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A New Model for Dietary Intake Instruments Based on Self-
Report and Biomarkers
Raymond J. Carroll
Texas A&M University (http://stat.tamu.edu/~carroll)
Victor Kipnis, Doug Midthune
National Cancer Institute
Laurence Freedman
Bar-Ilan University
Outline
• Attenuation & its impact (Review)• Reference instruments (Review)• Protein intake: contradictory
results from various studies• Assumptions: reference instruments• Urinary Nitrogen (UN) as a
biomarker• New model that “explains” the
contradictory results• Discussion & conclusions
Attenuation of the FFQ
• Usually denoted by • Defined as the slope in a linear
regression of usual intake on the FFQ
• Typically 0 < < 1• Relative risk (RR) is attenuated• Observed RR is from FFQ• True RR is from usual intake
• Observed RR = (True RR)
• True RR = (Observed RR)1/
Why Attenuation Matters (I)
• True RR = (Observed RR)1/
• Suppose Observed RR = 1.10• If = 0.3, then true relative risk is
1.101/0.3 = 1.37
• If = 0.1, then true relative risk is
1.101/0.1 = 2.59
• If you think that = 0.3, but really = 0.1, then you grossly underestimate true relative risk
Why Attenuation Matters (II)
• Sample sizes for studies to achieve a given power are proportional to 1/2
• Thus, if you think the attenuation is estimate, and the real attenuation is true, then your study is too small by the factor (estimate / true)2
• Thus, if you think estimate = 0.3, but in fact true = 0.1, then your study is too small by a factor of 9.
• Estimating attenuation is crucial!
Estimating Attenuation
= the slope in a linear regression of usual intake on the FFQ
• We do not observe usual intake!• Leads to the idea of a reference
instrument– 24 hour recalls– Diaries– Weighed food records– Biomarkers
• The general idea is to use the reference instrument to estimate the attenuation
Estimating Attenuation
= the slope in a linear regression of usual intake on the FFQ
• The trick: replace usual intake by the reference instrument
• Thus, estimate is the slope in a linear regression of the reference instrument on the FFQ
• Easily computed in a pilot study• As it turns out, not all reference
instruments are created equal• In designing a study, the choice of
reference instrument is crucial
Results from Various Studies
• We have data from 7 cohorts– 5 EPIC cohorts (24-hour recalls)– Cambridge pilot study (weighed
food records)– Norfolk study (diaries)
• These reference instruments are based on self-report
• All 7 have a biomarker for protein intake: urinary nitrogen (UN)
• We can thus contrast the attenuations of the reference instruments and the biomarker
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BiomarkerStandard
Attenuation CoefficientsBiomarker and StandardBiomarker average = 0.21Reference average = 0.33
An Illustration
• Norfolk (UK) study with diaries as reference instrument
• True RR = (Observed RR)1/
• Suppose Observed RR = 1.10 (diary) = 0.249
– True RR = 1.47 (UN) = 0.085
– True RR = 3.07• Difference in the epidemiological
implications of the two numbers is enormous
Design Issues
• Sample sizes for studies to achieve a given power are proportional to 1/2
• Thus, if you think the attenuation is estimate, and the real attenuation is true, then your study is too small by the factor (estimate / true)2
• Thus, if you think estimate = 0.249, but in fact true = 0.085, then your study is too small by a factor of 8.6.
• Estimating attenuation is crucial!
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Inflation
Sample Size Inflation FactorBiomarker versus Standard
7 studies with Protein Biomarker
Reference Instrument Assumptions
= the slope in a linear regression of usual intake on the FFQ
estimate is the slope in a linear regression of the reference instrument on the FFQ
• Necessary assumptions on the reference instrument– Unbiased for usual intake:
E(Reference|usual) = Usual– “Error” in reference instrument
uncorrelated with the FFQ
• We claim both assumptions are violated for standard self-report reference instruments
Model for the FFQ
• Flattened Slope: those with high intakes tend to underreport
• Pure or measurement error: different answers when taking the instrument multiple times
• Person-specific bias (new): 2 people with exactly the same usual intake will recall things differently, even if the FFQ is given many, many times
• The person-specific bias is a random effect unique to the individual, but vital to analysis
Model for the FFQ
• Flattened Slope• Measurement error • Person-specific bias• Let T(i) be usual intake• Our model is
FFQ(ij) = + T(i) + r(i) + (ij)• Note the color coordination!• Generally, < 1, hence the slope is
flattened• In our experience, the person-
specific bias contributes quite a lot of the overall random error
Model for the FFQ
• Flattened Slope• Measurement error • Person-specific bias
FFQ(ij) = + T(i) + r(i) + (ij)
• It makes sense that any self-report instrument has the same featuresDiary(ij) = + T(i) + s(i) + (ij)
• It also makes sense to believe that the person-specific biases are correlated
(r,s) = correlation{r(i),s(i)}• This correlation is critical!
Urinary Nitrogen as a Protein Biomarker
• We have undertaken a meta-analysis of five small feeding studies that measured log(protein intake) and log(UN)
• Let i = person, j = replicate, M(ij)= UN
• No flattened slope!• Tiny person-specific bias, can be
ignoredFFQ(ij) = + T(i) + r(i) + (ij)
Diary(ij) = + T(i) + s(i) + (ij)Biomarker(ij) = T(i) + (ij)
The Model Summarized
• Flattened Slope• Measurement error • Person-specific bias FFQ(ij) = + T(i) + r(i) + (ij)Diary(ij) = + T(i) + s(i) + (ij)Biomarker(ij) = T(i) + (ij)
(r,s) = correlation{r(i),s(i)}
If 1or (r,s) 0, then the Diary does not yield a correct estimate of attenuation (unbiased with error uncorrelated with the FFQ)
Analysis of the Norfolk Study
FFQ(ij) = + T(i) + r(i) + (ij)Diary(ij) = + T(i) + s(i) + (ij)Biomarker(ij) = T(i) + (ij)
(r,s) = correlation{r(i),s(i)}• We fit this model using maximum
likelihood = 0.639 (r,s) = 0.573 (NOTE!) – Attenuation(Diary, from model)
= .251– Attenuation(Biomarker, from
model) = .069
Does the Model Fit the Data?
• The model seems plausible• It gives results for attenuation that
are consistent with using the protein biomarker as a reference instrument
• It gives a partial explanation (correlated person-specific biases) for the wide discrepancy in estimated attenuations for different reference instruments
• It can be tested with the Norfolk and MRC data
Models Compared
• Compare published models• Saturated• Plummer-Clayton• Rosner, et al
– No flattened slope for diary– No person-specific bias for
diary– Errors in FFQ and diary
uncorrelated• Kaaks, et al
– No flattened slope for diary– Person-specific biases
uncorrelated
Models Compared
• Freedman, Carroll & Wax– No flattened slope for diary– No person-specific bias for
diary– Errors in diary and FFQ can be
correlated if done at same time• Kipnis, Freedman & Carroll
– No flattened slope for diary– Errors in diary and FFQ can be
correlated if done at same time
Models Compared• Spiegelman, et al
– No flattened slope for diary– No person specific biases
incorporated explicitly– Person-specific bias and
measurement error combined into total error at an exam time
– Total error in FFQ and total error in Diary have common correlation across repeated exam times, e.g., FFQ at first exam and Diary at second exam
– Seems implausible given our experience
Models Compared
• We compared the models on the basis of AIC
• 2(loglikelihood) - 2(#parameters)• The loglikelihood increases as
models become more complex• The blue term penalizes more
complex models, so that the loglikelihood has to increase in such a way as to overcome increased complexity of the model
AIC - 150 for Models
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Body Mass
• The model up to now has not included body mass
• There is concern that the results might be affected by this omission
• One can add body mass into the model, by adding a linear term, e.g., (noting the last line)
• FFQ(ij) = + T(i) + 1 B(i)
+ r(i) + (ij)
• Diary(ij) = + T(i) + 2 B(i)
+ s(i) + (ij)• Marker(ij) = T(i) + (ij)
Body Mass
• FFQ(ij) = + T(i) + 1 B(i) + r(i) + (ij)• Diary(ij) = + T(i) + 2 B(i)
+ s(i) + (ij)• Marker(ij) = T(i) + (ij)
• This model indicates that the means depend on body mass, but the variances do not
• We refit all the models, and still ours had highest AIC
• Attenuations were hardly changed at all: little impact of BMI
Body Mass• Prentice constructed a model that
had attenuation depending on body mass. His model was a special case of ours, but applied to BMI tertiles
• We refit his analysis to the EPIC, Cambridge and Norfolk cohorts, computing attenuation in each body mass tertile
• Prentice suggested that attenuation became more severe as BMI increased
• We see no such effect
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Attenuation
Weighted Average Attenuation and BMI: Protein Biomarker
Results of 11 cohorts (men+women)
Summary of Results
• Attenuation is the key parameter• It controls how badly relative risks
are affected by imprecision in instruments
• It controls the sample size necessary to achieve a given statistical power
• Designing experiments and instruments in order to estimate the attenuation is therefore crucial
Summary
• It is common to use a reference instrument based on self report to estimate the attenuation– 24-hour recalls– Diaries– Weighed food records
• For protein intake, where the UN biomarker is available, these self-report reference instruments clearly underestimate the magnitude of the problem of error and biases in FFQ’s
Summary
• We constructed a new model that may explain why it is that self-report reference instruments do so poorly
• The models have these features– flattened slopes– measurement errors– person-specific biases– correlation in the person-
specific biases• The newest feature of this model is
in allowing the person-specific biases to be correlated
Summary
• We compared the new model to other models proposed in the literature, using the Norfolk and MRC data sets
• Our model was NOT statistically significantly different from any other more complex model
• Our model WAS statistically significantly better than any submodel
• Our model had highest AIC in both data sets
Summary
• We also briefly discussed whether body mass plays an important role in these findings
• We added BMI to our models, with no change
• There is no indication that attenuation depends on body mass, even when we did separate analyses by BMI tertile
Summary
• It is worth remembering that in the Norfolk study, the estimated attenuations were– diary: 0.247– biomarker: 0.085
• The relative risks were affected. If observed RR is 1.10, true would be– diary: 1.47– biomarker: 3.07
• Designing a study with the diary to estimate attenuation results in an underestimation of sample size by a factor of 8.6
Future Studies
• Most analyses include energy intake in a relative risk model
• No data are available yet which have both a nutrient biomarker (protein) and an energy biomarker
• The NCI-OPEN study will have such data (reference instrument = 24-hour recall)
• Our models are easily generalized to the multivariate case
• We will see then whether adjusting for energy affects the attenuation of protein intake