A New Model for Dietary Intake Instruments Based

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

Attenuation Coefficients Biomarker and Standard Biomarker average = 0. 21 Reference 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!

Sample Size Inflation Factor Biomarker 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 personspecific 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 features Diary(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 metaanalysis 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 ignored FFQ(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 1 or (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

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

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 selfreport 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 selfreport reference instruments do so poorly • The models have these features – flattened slopes – measurement errors – person-specific biases – correlation in the personspecific 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