 5.15. 

Another major reason for plotting factors is the possibility that an optimum will be observed. This is illustrated genetically in Figure 16. It is clear that optimal behavior occurs often in the relationship of tr or log P to activity (Hansch and Fujita Takemoto et al. ). It is thus reasonable to include a term as a faaor in an analysis of biodata. However, the inclusion of squared terms for all factors in a design would be a problem relative to the probability of chance correlations. Since examples of optimal behavior for other faaors have been reported (e.g., for or a ), this possibility must be considered. 

A second limitation has to do with use of the stepwise multiple regression method. This method probably misses some correlations and as such leads to some underestimation of the incidence of chance correlations. 

As It has been pointed out by Topllss and Edwards (32), the higher the number of the possible Independent variables to consider In a QSAR study, the more probable the occurrence of chance correlations. Therefore, In order to enter a large number... 

Building a model from a large descriptor pool can lead to increased probability for chance correlations when excessive number of independent... 

Data Analysis Because of the danger of false conclusions if only one or two parameters were evaluated, it was deemed better to correlate every parameter with all the others, and to assemble the results in a triangular matrix, so that trends would become more apparent. The program CORREL described in Section 5.2 retains the sign of the correlation coefficient (positive or negative slope) and combines this with a confidence level (probability p of obtaining such a correlation by chance alone). 

Figure 4.28. Correlation graph for file PROFILE.dat. The facts that (a) 23 out of 55 combinations yield probabilities of error below p = 0.04 (42% expected due to chance alone =8%) and (b) that they fall into a clear pattern makes it highly probable that the peak areas [%] of the corresponding chromatograms follow a hidden set of rules. This is borne out by plotting the vectors two by two. Because a single-sided test is used, p cannot exceed 0.5.

Using the Student s t factors and the number of degrees of freedom, calculate the probabilities p that correlations are due to chance alone (error probabilities) these are interpreted as follows ... 

A widely used approach to establish model robustness is the randomization of response [25] (i.e., in our case of activities). It consists of repeating the calculation procedure with randomized activities and subsequent probability assessments of the resultant statistics. Frequently, it is used along with the cross validation. Sometimes, models based on the randomized data have high q values, which can be explained by a chance correlation or structural redundancy [26]. If all QSAR models obtained in the Y-randomization test have relatively high values for both and LOO (f, it implies that an acceptable QSAR model cannot be obtained for the given dataset by the current modeling method. 

Samples are the second key component for the success of HTS—they are the source of new leads. The number and diversity of the chemical entities present in a sample library are crucial for providing a reasonable chance of success. Sample libraries can be collections of natural compounds, combinatorial products, or previously synthesized molecules. As a first approximation, the probability of finding a hit is correlated directly to the number of different chemical entities present in the screened library. However, this is true only if the compounds present are indeed unique and unrelated. This is seldom the case. 

It has been shown that the more independent variables are involved in MLR QSAR analysis, the higher the probability of a chance correlation between predicted and observed activities, even if only a small portion of variables is included in the final QSAR equation (16). This conclusion is true not only for MLR QSAR, but also for any QSAR approach when the number of variables (descriptors) is comparable to or higher than the number of compounds in a data set. Thus, model validation is one of the most important aspects of QSAR analysis. 

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