Most nutritional epidemiology studies investigating trends between diet and heart disease use outcome-independent dimension reduction methods, like principal component analysis, to create dietary patterns. While these methods construct patterns that describe important aspects of food consumption, these patterns are not inherently related to heart disease. Incorporating disease data into the pattern construction offers the possibility of more concisely summarizing the most disease-related foods. Sparse partial least squares (SPLS), one such method, was found to have favorable interpretation and prediction properties in the continuous outcome setting; while selecting a subset of relevant foods, it constructed a few dietary patterns that were correlated with BMI while also capturing variation in diet composition. These results were validated with simulated data. We propose incorporating SPLS into the Cox proportional hazards model to analyze a right-censored survival outcome. We hypothesized that this method would inherit the beneficial parsimony properties seen in the continuous setting, and we assessed whether this proposed method could use the most relevant covariates to create a few patterns that were associated with a survival outcome. While the proposed method targets covariate-level sparsity (i.e. variable selection), one competitor method exists that integrates pattern-level parsimony and partial least squares (PLS) in the Cox model, but it imposes more model parameters than the proposed method. We compared the variable selection, pattern selection, and predictive performance of four survival methods (Lasso, PLS, competitor sparse PLS, and proposed SPLS) via a simulation study. Simulation settings were informed in part by the Multi-Ethnic Study of Atherosclerosis (MESA), which has detailed food frequency questionnaire data on a large multi-ethnic population-based sample (6814 participants aged 45-84), as well as subsequent cardiovascular disease follow-up for over 15 years. In most studied simulation settings, the proposed method selected all 9 relevant predictors and the fewest number of irrelevant predictors (of 15) while creating a similar number of patterns and maintaining predictive ability of the outcome. In the setting most comparable to MESA, PLS chose all 24 predictors (by default) and 3.4 patterns (C-statistic=0.90), the competitor SPLS selected 21.1 predictors and 4.4 patterns (C-statistic=0.91), Lasso chose 16.4 predictors (C-statistic=0.91), and the proposed SPLS selected 11.7 predictors and 4.3 patterns (C-statistic=0.91), on average. We will also present an analysis of a coronary event in MESA using these four survival methods. In conclusion, we propose that using methods like SPLS to summarize food intake can create more heart disease-tailored dietary patterns that can complement the current nutritional epidemiology literature.
An application of partial least squares for identifying dietary patterns in bone health
