Statnote 25: Stepwise multiple regression

An investigator may also wish to select a small subset of the X variables which give the best prediction of the Y variable. In this case, the question is how many variables should the regression equation include? One method would be to calculate the regression of Y on every subset of the X variables and choose the subset that gives the smallest mean square deviation from the regression. Most investigators, however, prefer to use a ‘stepwise multiple regression’ procedure. There are two forms of this analysis called the ‘step-up’ (or ‘forward’) method and the ‘step-down’ (or ‘backward’) method. This Statnote illustrates the use of stepwise multiple regression with reference to the scenario introduced in Statnote 24, viz., the influence of climatic variables on the growth of the crustose lichen Rhizocarpon geographicum (L.)DC.

Effects of syllabic complexity in predicting accuracy of repetition and direction of errors in patients with articulatory and phonological difficulties

The purpose of this paper is to demonstrate the existence of a strong and significant effect of complexity in aphasia independent from other variables including length. Complexity was found to be a strong and significant predictor of accurate repetition in a group of 13 Italian aphasic patients when it was entered in a regression equation either simultaneously or after a large number of other variables. Significant effects were found both when complexity was measured in terms of number of complex onsets (as in a recent paper by Nickels & Howard, 2004) and when it was measured in a more comprehensive way. Significant complexity effects were also found with matched lists contrasting simple and complex words and in analyses of errors. Effects of complexity, however, were restricted to patients with articulatory difficulties. Reasons for this association and for the lack of significant results in Nickels and Howard (2004) are discussed. © 2005 Psychology Press Ltd.

The role of illness perceptions:psychological distress and treatment seeking delay in patients with genital warts.

This study examined the relationships between illness perceptions, psychological distress and treatment-seeking delay in genital warts patients. Sixty-six genital warts patients were approached while attending a sexual health clinic. They completed a questionnaire assessing their illness perceptions, psychological distress and treatment-seeking delay. Negative perceptions of illness consequences and control and a perceived cyclical timeline were associated with increased psychological distress. Perceived illness consequences maintained significance in a multiple regression equation, which accounted for 25% variance in distress. Depression was associated with treatment-seeking delay (r = 0.28, P = 0.03). In conclusion, illness perceptions may play an important role in the experience of psychological distress in genital warts patients. The implications of these findings for the design of health-care interventions are discussed.

Towards the in silico identification of class II restricted T-cell epitopes:a partial least squares iterative self-consistent algorithm for affinity prediction

Motivation: The immunogenicity of peptides depends on their ability to bind to MHC molecules. MHC binding affinity prediction methods can save significant amounts of experimental work. The class II MHC binding site is open at both ends, making epitope prediction difficult because of the multiple binding ability of long peptides. Results: An iterative self-consistent partial least squares (PLS)-based additive method was applied to a set of 66 pep- tides no longer than 16 amino acids, binding to DRB1*0401. A regression equation containing the quantitative contributions of the amino acids at each of the nine positions was generated. Its predictability was tested using two external test sets which gave r pred =0.593 and r pred=0.655, respectively. Furthermore, it was benchmarked using 25 known T-cell epitopes restricted by DRB1*0401 and we compared our results with four other online predictive methods. The additive method showed the best result finding 24 of the 25 T-cell epitopes. Availability: Peptides used in the study are available from http://www.jenner.ac.uk/JenPep. The PLS method is available commercially in the SYBYL molecular modelling software package. The final model for affinity prediction of peptides binding to DRB1*0401 molecule is available at http://www.jenner.ac.uk/MHCPred. Models developed for DRB1*0101 and DRB1*0701 also are available in MHC- Pred

Statnote 24: Multiple regression

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. These methods can be used to determine whether there is a linear relationship between the two variables, whether the relationship is positive or negative, to test the degree of significance of the linear relationship, and to obtain an equation relating Y to X. This Statnote extends the methods of linear correlation and regression to situations where there are two or more X variables, i.e., 'multiple linear regression’.

Regression analysis of ranked segment parameters for optic nerve head classification:a pilot study

Purpose: To determine whether curve-fitting analysis of the ranked segment distributions of topographic optic nerve head (ONH) parameters, derived using the Heidelberg Retina Tomograph (HRT), provide a more effective statistical descriptor to differentiate the normal from the glaucomatous ONH. Methods: The sample comprised of 22 normal control subjects (mean age 66.9 years; S.D. 7.8) and 22 glaucoma patients (mean age 72.1 years; S.D. 6.9) confirmed by reproducible visual field defects on the Humphrey Field Analyser. Three 10°-images of the ONH were obtained using the HRT. The mean topography image was determined and the HRT software was used to calculate the rim volume, rim area to disc area ratio, normalised rim area to disc area ratio and retinal nerve fibre cross-sectional area for each patient at 10°-sectoral intervals. The values were ranked in descending order, and each ranked-segment curve of ordered values was fitted using the least squares method. Results: There was no difference in disc area between the groups. The group mean cup-disc area ratio was significantly lower in the normal group (0.204 ± 0.16) compared with the glaucoma group (0.533 ± 0.083) (p < 0.001). The visual field indices, mean deviation and corrected pattern S.D., were significantly greater (p < 0.001) in the glaucoma group (-9.09 dB ± 3.3 and 7.91 ± 3.4, respectively) compared with the normal group (-0.15 dB ± 0.9 and 0.95 dB ± 0.8, respectively). Univariate linear regression provided the best overall fit to the ranked segment data. The equation parameters of the regression line manually applied to the normalised rim area-disc area and the rim area-disc area ratio data, correctly classified 100% of normal subjects and glaucoma patients. In this study sample, the regression analysis of ranked segment parameters method was more effective than conventional ranked segment analysis, in which glaucoma patients were misclassified in approximately 50% of cases. Further investigation in larger samples will enable the calculation of confidence intervals for normality. These reference standards will then need to be investigated for an independent sample to fully validate the technique. Conclusions: Using a curve-fitting approach to fit ranked segment curves retains information relating to the topographic nature of neural loss. Such methodology appears to overcome some of the deficiencies of conventional ranked segment analysis, and subject to validation in larger scale studies, may potentially be of clinical utility for detecting and monitoring glaucomatous damage. © 2007 The College of Optometrists.