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
What nutrition epidemiologists
want to know …
Reduced
Rank
Regression
PCA or
Factor
Analysis
Cluster
Analysis
?
Dietary
Pattern
Dietary
Indices
Eg. Healthy
Eating Index
?
Disease
or
Health
Outcome
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
Food Intakes
Dietary
Patterns
•
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
Reduced Rank Regression – a novel
empirical approach
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
Food
Intake
Nutrients
Predictors
Responses
Or
Biomarkers
Disease
or
Outcome
of Interest
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
Example RRR - ALSPAC
Predictors
Food Group
Intakes
1st Dietary Pattern:
Energy-dense,
high in fat,
low in fibre
Responses
Nutrient
Intakes
Dietary
Pattern 1
3-day
food
diary
Fruit
Veg
F3
F4
F5
F6
F7
F8…
Fat
Fibre
Energy
Density
Dietary
Pattern 2
OBESITY
(fat mass)
Dietary
Pattern 3
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
ALSPAC –
change in Fat Mass
Index (z-score)
with a SD increase
in energy-dense,
high fat, low fibre
dietary pattern
z-score
Girls
Age
Dietary Pattern
FMI @ 9 y
n=2868
FMI @ 11 y
n=2274
FMI @ 13 y
n=2007
FMI @ 15 y
n=1556
7y
(95% CI)
p-value
0.08
(0.05 - 0.12)
<.0001
0.08
(0.03 - 0.12)
<0.001
0.07
(0.03 - 0.11)
<0.001
0.07
(0.02 - 0.12)
<0.001
0.05
(0.01 - 0.08)
0.01
0.04
(0.01 - 0.08)
0.04
0.05
(0.01 - 0.10)
0.02
10 y
13Y
Boys
-0.01
(-0.04 - 0.03)
0.68
Age
Dietary Pattern
FMI @ 9 y
n=2854
FMI @ 11 y
n=2118
FMI @ 13 y
n=1863
FMI @ 15 y
n=1345
7y
(95% CI)
p-value
0.09
(0.05 - 0.12)
<.0001
0.09
(0.05 - 0.13)
<.0001
0.06
(0.01 - 0.10)
0.012
0.07
(0.02 - 0.12)
0.006
0.01
(-0.03 - 0.04)
0.65
0.04
(0.01 - 0.08)
0.04
0.01
(-0.03 - 0.06)
0.64
10 y
13Y
-0.01
(-0.05 - 0.02)
0.45
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
EPIC Potsdam (Germany)
% Energy from saturated fat, PUFA,
MUFA, protein and carbohydrate
All cause mortality
EPIC Potsdam (Germany)
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
Dietary Pattern
•
•
Blood Glucose
Food
Intake
Insulin Resist.
Predictors
Responses
Diabetes
Should be on pathway;
Therefore must be susceptible to dietary intake – relevant to more novel biomarkers
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
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)
Gina Ambrosini
Risk of T2D in Framingham
Offspring Study
Imamura F et al. Generalizability of dietary patterns
associated with type 2 diabetes mellitus.
AJCN 2010; 90(4):1075-83
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
Gina Ambrosini
Acknowledgements
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)
Type 2 Diabetes
EPIC Potsdam (Germany)
Fibre, Magnesium, alcohol
Type 2 Diabetes
EPIC Potsdam (Germany)
% Energy from saturated fat, PUFA,
MUFA, protein and carbohydrate
All cause mortality
EPIC Potsdam (Germany)
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
Gina Ambrosini