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Design aspects of calibration studies in nutrition, with analysis of missing data in linear measurement error models

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  • Carroll, Raymond J.
  • Freedman, Laurence
  • Pee, David

Abstract

Motivated by an example in nutritional epidemiology, we investigate some design and analysis aspects of linear measurement error models with missing surrogate data. The specific problem investigated consists of an initial large sample in which the response (a food frequency questionnaire, FFQ) is observed, and then a smaller calibration study in which replicates of the error prone predictor are observed (food records or recalls, FR). The difference between our analysis and most of the measurement error model literature is that in our study, the selection into the calibration study can depend upon the value of the response. Rationale for this type of design is given. Two major problems are investigated. In the design of a calibration study, one has the option of larger sample sizes and fewer replicates, or smaller sample sizes and more replicates. Somewhat surprisingly, neither strategy is uniformly preferable in cases of practical interest. The answers depend on the instrument used (recalls or records) and the parameters of interest. The second problem investigated is one of analysis. In the usual linear model with no missing data, method of moments estimates and normal-theory maximum likelihood estimates are approximately equivalent, with the former method in most use because it can be calculated easily and explicitly. Both estimates are valid without any distributional assumptions. In contrast, in the missing data problem under consideration, only the moments estimate is distribution-free, but the maximum likelihood estimate has at least 50% greater precision in practical situations when normality obtains. Implications for the design of nutritional calibration studies are discussed.

Suggested Citation

  • Carroll, Raymond J. & Freedman, Laurence & Pee, David, 1997. "Design aspects of calibration studies in nutrition, with analysis of missing data in linear measurement error models," SFB 373 Discussion Papers 1997,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199712
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    References listed on IDEAS

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    1. Sarah M. Nusser & Alicia L. Carriquiry & Kevin W. Dodd, 1995. "Semiparametric Transformation Approach to Estimating Usual Daily Intake Distributions, A," Center for Agricultural and Rural Development (CARD) Publications 95-sr74, Center for Agricultural and Rural Development (CARD) at Iowa State University.
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    Cited by:

    1. Malka Gorfine & Nurit Lipshtat & Laurence S. Freedman & Ross L. Prentice, 2007. "Linear Measurement Error Models with Restricted Sampling," Biometrics, The International Biometric Society, vol. 63(1), pages 137-142, March.
    2. Huixia Judy Wang & Leonard A. Stefanski & Zhongyi Zhu, 2012. "Corrected-loss estimation for quantile regression with covariate measurement errors," Biometrika, Biometrika Trust, vol. 99(2), pages 405-421.
    3. C. Y. Wang, 2000. "Weighted Normality-Based Estimator in Correcting Correlation Coefficient Estimation Between Incomplete Nutrient Measurements," Biometrics, The International Biometric Society, vol. 56(1), pages 106-112, March.
    4. C. Y. Wang & Garnet L. Anderson & Ross L. Prentice, 1999. "Estimation of the Correlation Between Nutrient Intake Measures Under Restricted Sampling," Biometrics, The International Biometric Society, vol. 55(3), pages 711-717, September.
    5. Daniel W. Schafer, 2001. "Semiparametric Maximum Likelihood for Measurement Error Model Regression," Biometrics, The International Biometric Society, vol. 57(1), pages 53-61, March.
    6. Firouzeh Noghrehchi & Jakub Stoklosa & Spiridon Penev, 2020. "Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables," Computational Statistics, Springer, vol. 35(3), pages 1291-1317, September.

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