In multivariate analysis, independent variables are usually correlated to each other which can introduce multicollinearity in the regression models. One approach to solve this problem is to apply principal components analysis (PCA) over these variables. This method uses orthogonal transformation to represent sets of potentially correlated variables with principal components (PC) that are linearly uncorrelated. PCs are ordered so that the first PC has the largest possible variance and only some components are selected to represent the correlated variables. As a result, the dimension of the variable space is reduced. This tutorial illustrates how to perform PCA in R environment, the example is a simulated dataset in which two PCs are responsible for the majority of the variance in the data. Furthermore, the visualization of PCA is highlighted.

Background: Although there are solid findings regarding the detrimental effect of alcohol consumption, the existing evidence on the effect of other dietary factors on breast cancer (BC) risk is inconclusive. This study aimed to evaluate the association between dietary patterns and risk of BC in Spanish women, stratifying by menopausal status and tumour subtype, and to compare the results with those of Alternate Healthy Index (AHEI) and Alternate Mediterranean Diet Score (aMED). Methods: We recruited 1017 incident BC cases and 1017 matched healthy controls of similar age (±5 years) without a history of BC. The association between ‘a priori’ and ‘a posteriori’ developed dietary patterns and BC in general and according to menopausal status and intrinsic tumour subtypes (ER+/PR+ and HER2−; HER2+; and ER−/PR− and HER2−) was evaluated using logistic and multinomial regression models. Results: Adherence to the Western dietary pattern was related to higher risk of BC (OR for the top vs the bottom quartile 1.46 (95% CI 1.06–2.01)), especially in premenopausal women (OR=1.75; 95% CI 1.14–2.67). In contrast, the Mediterranean pattern was related to a lower risk (OR for the top quartile vs the bottom quartile 0.56 (95% CI 0.40–0.79)). Although the deleterious effect of the Western pattern was similarly observed in all tumour subtypes, the protective effect of our Mediterranean pattern was stronger for triple-negative tumours (OR=0.32; 95% CI 0.15–0.66 and P_{heterogeneity}=0.04). No association was found between adherence to the Prudent pattern and BC risk. The associations between ‘a priori’ indices and BC risk were less marked (OR for the top vs the bottom quartile of AHEI=0.69; 95% CI 0.51–0.94 and aMED=0.74; 95% CI 0.46–1.18)). Conclusions: Our results confirm the harmful effect of a Western diet on BC risk, and add new evidence on the benefits of a diet rich in fruits, vegetables, legumes, oily fish and vegetable oils for preventing all BC subtypes, and particularly triple-negative tumours.

To externally validate the previously identified effect on breast cancer risk of the Western, Prudent and Mediterranean dietary patterns. MCC-Spain is a multicase-control study that collected epidemiological information on 1181 incident cases of female breast cancer and 1682 healthy controls from 10 Spanish provinces. Three dietary patterns derived in another Spanish case-control study were analysed in the MCC-Spain study. These patterns were termed Western (high intakes of fatty and sugary products and red and processed meat), Prudent (high intakes of low-fat dairy products, vegetables, fruits, whole grains and juices) and Mediterranean (high intake of fish, vegetables, legumes, boiled potatoes, fruits, olives, and vegetable oil, and a low intake of juices). Their association with breast cancer was assessed using logistic regression models with random province-specific intercepts considering an interaction with menopausal status. Risk according to tumour subtypes - based on oestrogen (ER), progesterone (PR) and human epidermal growth factor 2 (HER2) receptors (ER+/PR+ & HER2-; HER2+; ER-/PR- & HER2-) - was evaluated with multinomial regression models. Breast cancer and histological subtype. Our results confirm most of the associations found in the previous case-control study. A high adherence to the Western dietary pattern seems to increase breast cancer risk in both premenopausal women (OR4thvs.1stquartile (95% CI):1.68 (1.02;2.79); OR1SD-increase (95% CI):1.19 (1.02;1.40)) and postmenopausal women (OR4thvs.1stquartile(95% CI):1.48(1.07;2.05); OR1SD-increase(95% CI): 1.14 (1.01;1.29)). While high adherence to the Prudent pattern did not show any effect on breast cancer, the Mediterranean dietary pattern seemed to be protective, but only among postmenopausal women (OR4thvs.1stquartile (95% CI): 0.72 (95% CI 0.53;0.98); p-int=0.075). There were no significant differences by tumour subtype. Dietary recommendations based on a departure from the Western dietary pattern in favour of the Mediterranean diet could reduce breast cancer risk in the general population.

Carotenoid and vitamin C intakes, assessed by FFQ, have been positively associated with plasma concentrations in different populations. However, the influence of BMI on these associations has not been explored in detail. We explored in a cross-sectional study the relation between dietary carotenoid and vitamin C intakes, using a 135-item FFQ, with their plasma concentrations by BMI categories in 252 men and 293 women, 65 years and older. For men and women combined, significant (P < 0·05) Pearson correlations were observed between energy-adjusted dietary intakes and plasma concentrations (carotenoids adjusted for cholesterol) for: α-carotene 0·21, β-carotene 0·19, lycopene 0·18, β-cryptoxanthin 0·20 and vitamin C 0·36. Multiple linear regression analyses showed that the intake of carotenoids and vitamin C were significant predictors of their respective plasma concentration (P < 0·01), and that BMI was inversely associated with plasma concentration of carotenoids (P ≤ 0·01) but not with plasma vitamin C. In addition, we observed significant interactions between BMI and the intakes of α-carotene and lutein + zeaxanthin, and to a lower extent β-carotene, suggesting that these intakes in subjects with high BMI were not good predictors of their plasma concentration. The present data suggest that plasma carotenoids and vitamin C may be good markers of dietary intake in elderly subjects, but not so for α-carotene, β-carotene and lutein + zeaxanthin in obese subjects.