The Annals of Applied Statistics

An estimating equations approach to fitting latent exposure models with longitudinal health outcomes

Brisa N. Sánchez, Esben Budtz-Jørgensen, and Louise M. Ryan

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Abstract

The analysis of data arising from environmental health studies which collect a large number of measures of exposure can benefit from using latent variable models to summarize exposure information. However, difficulties with estimation of model parameters may arise since existing fitting procedures for linear latent variable models require correctly specified residual variance structures for unbiased estimation of regression parameters quantifying the association between (latent) exposure and health outcomes. We propose an estimating equations approach for latent exposure models with longitudinal health outcomes which is robust to misspecification of the outcome variance. We show that compared to maximum likelihood, the loss of efficiency of the proposed method is relatively small when the model is correctly specified. The proposed equations formalize the ad-hoc regression on factor scores procedure, and generalize regression calibration. We propose two weighting schemes for the equations, and compare their efficiency. We apply this method to a study of the effects of in-utero lead exposure on child development.

Article information

Source
Ann. Appl. Stat. Volume 3, Number 2 (2009), 830-856.

Dates
First available in Project Euclid: 22 June 2009

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1245676197

Digital Object Identifier
doi:10.1214/08-AOAS226

Mathematical Reviews number (MathSciNet)
MR2750684

Zentralblatt MATH identifier
1166.62084

Keywords
Factor score regression measurement error dimension reduction lead exposure

Citation

Sánchez, Brisa N.; Budtz-Jørgensen, Esben; Ryan, Louise M. An estimating equations approach to fitting latent exposure models with longitudinal health outcomes. Ann. Appl. Stat. 3 (2009), no. 2, 830--856. doi:10.1214/08-AOAS226. http://projecteuclid.org/euclid.aoas/1245676197.


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Supplemental materials

  • Supplementary material: Supplement A: Supplement to “An estimating equations approach to fitting latent exposure models with longitudinal responses”.
    Digital Object Identifier: doi:10.1214/08-AOAS226SUPPA
    Supplemental files available for subscribers.
  • Supplementary material: Supplement B: Computer code supplement to “An estimating equations approach to fitting latent exposure models with longitudinal responses”.
    Digital Object Identifier: doi:10.1214/08-AOAS226SUPPB
    Supplemental files available for subscribers.

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