Generalized multiple indicators, multiple causes measurement error models

Generalized Multiple Indicators, Multiple Causes Measurement Error Models (G-MIMIC ME) can be used to study the effects of an unobservable latent variable on a set of outcomes when the causes of the latent variables are unobserved. The errors associated with the unobserved causal variables can be due to either bias recall or day-to-day variability. Another potential source of error, the Berkson error, is due to individual variations that arise from the assignment of group data to individual subjects. In this article, we accomplish the following: (a) extend the classical linear MIMIC models to allow both Berkson and classical measurement errors where the distributions of the outcome variables belong in the exponential family, (b) develop likelihood based estimation methods using the MC-EM algorithm and (c) estimate the variance of the classical measurement error associated with the approximation of the amount of radiation dose received by atomic bomb survivors at the time of their exposure. The G-MIMIC ME model is applied to study the effect of genetic damage, a latent construct based on exposure to radiation, and the effect of radiation dose on physical indicators of genetic damage.

[1]  Tomonori Hayashi,et al.  Individual variation of somatic gene mutability in relation to cancer susceptibility: prospective study on erythrocyte glycophorin a gene mutations of atomic bomb survivors. , 2005, Cancer research.

[2]  D O Stram,et al.  An estimate of the magnitude of random errors in the DS86 dosimetry from data on chromosome aberrations and severe epilation. , 1991, Radiation research.

[3]  Michael Fenech,et al.  Biomarkers of genetic damage for cancer epidemiology. , 2002, Toxicology.

[4]  Alexander Kukush,et al.  Measurement Error Models , 2011, International Encyclopedia of Statistical Science.

[5]  Raymond J. Carroll,et al.  On errors-in-variables for binary regression models , 1984 .

[6]  A. Awa,et al.  Analysis of chromosome aberrations in atomic bomb survivors for dose assessment: Studies at the radiation effects research foundation from 1968 to 1993 , 1997, Stem cells.

[7]  D O Stram,et al.  Stable chromosome aberrations among A-bomb survivors: an update. , 1993, Radiation research.

[8]  George Casella,et al.  Implementations of the Monte Carlo EM Algorithm , 2001 .

[9]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[10]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[11]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Ethel S Gilbert,et al.  Some Statistical Implications of Dose Uncertainty in Radiation Dose–Response Analyses , 2006, Radiation research.

[13]  A. Zellner.  Estimation of Regression Relationships Containing Unobservable Independent Variables , 1970 .

[14]  D. Oakes.  Direct calculation of the information matrix via the EM , 1999 .

[15]  F. O. Hoffman,et al.  Semiparametric Regression Modeling with Mixtures of Berkson and Classical Error, with Application to Fallout from the Nevada Test Site , 2002, Biometrics.

[16]  Austin Miller.  Statistical methods for biodosimetry in the presence of both Berkson and classical measurement error , 2009 .

[17]  A. Goldberger.  STRUCTURAL EQUATION METHODS IN THE SOCIAL SCIENCES , 1972 .

[18]  G. C. Wei,et al.  A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms , 1990 .

[19]  A. Goldberger,et al.  Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable , 1975 .

[20]  Stan Lipovetsky,et al.  Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models , 2005, Technometrics.

[21]  S G Grant,et al.  In vivo somatic mutation and segregation at the human glycophorin A (GPA) locus: phenotypic variation encompassing both gene-specific and chromosomal mechanisms. , 1993, Mutation research.

[22]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[23]  Sarwat Sultana,et al.  Radiation-induced biomarkers for the detection and assessment of absorbed radiation doses , 2010, Journal of pharmacy & bioallied sciences.