Using latent variables to eliminate multicollinearity effect in a logistic regression on risk factors for breast cancer

Logistic regression is one of the most widely used generalized linear models for analysis of the relationships between one or more explanatory variables and a categorical response. Strong correlations among explanatory variables [multicollinearity] reduce the efficiency of model to a considerable degree. In this study we used latent variables to reduce the effects of multicollinearity in the analysis of a case-control study. Our data come from a case-control study in which 300 women with breast cancer were compared to 300 controls. Five highly correlated quantitative variables were selected to assess the effect of multicollinearity. First, an ordinary logistic regression model was fitted to the data. Then, to remove the effect of multicollinearity, two latent variables were generated using factor analysis and principal components analysis methods. Parameters of logistic regression were estimated using these latent as explanatory variables. We used the estimated standard errors of the parameters to compare the efficiency of models. The logistic regression based on five primary variables produced unusual odds ratio estimates for age at first pregnancy [OR=67960, 95%CI; 10184-453503] and for total length of breast feeding [OR=0]. On the other hand the parameters estimated for logistic regression on latent variables generated by both factor analysis and principal components analysis were statistically significant [P<0.003]. The standard errors were smaller than with ordinary Logistic regression on original variables. The factors and components generated by the two methods explained at least 85% of the total variance. This research showed that the standard errors of the estimated parameters in logistic regression based on latent variables were considerably smaller than that of model for original variables. Therefore models including latent variables could be more efficient when there is multicollinearity among the risk factors for breast cancer

Estimation of the gene-environment interaction in breast cancer patients

There is growing interest in assessing gene-environment interaction in the course of case-control studies. Difficulties related to the sampling of controls have led to the development of a range of non-traditional methods that do not require controls for estimating gene-environment interaction. One of these new modalities is the case-only approach, in which the assessment of gene-environment interaction is based on information from the cases only. The present article describes the application of this approach to data from breast cancer patients and compares its efficacy with that of a traditional case-control analysis. We used age at first pregnancy, number of live birth, menopause and the total number of post-menopausal years as the [environment] factors and family history of breast cancer as the [gene] factor. We computed standard errors, 95% confidence intervals and [-2 log likelihood] to compare efficiency between case-control and case-only analyses. We observed significant interaction between menopause and family history of breast cancer by both methods [OR=4.32 CI: 1.10-16.90 for case-control analysis and OR=3.40 CI: 1.17-9.87 for case-only analysis]. There was also a significant interaction effect between total years after menopause and family history of breast cancer [OR=1.07 CI: 0.98-1.16 in case-control analysis and OR=1.07 CI: 1.01-1.12 in case-only analysis]. The case-only approach yielded narrower confidence intervals for the odds ratio, and the [-2 log likelihood] values computed by this method were correspondingly smaller. Comparison of confidence intervals and [-2 log likelihood] values shows that the estimation of gene-environment interaction in breast cancer would be more efficient with the case-only approach than with the traditional case-control analysis