RE: "IMPLICATIONS OF A NEW DIETARY MEASUREMENT ERROR MODEL FOR ESTIMATION OF RELATIVE RISK: APPLICATION TO FOUR CALIBRATION STUDIES"

Karin B. Michels and Nicholas E. Day

Strangeways Research Laboratory Institute of Public Health University of CambridgeWorts Causeway Cambridge CB1 8RN, United Kingdom

We read with interest the recent contribution by Kipnis et al. (1Go) suggesting a new model for the correction of measurement error in the assessment of dietary intake. The authors questioned the adequacy of standard methods of correcting relative risks for measurement error and concluded that failure to detect an association in diet research may well be due to residual attenuation of the risk estimate. They suggested that available methods do not adequately account for the correlation between person-specific biases in a food frequency questionnaire (FFQ) and a reference instrument. Claiming to be unaware of any data that would allow them to estimate the correlation of person-specific biases, the authors supported their assumptions with sensitivity analyses using data from four calibration studies.

However, one of the references Kipnis et al. cited—a two-part paper by Plummer and Clayton (2Go, 3Go)—provides relevant data with which to estimate the correlation in question. Plummer and Clayton employed data on nitrogen intake from a pilot project of the European Prospective Investigation of Cancer and Nutrition (EPIC) Norfolk (Cambridge, United Kingdom) that were collected using four diet assessment methods (4-day weighed records, 7-day diaries, an FFQ, and a 24-hour recall) and 24-hour urine samples. The urinary values can be assumed to have had errors that were uncorrelated with the errors of the other assessment methods, thus allowing quantification of the error correlations of the dietary assessment methods. From table 2 in the second part of Plummer and Clayton's paper (3Go), we can calculate an average error correlation for repeated administrations of FFQs (corr({varepsilon}i',{varepsilon}j') = 0.38) and 7-day diet records (corr(µi'j') = 0.53) and the error correlation between the FFQ and the diet record (corr({varepsilon}'') = 0.21). With this information and using the formulae and assumptions made by Kipnis et al. (1Go), we can calculate the correlation between person-specific biases for nitrogen intake from the FFQ and the diet record as a reference instrument, as follows.

Following Kipnis et al., the covariance of the person-specific biases from the FFQ (r) and the reference instrument (s) is

(1)

Plummer and Clayton define this covariance in terms of the total error (person-specific plus random error) for the FFQ ({varepsilon}') and the diet record (µ') as

(2)

We can solve these two equations for corr(r,s):

(3)

In view of the values in Kipnis et al.'s table 2, a correlation between person-specific biases of 0.47 translates to a substantial attenuation factor. Therefore, the deattenuated relative risk would be substantially larger than the one observed. This result is consistent with larger validation studies carried out in EPIC Norfolk that are currently being analyzed.

REFERENCES

  1. Kipnis V, Carroll RJ, Freedman LS, et al. Implications of a new dietary measurement error model for estimation of relative risk: application to four calibration studies. Am J Epidemiol 1999;150:642–51.[Abstract]
  2. Plummer M, Clayton D. Measurement error in dietary assessment: an investigation using covariance structure models. Part I. Stat Med 1993;12:925–35.
  3. Plummer M, Clayton D. Measurement error in dietary assessment: an investigation using covariance structure models. Part II. Stat Med 1993;12:937–48.

 

THE AUTHORS REPLY

Victor Kipnis, Raymond J. Carroll, Laurence S. Freedman and Li Li

Biometry Research Group Division of Cancer Prevention National Cancer Institute Bethesda, MD 20892
Department of Statistics Texas A&M University College Station, TX 77843
Department of Mathematics, Statistics and Computer Science Bar Ilan University Ramat Gan 52900, Israel
Department of Family Practice University of Kentucky Lexington, KY 40506

We thank Drs. Michels and Day (1Go) for their comments on our paper (2Go), in which we suggested a new dietary measurement error model and evaluated its implications for estimation of diet-disease associations. In particular, our model indicates that failure of the standard correction for measurement error to account for correlated person-specific biases in food frequency questionnaires (FFQs) and reference instruments, such as 24-hour recalls or multiple-day food records, can lead to underestimated relative risks. This "residual attenuation" becomes substantial if the correlation between person-specific biases in an FFQ and a reference instrument exceeds 0.3. Without access to data on unbiased biomarker measurements, our results were based on a sensitivity analysis of four conventional calibration studies. Michels and Day (1Go) note that Plummer and Clayton (3Go, 4Go) provided relevant data for estimation of the correlation in question. According to their calculations, the correlation between person-specific biases in the FFQ and 7-day diet records is 0.47. Tempting as it may be to admit our oversight and use this result as a confirmation of the assumptions behind our model and its implications, we add the following notes of caution.

Firstly, the results of Plummer and Clayton were based on a much more general model (4Go, model II(c)) that includes ours as a special case. Without introducing person-specific biases, their model specifies only that within-person errors in urinary values be independent of errors in urinary and dietary assessment measurements taken in different seasons. All other parameters, including group-specific biases ("scaling biases" in the terminology of Plummer and Clayton) and within-person error variances and covariances, are allowed to vary both in repeat administrations of the same instrument and across instruments. In contrast, in our model these parameters are assumed to be constant in repeat administrations of the same instrument, with the error variance-covariance matrix being fully specified by person-specific biases and within-person random errors (2Go). To overcome the difference between the two models, Michels and Day suggest averaging over error correlations for repeat instrument administrations provided in the second paper by Plummer and Clayton (4Go, table 2). Plummer and Clayton fitted their model to the data set with many missing values using the method of maximum likelihood. As a result, averaging error correlations estimated by a much more general model, with the number of parameters exceeding the number of observations, may produce results different from the estimated correlations obtained by fitting our model directly to the same data.

Secondly, Michels and Day seem to ignore the fact that the 7-day dietary record was modified in season 4, and, perhaps more importantly, a different FFQ was used in season 3 (3Go, 4Go). Both the two different modifications of the 7-day diaries and, especially, the two different FFQs seem to have quite different error structures (5Go). Averaging error correlations in this situation may produce rather confusing results.

In summary, the calculations suggested by Michels and Day are indeed important to stimulate an interest in the problem of correlated person-specific biases in dietary assessment instruments. However, in our view, they should only be taken as indications and probably should not be used in place of the results obtained by fitting the new model to the original data.

REFERENCES

  1. Michels KB, Day N. Re: "Implications of a new dietary measurement error model for estimation of relative risk: application to four calibration studies." (Letter). Am J Epidemiol 2000;152:494–5.[Free Full Text]
  2. Kipnis V, Carroll RJ, Freedman LS, et al. Implications of a new dietary measurement error model for estimation of relative risk: application to four calibration studies. Am J Epidemiol 1999;150:642–51.[Abstract]
  3. Plummer M, Clayton D. Measurement error in dietary assessment: an investigation using covariance structure models. Part I. Stat Med 1993;12:925–35.
  4. Plummer M, Clayton D. Measurement error in dietary assessment: an investigation using covariance structure models. Part II. Stat Med 1993;12:937–48.
  5. Bingham SA, Cassidy A, Cole TJ, et al. Validation of weighed records and other methods of dietary assessment using the 24 h urine nitrogen technique and other biological markers. Br J Nutr 1995;73:531–50.[ISI][Medline]