Regression analysis comparison studies

Figure 14-28 Distances from data points to the line in the vertical direction in WLR assuming proportional standard deviations for random errors in x2 and no random error in xl. (From Linnet K. Necessary sample size for method comparison studies based on regression analysis. Clin Chem 1999 45 882-94.)...

According to current practice in method comparison studies, it is usual to apply unweighted forms of regression analysis (i.e., OLR and the Deming procedure), even though the SDs vary with the measured concentration, as occurs... 

From Linnet K. Necessary sample size for method comparison studies based on regression analysis. Clin Chem 1999 45 882-94,... 

Data on age, sex, smoking and drinking, etc. were gathered after completion of the study. Statistical comparisons were made by applying 2 tailed x -test and Student s t-test. A multiple regression analysis was performed to explore any association of factors such as age, sex, smoking and drinking habits, and location. 

A number of different approaches have been taken by researchers examining the relationship between accident statistics and employee job tenure (how long the employee has worked in the job). In some studies, researchers have formed groups of employees based on their job tenure and compared accident rates across the groups. Unfortunately, not all studies that have used this group comparison approach to study the relationship between job tenure and accidents have attempted to control for employee age across the groups. Other studies have used job tenure as a predictor variable in regression analysis or simply correlation analysis in an attempt to find associations between an employee s job tenure and accidents. 

Sensitisation. The observation from early studies that individuals who had been previously exposed to SM were more sensitive than naive individuals is supported by comparisons using the dose response of naive individuals in the mass sensitivity trials described above and the dose response curve for subjects previously burned by SM (Figure 5.6). The EDjo is significantly lower in previously burned subjects than in naive subjects (p < 0.001, F-test) and the probit slope is significantly shallower p < 0.001, analysis of variance on regression analysis). 

A single index can absorb a limited amount of structural information and often needs to be combined with information that other indices carry. Wiener used two descriptors, W and P (paths of length 3), to correlate selected thermodynamic properties of alkanes and structurally related amides, alcohols, and fatty acids. Selection of topological indices for regression analysis and other studies is always somewhat arbitrary, just as the selection of a coordinate system is in solving mathematical problems in calculus. The solution of problems, naturally, does not depend on the choice of coordinates, but solving of the problem may. Similarly, in structure-property-activity studies the relative magnitude of the computed result for two structures is not necessarily sensitive to the choice of descriptors, but the possibility of a simple interpretation of results may depend on the selection of descriptors. It is therefore desirable to use descriptors that are structurally related as this will facilitate comparison and interpretation of the results obtained for different molecules. We will review here several sets of structurally related molecular descriptors. 

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