A New Model for Dietary Intake Instruments Based on Self-Report and Biomarkers

1. 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

2. Outline • Attenuation& its impact (Review) • Reference instruments (Review) • Protein intake: contradictory resultsfrom various studies • Assumptions: reference instruments • Urinary Nitrogen (UN) as a biomarker • New model that “explains” the contradictory results • Discussion & conclusions

3. 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)l • True RR = (Observed RR)1/l

4. Why Attenuation Matters (I) • True RR = (Observed RR)1/l • 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

5. 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!

6. 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 

7. 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

8. 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

9. Attenuation CoefficientsBiomarker and StandardBiomarker average = 0.21Reference average = 0.33

10. An Illustration • Norfolk (UK) study with diaries as reference instrument • True RR = (Observed RR)1/l • 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

11. 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!

12. Sample Size Inflation FactorBiomarker versus Standard7 studies with Protein Biomarker

13. Reference Instrument Assumptions •  =the slope in a linear regression of usual intake on the FFQ • estimateis 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

14. 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

15. 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

16. 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!

17. 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 ignored FFQ(ij) =  + T(i) + r(i) + (ij) Diary(ij) =  + T(i) + s(i) + (ij) Biomarker(ij) = T(i) + (ij)

18. 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)

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. AIC - 150 for Models

26. 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)

27. 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

28. 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

29. Weighted Average Attenuation and BMI: Protein BiomarkerResults of 11 cohorts (men+women)

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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