Reduced Rank Regression – a powerful statistical method for identifying empirical dietary patterns Gina Ambrosini PhD Senior Research Scientist MRC Human Nutrition Research, Cambridge EUCCONET International Workshop, Bristol October 2011

Why dietary patterns ? The human diet is complex – we do not eat nutrients or foods in isolation Single food/nutrient studies are frequently null e.g. fat intake and obesity; these do not consider total dietary intake Strong co-linearity between dietary variables; ; difficult to separate effects, may be too small to detect Numerous dietary variables (foods & nutrients) lead to too many statistical tests Studies of dietary patterns i.e. combinations of total food intake can overcome many of these problems Studies of single foods or nutrients ignore the complexity of the human diet; synergism

What nutrition epidemiologists want to know … Reduced Rank Regression ? ? Disease or Health Outcome Dietary Pattern PCA or Factor Analysis Empirical versus other patterns; PCA and cluster methods are exploratory, depend on study population covariance matrix, therefore reproducbility in different populations unknown; not hypothesis based or disease specfici. PCA, factor and cluster are exploratory methods; depend on study population and covariance matrix Study specific: reproducibility unknown in different populations Explain variation in food intakes but not necessarily nutrients – the end product of diet Clusters are based on membership; non-quantitative Not disease-specific or hypothesis-based Cluster Analysis Dietary Indices Eg. Healthy Eating Index

Empirical Dietary Patterns E.g. Principal Components Analysis (PCA), Factor Analysis and Cluster Analysis Data reduction techniques; identify latent constructs in data = patterns Take advantage of co-linearity Consider total diet; ‘real-life’ consumption and synergism Produce uncorrelated dietary patterns (or clusters) suitable for multivariate models Exploratory, data-driven, study specific: reproducibility unknown in different populations Explain variation in food intakes but not necessarily nutrients – the end product of diet Not disease-specific or hypothesis-based Food Intakes These methods have been most frequently used in the published literature Dietary Patterns

Reduced Rank Regression – a novel empirical approach In 2004 … researchers in Germany … presented

Reduced Rank Regression (RRR) A hypothesis-based empirical method for identifying dietary patterns Similar to PCA and factor analysis but requires a 2nd set of data = response variables Response variables should be on the pathway between food intake and outcome of interest RRR dietary patterns are linear combinations of food intake that explain the maximum variation in a set of response variables Dietary Pattern So, let me walk you through this … As nutrition scientists, we expect that the food we eat contains particular nutrients and non-nutrient active ingredients that have health effects in the body. We ingest food, from which nutrients are absorbed and have different effects in the body to influence disease risk. We know that for example, saturated fats sourced from animal-based foods eg. butter, milk, meats, contribute to the development of calcified plaques in blood vessels and ultimately arteriosclerosis… Now imagine that we can identify dietary patterns or combinations of food that are specifically linked to selected nutrient intakes or even biomarkers that are susceptible to dietary intake e.g blood cholesterol Response variables should be intermediates on the biological pathway between predictors and health outcome of interest Disease or Outcome of Interest Food Intake Nutrients Or Biomarkers Predictors Responses

Example - ALSPAC Measured dietary intake using a 3d food diary at 7, 10 and 13 years of age We hypothesised that: a dietary pattern that could explain the variation in dietary energy density, % energy from fat, and fibre at 7, 10 and 13 y would be prospectively assoc with body fatness measured at 9, 11, 13, 15 y

Each dietary pattern is a linear combination of weighted food intakes Example RRR - ALSPAC 1st Dietary Pattern: Energy-dense, high in fat, low in fibre Predictors Food Group Intakes Responses Nutrient Intakes Dietary Pattern 1 Fat Fruit Veg Dietary Pattern 2 3-day food diary F3 F4 OBESITY(fat mass) Fibre F5 F6 Energy Density Dietary Pattern 3 F7 F8… Explain what dietary pattern z-score means … level of adherence to dietary pattern Each dietary pattern is a linear combination of weighted food intakes that explains the max variation in ALL response variables -1st pattern often explains the most Such that for each dietary pattern a z-score is calculated as = W1(Food1 Intake) + W2(Food2 Intake) + W3(Food3 Intake) + …

ALSPAC energy-dense, high fat, low fibre dietary pattern This pattern was virtually identical when we conducted RRR at 7 years of age …

Girls  Age FMI @ 9 y FMI @ 11 y FMI @ 13 y FMI @ 15 y    Dietary Pattern n=2868 n=2274 n=2007 n=1556 7 y 0.08 0.07 (95% CI) (0.05 - 0.12) (0.03 - 0.12) (0.03 - 0.11) (0.02 - 0.12) p-value <.0001 <0.001 10 y 0.05 0.04 (0.01 - 0.08) (0.01 - 0.10) 0.01 0.02 13Y -0.01 (-0.04 - 0.03) 0.68 Boys n=2854 n=2118 n=1863 n=1345 0.09 0.06 (0.05 - 0.13) 0.012 0.006 (-0.03 - 0.04) (-0.03 - 0.06) 0.65 0.64 (-0.05 - 0.02) 0.45 ALSPAC – change in Fat Mass Index (z-score) with a SD increase in energy-dense, high fat, low fibre dietary pattern z-score These results are based on linear regression using completers only, i.e. only subjects who provided data at all relevant time points – longitudinal analyses utilising more subjects are currently underway and are showing similar relationships Adjusted for age at fat mass assessment, dietary misreporting, physical activity (cpm)

Cross-cohort comparisons: ALSPAC v Raine Study PhD project – Geeta Appannah University of Cambridge and MRC Human Nutrition Research: An almost identical energy-dense, high fat, low fibre dietary pattern seen at 14 and 17 y in The Western Australian Pregnancy Cohort (Raine) Study, a contemporaneous birth cohort. Similar factor loadings for an energy-dense, high fat, low fibre dietary pattern in a FFQ and a food diary at 14 y of age in the Raine Study Geeta Appannah, MRC Human Nutrition Research

Comparisons of RRR and PCA patterns Study RRR response variables Outcome Multi-Ethnic Study of Atherosclerosis (US) CRP, IL-6, Fibrinogen, Homocysteine Sub-clinical atherosclerosis EPIC Potsdam (Germany) Fibre, Magnesium, alcohol Type 2 Diabetes % Energy from saturated fat, PUFA, MUFA, protein and carbohydrate All cause mortality SFA, MUFA, n-3 PUFA, n-6 PUFA Breast cancer incidence Tehran Lipids and Glucose Study Total fat, PUFA/sat fat, cholesterol, fibre, calcium Obesity Although the PCA and RRR patterns in these studies had similar nutrient profiles; these studies reported stronger associations between RRR-based dietary patterns and outcomes RRR patterns explain more variation in the response variables Gina Ambrosini

Caution - using biomarkers as response variables Biomarkers as response variables should be chosen carefully: So they are true intermediates and not a proxy for the outcome of interest Should be on pathway; Therefore must be susceptible to dietary intake – relevant to more novel biomarkers Dietary Pattern Diabetes Food Intake Blood Glucose Insulin Resist. Predictors Responses Gina Ambrosini

Generalisability of RRR patterns Imamura et al (2010) applied RRR dietary patterns that were associated with type 2 diabetes in three different cohorts to the Framingham Offspring Study All patterns were characterised by high intakes of meat products, refined grains and soft drinks Dietary Pattern RRR response variables Risk of T2D in Framingham Offspring Study EPIC Potsdam (Germany) Fibre, Magnesium, alcohol 1.14 (0.99 – 1.32) Nurses Health Study (US) Inflammatory markers 1.44 (1.25 – 1.66) Whitehall II (UK) Insulin resistance * 1.16 (1.00 – 1.35) Imamura F et al. Generalizability of dietary patterns associated with type 2 diabetes mellitus. AJCN 2010; 90(4):1075-83 Gina Ambrosini

Limitations RRR appears to be a robust and powerful method, however: Reproducibility, generalisability of patterns – only 1 published study RRR depends on existing knowledge in order to choose response variables Response variables must be chosen very carefully to avoid circular analysis Biomarkers as response variables: must be an intermediate and not a proxy for the outcome/disease If response variables are not intermediates, then false relationships may be observed b/w dietary pattern and health outcome, as response variable is a proxy for outcome Gina Ambrosini

Acknowledgements Funding from: Dr Pauline Emmett, Dr Kate Northstone, & the ALSPAC Study Team Ms Geeta Appannah, PhD scholar, MRC Human Nutrition Research Mr David Johns, PhD scholar, MRC Human Nutrition Research Dr Anna Karin Lindroos, Swedish Food Authority, Uppsala (prev. HNR) Funding from:

MRC Human Nutrition Research Cambridge, UK Gina.Ambrosini@mrc-hnr.cam.ac.uk

Reported Associations with Other RRR Dietary Patterns Study RRR response variables Outcome Multi-Ethnic Study of Atherosclerosis (US) CRP, IL-6, Fibrinogen, Homocysteine Sub-clinical atherosclerosis Insulin Resistance Atherosclerosis Study (US multi-ethnic cohort) Plasminogen activator inhibitor 1, Fibrinogen Carotid artery atherosclerosis (IMT, CAC) Coronary Risk Factors for Atherosclerosis in Women (CORA) Germany LDL and HDL cholesterol lipoprotein (a) CRP, C-peptide (insulin resist) Coronary artery disease Nurses Health Study (US) Inflammatory markers Type 2 Diabetes Framingham Offspring Study (US) BMI, fasting HDL-C, TG, glucose, hypertension (BP residuals) EPIC Potsdam (Germany) Fibre, Magnesium, alcohol % Energy from saturated fat, PUFA, MUFA, protein and carbohydrate All cause mortality SFA, MUFA, n-3 PUFA, n-6 PUFA Breast cancer incidence Tehran Lipids and Glucose Study Total fat, PUFA/sat fat, cholesterol, fibre, calcium Obesity ALSPAC Energy density % energy from fat Fibre density Child obesity at 7, 9, 11, 13, 15y The studies highlighted in red have tested PCA-derived dietary patterns as well and reported stronger associations between RRR-based dietary patterns and their health outcome Gina Ambrosini